Unlike multiobjective optimization (MOO), multimodal multiobjective optimization (MMMOO) should approximate the entire Pareto set, even if a portion of it maps onto the entire Pareto front. This study introduces a novel evolution strategy with adaptive fitness sharing (AFS) for MMMOO. The method, called, AFS-MMMO-ES, calculates an overall fitness for each solution in the selection pool based on its rank-wise hypervolume contribution, Pareto rank, and niche count in the decision space. Since the optimal niche radius is problem-dependent, this study introduces a novel strategy for on-the-fly adaptation of the niche radius. Simulations on meticulously designed test problems are performed to confirm the efficacy and reliability of this strategy in learning the optimal niche radius, as well as its significant impact on enhancing robustness and performance. Furthermore, AFS-MMMO-ES can easily reflect the relative importance of decision space diversity based on the decision-maker’s preference, a practically important feature that has been overlooked in this research field. Finally, the performance of AFS-MMMO-ES is assessed and compared with several successful MMMOO methods on a widely accepted test suite for MMMOO. Comparisons of numerical results reveal the robustness and superiority of AFS-MMMO-ES over its competitors.

In the Internet of Battlefield Things domain, optimal sensor placement is critical for both tactical and strategic considerations in military surveillance scenarios. Finding the optimal sensor positions for informed decision-making in critical and highly constrained environments is challenging. This paper formulates the problem and proposes a differential evolution algorithm to maximise a military base station's situational awareness by efficiently finding the optimal sensor positions, enabling timely identification and notification of potential enemy threats. The proposed algorithm also adopts heuristic initialisation and a repair method to improve performance. The approach is tested on 21 scenarios, each varying in the number of sensors, the number and size of obstacles, and the expected directions of enemy attacks. The study's results demonstrate the effectiveness of the newly introduced approach.

Addressing large-scale optimization problems with numerous variables and constraints poses difficulties. Ineffectively handling the constraints can result in solutions that are either not optimal or infeasible. In our research, we utilized the constraint-objective cooperative coevolution framework with the FDfar (Feasibility distance-far) method, which is a constraint consensus approach. Our proposed algorithm involves decomposing a complex problem into smaller, more manageable subproblems (subcomponents) using the Recursive Differential Grouping technique, which assigns interrelated variables to the same subcomponent. Then, the FDfar method is selectively applied to a randomly chosen solution to enhance its feasibility. Subsequently, the population is updated while considering the newly generated solution from the FDfar method. We then assess the impact of each subcomponent on both the objective function and the constraints to identify the most effective subcomponent for evolution. The chosen subcomponent then undergoes further evolution using Differential Evolution. We tested our algorithm on a set of 12 benchmark problems. The results from these tests consistently indicated that our approach outperforms other leading methods, not only in making solutions feasible but also in improving their overall quality.

Integrated decision-making regarding the selection and scheduling of a project portfolio, referred to as the project portfolio selection and scheduling problem (PPSSP), can contribute to the more favorable performance of many organizations. However, the optimization of large-scale PPSSP involving a large number of projects and complex constraints remains challenging. While exact solvers offer guaranteed optimal solutions, they are computationally intractable in large-scale PPSSP. On the contrary, metaheuristics search for approximated solutions within a reasonable time. This paper investigates the performance of a commercial exact solver and metaheuristics in addressing large- scale PPSSP within a limited time. In addition, hybrid approaches are proposed to combine the exact solver and metaheuristics in different ways to address PPSSP. Experiments are conducted on PPSSP instances with an increasing number of projects (up to 6000), demonstrating the superiority of metaheuristics in addressing large-scale PPSSP within a short time and the effectiveness of combining metaheuristics in Gurobi in facilitating the optimization process.

In recent decades, large-scale optimization has received significant research attention; however, most of these studies have not considered problems with functional constraints. The introduction of constraints significantly amplifies the difficulty of solving optimization problems. Given the preva-lence of high-dimensional constrained optimization problems in real-world applications, a critical need has emerged for an in-depth exploration of this research domain. This paper presents a novel framework that can tackle complex, large-scale constrained optimisation problems. The framework incorpo-rates a decomposition method that leverages interactions among decision variables, employing a contribution-based strategy to prioritize subproblems that have more substantial influence on enhancing solution quality. Furthermore, the framework integrates constraint consensus to mitigate constraint violations throughout the search process. The proposed algorithm is evaluated on a test suite of constrained overlapping problems, revealing its superior performance when compared to other state-of-the-art algorithms.

This paper considers a fleet of electric vehicles and drones that deliver goods collaboratively. To determine the optimal routes of this electric vehicle-drone routing problem, the problem is formulated as a mixed-integer linear program to minimize the total operational costs. To solve the model, we develop an adaptive memetic algorithm that employs a multi-operator concept with a Q-learning-based selection mechanism and a set of local search operators for exploring the complex search space of the problem. Using extensive numerical experiments, we prove the effectiveness of our proposal and reveal some interesting managerial insights.

Community microgrids, as an emerging technology, offer resiliency in operation for smart grids. Microgrids are seeing an increased penetration of eco-friendly electric vehicles (EVs) in recent years. However, the uncontrolled charging of EVs can easily overwhelm such electric networks. In this work, we propose an efficient demand response (DR) scheme based on dynamic pricing to enhance the capacity of the microgrid to securely host a large number of EVs. A hierarchical two-level optimization framework is introduced to realize the DR scheme. At the upper level, the dynamic prices for the participating users in DR are optimized while at the lower level, each user optimizes its energy consumption based on the price signal from the upper level. An evolutionary algorithm and a mixed-integer linear programming model is employed to solve the upper and lower level problems, respectively. Energy scheduling problems of the users are solved in a distributed manner which adds to the scalability of the approach. The proposed DR scheme is tested on a microgrid system adopted from the IEEE European low-voltage distribution network. Numerical experiments confirm the effectiveness of the proposed DR scheme compared to the benchmark pricing policies from the literature.

Explicit and implicit averaging are two well-known strategies for noisy optimization. Both strategies can counteract the disruptive effect of noise; however, a critical question remains: which one is more efficient? This question has been raised in many studies, with conflicting preferences and, in some cases, findings. Nevertheless, theoretical findings on the noisy sphere problem with additive Gaussian noise supports the superiority of implicit averaging, which may have had a strong impact on the preference of implicit averaging in more recent evolutionary methods for noisy optimization. This study speculates that the analytically supported superiority of implicit averaging relies on specific features of the noisy sphere problem with additive noise, which cannot be generalized to other problems. It enumerates these features and designs controlled numerical experiments to investigate this potential reliance. Each experiment gradually suppresses one specific feature, and the progress rate is numerically calculated for different values of the sample size given a fixed evaluation budget. Our empirical results indicate that for a wide range of noise strength and evaluation budget per iteration, the more these specific features are suppressed, the more the optimal averaging strategy deviates from implicit toward explicit averaging, which confirms our speculations. Consequently, the optimal sample size, which is regarded as the tradeoff between implicit and explicit averaging, depends on the problem characteristics and should be learned during optimization for maximum efficiency.

Many practical decision-making problems involve changing data and parameters with time. Solving such problems requires a custom-designed algorithm that can efficiently handle the repeatedly changing problem, in fact, its changing search space. In this paper, we consider constrained optimisation problems where the coefficients of the objective function change. We propose a framework that adaptively deals with linear and nonlinear components by satisfying the constraints within a limited time. Furthermore, we introduce a new mechanism to identify the sensitivity of variables, determine the rate of changes in the coefficients of the decision variables, and propose a heuristic to update the population efficiently after every change. The experimental results demonstrate that the proposed approach is able to obtain better solutions than those without having these new components.

Existing solution approaches for handling disruptions in project scheduling use either proactive or reactive methods. However, both techniques suffer from some drawbacks that affect the performance of the optimization process in obtaining good quality schedules. Therefore, in this article, we develop an auto-configured multioperator evolutionary approach, with a novel pro-reactive scheme for handling disruptions in multimode resource-constrained project scheduling problems (MM-RCPSPs). In this article, our primary objective is to minimize the makespan of a project. However, we also have secondary objectives, such as maximizing the free resources (FRs) and minimizing the deviation of activity finishing time. As the existence of FR may lead to a suboptimal solution, we propose a new operator for the evolutionary approach and two new heuristics to enhance the algorithm's performance. The proposed methodology is tested and analyzed by solving a set of benchmark problems, with its results showing its superiority with respect to state-of-the-art algorithms in terms of the quality of the solutions obtained.

The covariance matrix self-adaptation evolution strategy with repelling subpopulations (RS-CMSA-ES) is one of the most successful multimodal optimization (MMO) methods currently available. However, some of its components may become inefficient in certain situations. This study introduces the second variant of this method, called RS-CMSA-ESII. It improves the adaptation schemes for the normalized taboo distances of the archived solutions and the covariance matrix of the subpopulation, the termination criteria for the subpopulations, and the way in which the infeasible solutions are treated. It also improves the time complexity of RS-CMSA-ES by updating the initialization procedure of a subpopulation and developing a more accurate metric for determining critical taboo regions. The effects of these modifications are illustrated by designing controlled numerical simulations. RS-CMSA-ESII is then compared with the most successful and recent niching methods for MMO on a widely adopted test suite. The results obtained reveal the superiority of RS-CMSA-ESII over these methods, including the winners of the competition on niching methods for MMO in previous years. Besides, this study extends RS-CMSA-ESII to dynamic MMO and compares it with a few recently proposed methods on the modified moving peak benchmark functions.

There has been a considerable amount of research on the development of metaheuristic methods for resource-constrained project scheduling problems. Early methods followed the building blocks and even the formulation of well-understood metaheuristic methods as well as simple but effective heuristics such as forward-backward improvement. In contrast, more recent methods employ less familiar, more complex (hybrid) metaheuristics and non-standard components and formulations. Although the former may provide better results on standard test problems, it is not easy to understand how each component has contributed to improving the results and why a deviation from well-established formulations, components and methods was necessary. This research advances our knowledge about the impact of different strategies and components of customized genetic algorithms (some of which have been proposed in this study) on the optimization results. This task is performed by developing a comprehensive genetic algorithm with several familiar and potentially effective components. A modular analysis is then performed in which one component is suppressed at a time, and the resultant performance decline is analyzed. With hindsight from the modular analysis, a simple method is suggested and the importance of each component is clarified. Thus, no further simplification can be performed without compromising efficiency. Our preliminary results reveal that this customized genetic algorithm outperforms many existing methods and can compete with the most successful ones, which, in many cases, are much more complex than our approach.

Big data optimization has become an important research topic in many disciplines. These optimization problems involve a large volume of data, from different sources, in different formats, that are generated at a high speed. For example, in the healthcare sector, electroencephalography (EEG), which is a method for monitoring brain signals and typically used to diagnose neurological disorders, generates a large amount of data which, however, is often captured with artifacts added from non-brain sources. Evolutionary algorithms are considered one of the most successful approaches for solving many such complex optimization problems. In this paper, a differential evolution algorithm is developed to remove artifacts from EEG signals of interest, by using the parallel computing ability of a Graphics Processing Unit. Two levels of parallelization, variable and individual, are implemented, with a gradient-based local search and adaptive control parameters incorporated in order to enhance a search's convergence. The proposed algorithm is tested using six single objective problems from the 2015 big data optimization competition problems with 1024, 3072 and 4864 decision variables, as both noise-free and with white noise. The results presented in this paper indicate that the proposed algorithm is capable of achieving high-quality solutions, and is up to 374.7 faster than the state-of-the-art algorithms.

This study develops an adaptive multilevel prediction (AMLP) method to detect and track multiple global optima over time. First, it formulates a multilevel prediction approach in which a higher level prediction improves the accuracy of the lower level prediction to reduce the prediction error, enabling it to capture more complex patterns in the changes. However, a higher level prediction is more sensitive to input errors and the randomness in the pattern of the change. To overcome this challenge, this study employs an adaptive mechanism which can determine the near-optimal prediction level at each time step. At the same time, AMLP calculates the strength of the diversity introduced after a change based on the estimated prediction error. A successful static multimodal optimizer is augmented with AMLP, for which AMLP determines the location and the mutation strength of the initialized subpopulations. An existing dynamic benchmark generator is improved so that it can generate dynamic test problems with more complex patterns in their changes. In particular, this dynamic benchmark generator allows for controlling the randomness of the pattern in the change to simulate dynamic problems with different degrees of predictability. A few controlled experiments are first performed to provide insight into different components of AMLP. Then, AMLP is compared with some of the most successful prediction methods when they are incorporated into the developed dynamic multimodal optimization method. Eleven dynamic cases with different change severity, change frequency, predictability, problem dimensionality, and the number of global minima are considered. The numerical results show the superiority of AMLP over other prediction methods.

Developing a Deep Convolutional Neural Network (DCNN) is a challenging task that involves deep learning with significant effort required to configure the network topology. The design of a 3D DCNN not only requires a good complicated structure but also a considerable number of appropriate parameters to run effectively. Evolutionary computation is an effective approach that can find an optimum network structure and/or its parameters automatically. Note that the Neuroevolution approach is computationally costly, even for developing 2D networks. As it is expected that it will require even more massive computation to develop 3D Neuroevolutionary networks, this research topic has not been investigated until now. In this article, in addition to developing 3D networks, we investigate the possibility of using 2D images and 2D Neuroevolutionary networks to develop 3D networks for 3D volume segmentation. In doing so, we propose to first establish new evolutionary 2D deep networks for medical image segmentation and then convert the 2D networks to 3D networks in order to obtain optimal evolutionary 3D deep convolutional neural networks. The proposed approach results in a massive saving in computational and processing time to develop 3D networks, while achieved high accuracy for 3D medical image segmentation of nine various datasets.

One of the challenges that appear in solving constrained optimization problems is to quickly locate the search areas of interest. Although the initial solutions of any optimization algorithm have a significant effect on its performance, none of the existing initialization methods can provide direct information about the objective function and constraints of the problem to be solved. In this paper, a technique for generating initial solutions is proposed, which provides useful information about the behavior of both the objective function and the constraints. Based on such information, an automatic mechanism for selecting individuals, from the search areas of interest, is introduced. The proposed method is adopted with different evolutionary algorithms and tested on the CEC2006 and the CEC2010 test problems. The results obtained show the benefits of the proposed method in enhancing the performance, and reducing the average computational time, of several algorithms with respect to their versions adopting other initialization techniques.

Over the last few decades, many solution approaches have been developed for solving different variants of resourceconstrained project scheduling problems (RCPSPs). In most of them, it is assumed that a project consists of some homogeneous activities that require all types of resources over the entire project horizon. On the contrary, many real-world projects consist of heterogeneous activities that use different types of resources at different time instants during the project execution. The application of existing approaches, developed for RCPSPs with homogeneous activities, in solving RCPSPs with heterogeneous activities is computationally expensive. In this paper, we propose a heuristic embedded genetic algorithm to address RCPSPs with heterogeneous activities. Two heuristics are proposed to obtain high-quality feasible solutions. The first heuristic is based on priority rules while the second one based on a new neighbourhood swapping matrix. To evaluate the performance of the proposed algorithm, we solve a number of real-world and modified test problems, and the obtained results are compared with an existing algorithm. It is found that the proposed approach obtains highquality solutions with a significantly lower computational time compared to other algorithms.

Future force design is a crucial task that assists in the creation of an effective future defence force. The primary objective of this task is to select a set of projects, within a fixed planning window and subject to budgetary constraints, that will lead to improved capabilities. While inherently related to the well-known multi-period knapsack problem, addressing this problem in the context of the defence sector gives rise to a number of unique nuances and associated challenges. Furthermore, the literature pertaining to the selection and scheduling of projects for capability-based planning in the defence sector is rather limited. To address this literature gap, this paper formalizes a multi-period project selection and scheduling problem inspired by future force design. Numerous heuristics, both random and deterministic, along with a hybrid genetic algorithm, are employed to optimize a set of instances of the proposed problem formulation with various characteristics derived from real-world, public defence data made available by the Australian Department of Defence.

This study develops a prediction-based reinitialization approach that is comprised of three components for dynamic multiobjective optimization (DMO). The first component is a controlled translation of the population centroid, which analyzes the successive movement of the population Pareto optimal set (POS) at the end of each problem instance. The second and third components are directional and random variation. In addition, a metric to quantify the variation in the POS that does not fit in a simple translation is proposed. The rationale behind each component is explained and demonstrated in some carefully designed descriptive experiments. Different variants of the proposed strategy are assessed and compared with two recently proposed reinitialization strategies, on an accredited test suite for DMO. A comparison of the numerical results reveals that unlike the random variation, the directional variation operator significantly improves the performance. Overall, our proposed strategy considerably outperforms the other considered strategies, especially when the evaluation budget for each problem instance is limited.

Several research studies have been carried out on the integration of quantum operators and evolutionary algorithms. However, the performance of such integration remains questionable and needs further research for drawing a useful conclusion. Therefore, this paper takes a step forward to analyze the effect of integrating quantum entanglement and quantum NOT gate with the well-known differential evolution algorithm. The performance of different algorithm designs has been evaluated by solving a number of unconstrained real parameter single objective optimization problems. Although the integration of quantum entanglement helps to get competitive results, the overall experimental results with quantum operators are not convincing enough, especially when there are no inter-dependency among decision variables. This in turn opens up new research directions to deepen the knowledge in the design of quantum evolutionary algorithms.

Over the last few decades, project scheduling problems have been solved under a set of resource constraints, which are assumed fixed throughout the project horizon. However, in real-life applications, resources may change over time due to maintenance or because the resources are needed for another project. Therefore, this research introduces a hybrid evolutionary framework, based on two multi-operator evolutionary algorithms, and a heuristic technique, for a multi-mode project scheduling under irregular resources changes. The framework simultaneously considers both algorithms and self-adaptively emphasizes the one which performs comparatively better. The heuristic considers two variants of handling techniques for irregular resources. One is based on inserting buffer activities to characterize resources unavailable, and another is based on a modified serial generation scheme, that determines the best modes of the activities at each time period based on irregular resources. The framework is tested by solving a set of test problems, with the renewable resources considered irregular over the project horizon. The results demonstrate that the multi-method algorithm has some advantages for scheduling a project, under both regular and irregular resources.

During the last two decades, many multioperator- and multimethod-based evolutionary algorithms for solving optimization problems have been proposed. Although, in general terms, they outperform single-operator-based traditional ones, they do not perform consistently for all the problems tested in the literature. The designs of such algorithms usually follow a trial and error approach that can be improved by using a rule-based approach. In this paper, we propose a new way for two algorithms to cooperate as an effective team, in which a heuristic is applied using fuzzy rules of two complementary characteristics, the quality of solutions and diversity in the population. In this process, two subpopulations are used, one for each algorithm, with greater emphasis placed on the better-performing one. Inferior algorithms learn from trusted ones and a fine-tuning procedure is applied in the later stages of the evolutionary process. The proposed algorithm was analyzed on the CEC2014 unconstrained problems and then tested on other three sets (CEC2013, CEC2005, and 12 classical problems), with its results showing a high success rate and that it outperformed both single-operator-based and different state-of-the-art algorithms.

Evolutionary algorithms have shown their promise in coping with many-objective optimization problems. However, the strategies of balancing convergence and diversity and the effectiveness of handling problems with irregular Pareto fronts (PFs) are still far from perfect. To address these issues, this paper proposes an adaptive sorting-based evolutionary algorithm based on the idea of decomposition. First, we propose an adaptive sorting-based environmental selection strategy. Solutions in each subpopulation (partitioned by reference vectors) are sorted based on their convergence. Those with better convergence are further sorted based on their diversity, then being selected according to their sorting levels. Second, we provide an adaptive promising subpopulation sorting-based environmental selection strategy for problems which may have irregular PFs. This strategy provides additional sorting-based selection effort on promising subpopulations after the general environmental selection process. Third, we extend the algorithm to handle constraints. Finally, we conduct an extensive experimental study on the proposed algorithm by comparing with start-of-the-state algorithms. Results demonstrate the superiority of the proposed algorithm.

High-dimensional data clustering is of great importance in the big data era. Multi-objective evolutionary soft subspace clustering (SSC) algorithms have shown promise in handling such datasets, but the objective functions and local search strategies used have not yet been well investigated. To consider these issues, this paper proposes an improved multiobjective evolutionary approach with new objective function and local search operator for clustering high-dimensional data. First, a new objective function is provided, which optimizes the clustering validity indexes and additional item simultaneously to overcome the difficulty of coefficient settings in the objective functions of existing SSC approaches. Second, an improved local search operator is introduced, which updates the weights of features by considering both the within-class compactness and between-class separation to capture a more comprehensive data structure. An experimental study with comparison with state-of-the-art SSC methods demonstrates the efficiency of the proposed approach.

Although many evolutionary algorithms (EAs) have successfully solved different optimization problems, no single EA has consistently been the best for all these problems. During the last decade, to alleviate this limitation, many proposals which utilize multiple EAs in a single algorithmic framework, called multi-methods or multi-operators, have been introduced. However, there is still room to enhance their performance. In this paper, an improved variant of a united multi-operator algorithm is introduced with few improvements that are capable of providing a balance between diversification and intensification properties during the optimization. The proposed algorithm is tested on the CEC2017 unconstrained benchmark problems, with the results revealing that the proposed algorithm is capable of producing high quality solutions compared with those of state-of-the-art algorithms.

Over the last two decades, many different differential evolution (DE) variants have been developed for solving constrained optimization problems. However, none of them performs consistently when solving different types of problems. To deal with this drawback, multiple search operators are used under a single DE algorithm structure where a higher selection pressure is placed on the best performing operator during the evolutionary process. In this paper, we propose to use the landscape information of the problem in the design of the selection mechanism. The performance of this algorithm with the proposed selection mechanism is analysed by solving 10 real-world constrained optimization problems. The experimental results revealed that the proposed algorithm is capable of producing high quality solutions compared to those of state-of-the-art algorithms.

Many real-world decision problems involve uncertain parameters. The Resource Constrained Project Scheduling Problem (RCPSP) is one of those problems in which the activity durations are usually uncertain. Over the last decade, a good number of solution approaches have been developed to solve such problems, among them the population based algorithms received great attention. In the solution approaches, a large number of scenarios are usually evaluated which is computationally expensive. In this paper, as an attempt to reduce the computational time, we propose few alternative approaches and experiment them with an assumption that the uncertain parameters are random variables. For experimental study, these variables are generated using four different probability distributions. The proposed approaches are compared with the traditional scenario based approach by solving 10 well-known benchmark problems with 30 activities. The results revealed that it has advantages in terms of solution quality and computational time.

In Simulation Optimization, the computational cost, due to the huge number of simulation replications along with the optimization process cost, is considered as a key challenge. This encourages the investigation of the effect of the number of simulation replications on the performance of the optimization algorithm, in terms of the solution fidelity versus the computational cost. Existing simulation replication strategies with optimization algorithms have been proposed utilizing a single probability distribution to fit their parameter settings for solving stochastic simulation problems. In this paper, simulation replication strategies are developed by a proposed Strategy Design Technique using three distributions: Bimodal Gaussian, Exponential, and Poisson for involving discrete and continuous stochastic parameters. A Differential Evolution algorithm is hybridized with Monte-Carlo simulation to solve a set of stochastic, continuous and constrained problems, using the designed strategies. Several experiments are conducted, using modified IEEE-CEC'2006 test problems. Optimization results' fidelity is empirically assessed in terms of a proposed probability of correct final selection of the solution. It reflects the ability of the proposed simulation strategies to direct the Differential Evolutionary algorithm in the search space, even under different stochastic settings and low simulation budget. Additional experiments have been conducted to study the compromising between the simulation and the optimization budgets under different settings using the same total computational load. The results indicate that the proposed strategies obtain robust results with a remarkable reduction in the simulation budget, under different stochastic settings.

Determining the Nash equilibria (NEs) in a competitive electricity market is a challenging economic game problem. Although finding one equilibrium has been well studied, detecting multiple ones is more practical and difficult, with a few attempts to solve such discrete game problems. However, most of the reallife game problems, such an energy market is a continuous one containing infinite sets of strategy that can be adopted by each player. Therefore, in this paper, a co-evolutionary approach is proposed for detecting multiple NEs in a single run involving continuous games among N-players. Five standard test functions and three IEEE energy market problems in three different scenarios are solved, and their results are compared with those obtained from state-of-the-art algorithms. The results clearly show the benefits of the proposed approach in terms of both the quality of solutions and efficiency.

Over the last two decades, many different evolutionary algorithms (EAs) have been proposed for solving optimization problems. However, no single EA has consistently been the best for solving a wide range of them. In the literature, this drawback has been tackled by using multiple EAs in a single framework. In this paper, a new multi-method based EA that utilizes the search ability of multi-operator differential evolution algorithm (MODE) and covariance matrix adaptation evolution strategy CMA-ES algorithm in a single framework, has been presented, with the orthogonal experimental design (OED) and factor analysis (FA) used to select the proper combination of mutation strategies, control parameters adaptation strategies, and crossover operators. To judge the performance of this algorithm, 30 problems are solved from the CEC2017 competition and their results are analyzed.

It is well known that the performances of evolutionary algorithms are influenced by the quality of their initial populations. Over the years, many different techniques for generating an initial population by uniformly covering as much of the search space as possible have been proposed. However, none of these approaches considers any input from the function that must be evolved using that population. In this paper, a new initialization technique, which can be considered a heuristic space-filling approach, based on both function to be optimized and search space, is proposed. It was tested on two well-known unconstrained sets of benchmark problems using several computational intelligence algorithms. The results obtained reflected its benefits as the performances of all these algorithms were significantly improved compared with those of the same algorithms with currently available initialization techniques. The new technique also proved its capability to provide useful information about the function's behavior and, for some test problems, the initial population produced high-quality solutions. This method was also tested on a few multiobjective problems, with the results demonstrating its benefits.

Over the past few years, the success of multi-operator and multi-method algorithms encouraged researchers to combine them within a single framework. Although these algorithms have shown promising results, there are still rooms for further improvements. In this paper, we propose a new way of combining multiple evolutionary algorithms, each of which may run with multiple search operators. In its process, the algorithm gradually places emphasis on the better-performing multi-operator algorithm, as well as its own search operators. Such a process is designed based on the quality of solutions produced and diversity of the population. The proposed algorithm is assessed on the CEC2016 competition problems on single objective realparameter optimization, with the results demonstrating its ability to attain better results than those of state-of-the-art algorithms.

Over the last two decades, many differential evolution algorithms have been introduced to solve constrained optimization problems. Due to the variability of characteristics of such problems, no single algorithm performs consistently well over all of them. In this paper, for a better coverage of the problem characteristics, we introduce an enhanced multi-operator differential evolution algorithm, which utilizes the strengths of multiple search operators at each generation, and places more emphasis on the best-performing ones during the optimization process based on three measures: (1) the quality of solutions; (2) the feasibility rate; and (3) diversity. In addition, an improved self-adaptive mechanism for automatically controlling the scaling factor and crossover rate is proposed. The performance of the algorithm is assessed using a well-known set of constrained problems, with the experimental results demonstrating that it is superior to state-of-the-art algorithms.

Determining the optimal bidding strategies in a competitive electricity market has become an important research topic over the last few decades. In this paper, a supply function equilibrium game model is considered and formulated as a bilevel optimization problem, where the upper level is used to maximize the individual profit of each supplier and the lower one to minimize the overall operating cost. To solve this problem, a co-evolutionary approach is designed in which each supplier uses its own sub-population of a genetic algorithm to maximize its profit through a bidding strategy based on each of its generators' cost coefficients, while either a self-adaptive differential evolution or sequential quadratic programming is used to optimally allocate the generation of each supplier by minimizing the operation cost. To validate the results obtained from the proposed method, an iterative method is also used to solve the two well-known benchmarks in the literature. The results are compared with those from a state-of-art method in the literature which reveals that the co-evolutionary approach has some merits in terms of quality and reliability.

Until now, numerous mutation strategies have been introduced as search operators within the differential evolution (DE) algorithm. These operators are designed mainly to improve fitness value while also maintaining diversity in the population, but they do not directly act to reduce constraint violations of constrained problems. Interestingly, the so-called constraint handling techniques, used with most evolutionary algorithms, are not a part of the actual search process. Instead, the constraint violations are only considered in the ranking and selection of individuals for participation in the search process. This paper introduces a new DE mutation operator that incorporates a mechanism, based on constraint consensus, that can directly help to reduce the constraint violations during the evolutionary search process. The proposed DE algorithm has been tested on a set of well-known constrained benchmark problems. The experimental results show that the proposed algorithm is able to obtain better solutions, compared to the standard DE algorithm, with significantly reduced computational effort. The algorithm also outperforms state-of-the-art algorithms.

Resource constrained project scheduling problem (RCPSP) is considered to be an NP hard problem. Over the last few decades, many different approaches have been developed in order to solve RCPSPs optimally within a reasonable time limit. However, no existing approach is well-accepted in this regard. In this paper, for efficiently solving RCPSPs, a memetic algorithm is proposed. The proposed algorithm incorporates local search techniques and adaptive mutation with a carefully designed genetic algorithm. To judge the performance of the proposed algorithm, we have solved 31 benchmark problems (16 with 30 activities, and 15 problems with 60 activities), and compared the quality of solutions and computational time with other state-of-the-art algorithms. The results show that our proposed algorithm achieved good quality solutions with a significantly lower computational time.

During the last few eras, evolutionary algorithms have been adopted to tackle cyber-terrorism. Among them, genetic algorithms and genetic programming were popular choices. Recently, it has been shown that differential evolution was more successful in solving a wide range of optimization problems. However, a very limited number of research studies have been conducted for intrusion detection using differential evolution. In this paper, we will adapt differential evolution algorithm for anomaly detection, along with proposing a new fitness function to measure the quality of each individual in the population. The proposed method is trained and tested on the 10%KDD99 cup data and compared against existing methodologies. The results show the effectiveness of using differential evolution in detecting anomalies by achieving an average true positive rate of 100%, while the average false positive rate is only 0.582%.

Recently, the success history based parameter adaptation for differential evolution algorithm with linear population size reduction has been claimed to be a great algorithm for solving optimization problems. Neuro-dynamic is another recent approach that has shown remarkable convergence for certain problems, even for high dimensional cases. In this paper, we proposed a new algorithm by embedding the concept of neuro-dynamic into a modified success history based parameter adaptation for differential evolution with linear population size reduction. We have also proposed an adaptive mechanism for the appropriate use of the success history based parameter adaptation for differential evolution with linear population size reduction and neuro-dynamic during the search process. The new algorithm has been tested on the CEC'2015 single objective real-parameter competition problems. The experimental results show that the proposed algorithm is capable of producing good solutions that are clearly better than those obtained from the success history based parameter adaptation for differential evolution with linear population size reduction and a few of the other state-of-the-art algorithms considered in this paper.

Many infrastructures, such as those of finance and banking, transportation, military and telecommunications, are highly dependent on the Internet. However, as the Internet’s underlying structural protocols and governance can be disturbed by intruders, for its smooth operation, it is important to minimize such disturbances. Of the available techniques for achieving this, computational intelligence methodologies, such as evolutionary algorithms and swarm intelligence approaches, are popular and have been successfully applied to detect intrusions. In this paper, we present an overview of these techniques and related literature on intrusion detection, analyze their research contributions, compare their approaches and discuss new research directions which will provide useful insights for intrusion detection researchers and practitioners.

Decomposition-based evolutionary algorithms have been quite successful in solving optimization problems involving two and three objectives. Recently, there have been some attempts to exploit the strengths of decomposition-based approaches to deal with many objective optimization problems. Performance of such approaches are largely dependent on three key factors: 1) means of reference point generation; 2) schemes to simultaneously deal with convergence and diversity; and 3) methods to associate solutions to reference directions. In this paper, we introduce a decomposition-based evolutionary algorithm wherein uniformly distributed reference points are generated via systematic sampling, balance between convergence and diversity is maintained using two independent distance measures, and a simple preemptive distance comparison scheme is used for association. In order to deal with constraints, an adaptive epsilon formulation is used. The performance of the algorithm is evaluated using standard benchmark problems, i.e., DTLZ1-DTLZ4 for 3, 5, 8, 10, and 15 objectives, WFG1-WFG9, the car side impact problem, the water resource management problem, and the constrained ten-objective general aviation aircraft design problem. Results of problems involving redundant objectives and disconnected Pareto fronts are also included in this paper to illustrate the capability of the algorithm. The study clearly highlights that the proposed algorithm is better or at par with recent reference direction-based approaches for many objective optimization.

In this paper, a surrogate-assisted differential evolution (DE) algorithm is proposed to solve the computationally expensive optimization problems. In it, the Kriging model is used to approximate the objective function, while DE employs a mechanism to dynamically select the best performing combinations of parameters (amplification factor, crossover rate and population size). The performance of the algorithm is tested on the WCCI2014 competition on expensive single objective optimization problems. The experimental results demonstrate that the proposed algorithm has the ability to obtain good solutions.

Multi-method and multi-operator evolutionary algorithms (EAs) have shown superiority to any single EAs with a single operator. To further improve the performance of such algorithms, in this research study, a united multi-operator EAs framework is proposed, in which two EAs, each with multiple search operators, are used. During the evolution process, the algorithm emphasizes on the best performing multi-operator EA, as well as the search operator. The proposed algorithm is tested on a well-known set of constrained problems with 10D and 30D. The results show that the proposed algorithm scales well and is superior to the-state-of-the-art algorithms, especially for the 30D test problems.

This paper puts forward a proposal for combining multi-operator evolutionary algorithms (EAs), in which three EAs, each with multiple search operators, are used. During the evolution process, the algorithm gradually emphasizes on the best performing multi-operator EA, as well as the search operator. The proposed algorithm is tested on the CEC2014 single objective real-parameter competition. The results show that the proposed algorithm has the ability to reach good solutions.

Autonomous vehicles are frequently deployed in environments where only certain trajectories are feasible. Classical trajectory generation methods attempt to find a feasible trajectory that satisfies a set of constraints. In some cases the optimal trajectory may be known, but it is hidden from the autonomous vehicle. Under such circumstance the vehicle must discover a feasible trajectory. This paper describes a multi-agent system that uses a combination of reinforcement learning and differential evolution to generate a trajectory that is ε-close to a target trajectory that is hidden.

In the literature, a considerable number of mutation operators have been proposed, which are the key search operators in differential evolution algorithm for solving optimization problems. Although those operators were developed in the context of unconstrained optimization, they were widely used in constrained optimization. However, those operators did not contain any mechanism that would reduce the constraint violation in the search process. Therefore, in this paper, a new mutation operator based on the constraint consensus method is proposed, which can help infeasible points reach the feasible region quickly. The algorithm is tested on the CEC2010 constrained benchmark problems. The experimental results show that the proposed algorithm is able to obtain better solutions in comparison with the state-of-the-art algorithms.

The Permutation Flow Shop Scheduling Problem (PFSP) is considered to be one of the complex combinatorial optimization problems. For PFSPs, the schedule is produced under ideal conditions that usually ignore any type of process interruption. In practice, the production process is interrupted due to many different reasons, such as machine unavailability and breakdowns. In this paper, we propose a Genetic Algorithm (GA) based approach to deal with process interruptions at different points in time in Permutation Shop Floor scenarios. We have considered two types of process interruption events. The first one is predictive, where the interruption information is known well in advance, and the second one is reactive, where the interruption information is not known until the breakdown occurs. An extensive set of experiments has been carried out, which demonstrate the usefulness of the proposed approach.

Large scale constrained problems are complex problems due to their dimensionality, structure, in addition to their constraints. The performance of EAs decreases when the problem dimension increases. Decomposition-based EAs can overcome this drawback, but their performance would be affected if the interdependent variables were optimized in different subproblems. The use of EAs with variables interaction identification technique handles this issue by identifying better arrangements for decomposing a large problem into subproblems in a way that minimizes the interdependencies between them. The only technique in the literature that has been developed to identify the variables interdependency in constrained problems is the Variable Interaction Identification for Constrained problems (VIIC). This technique is tested in this paper on a real-world problem at three large dimensions which are large scale constrained optimization problems. The performance of the decomposition-based EA that uses VIIC is compared to Random Grouping approach for decomposition, for 5-Units, 10-Units, and 30-Units DED problems.

Over the last few decades, a number of differential evolution (DE) algorithms have been proposed with excellent performance on mathematical benchmarks. However, like any other optimization algorithm, the success of DE is highly dependent on the search operators and control parameters that are often decided a priori. The selection of the parameter values is itself a combinatorial optimization problem. Although a considerable number of investigations have been conducted with regards to parameter selection, it is known to be a tedious task. In this paper, a DE algorithm is proposed that uses a new mechanism to dynamically select the best performing combinations of parameters (amplification factor, crossover rate, and the population size) for a problem during the course of a single run. The performance of the algorithm is judged by solving three well known sets of optimization test problems (two constrained and one unconstrained). The results demonstrate that the proposed algorithm not only saves the computational time, but also shows better performance over the state-of-the-art algorithms. The proposed mechanism can easily be applied to other population-based algorithms.

In this paper, we consider the reliable broadcast and multicast lifetime maximization problems in energy-constrained wireless ad hoc networks, such as wireless sensor networks for environment monitoring and wireless ad hoc networks consisting of laptops or PDAs with limited battery capacities. In packet loss-free networks, the optimal solution of lifetime maximization problem can be easily obtained by tree-based algorithms. In unreliable networks, we formulate them as min-max tree problems and prove them NP-complete by a reduction from a well-known minimum degree spanning tree problem. A link quality-aware heuristic algorithm called Maximum Lifetime Reliable Broadcast Tree (MLRBT) is proposed to build a broadcast tree that maximizes the network lifetime. The reliable multicast lifetime maximization problem can be solved as well by pruning the broadcast tree produced by the MLRBT algorithm. The time complexity analysis of both algorithms is also provided. Simulation results show that the proposed algorithms can significantly increase the network lifetime compared with the traditional algorithms under various distributions of error probability on lossy wireless links.

Many genetic algorithms variants have been introduced for solving different classes of optimization problems. The success of any GA depends on the design of its search operators, as well as its parameters. In this paper, we propose a new three-parent crossover. In addition, we design a diversity operator which works with an archive of selected individuals. The algorithm has been applied to solve all the CEC'2013 competition problems on real-parameter optimization. The solutions obtained are either optimal or very close to the known best solutions.

Recently, Particle Swarm Optimizer (PSO) has become a popular tool for solving constrained optimization problems. However, there is no guarantee that PSO will perform consistently well for all problems and will not be trapped in local optima. In this paper, a PSO algorithm is introduced that uses two new mechanisms, the first one to maintain a better balance between intensification and diversification and the second one to escape from local solutions. Furthermore, all the basic parameters are determined self-adaptively. The performance of the proposed algorithm is analyzed by solving the CEC2010 constrained optimization problems. The algorithm shows consistent performance, and is superior to other state-of-the-art algorithms.

The performance of Differential Evolution (DE) algorithms is known to be highly dependent on its search operators and control parameters. The selection of the parameter values is a tedious task. In this paper, a DE algorithm is proposed that configures the values of two parameters (amplification factor and crossover rate) automatically during its course of evolution. For this purpose, we considered a set of values as input for each of the parameters. The algorithm has been applied to solve a set of test problems introduced in IEEE CEC'2013 competition. The results of the test problems are compared with the known best solutions and the approach can be applied to other population based algorithms.

The Permutation Flow Shop Scheduling Problem (PFSP) is a well-known combinatorial optimization problem. In this paper, a Genetic Algorithm (GA) based approach has been developed to solve PFSP, with the objective of minimizing the makespan for a set of jobs. Two new priority rules; such as Gap Filling (GF) technique and Job Shifting (JS), have been introduced to enhance the performance of the GA. The algorithm has been used to solve a set of standard benchmark problems and the results have been compared with state-of-the-art algorithms. The comparison demonstrates that the overall performance of the algorithm is quite satisfactory.

In this paper, we discuss a practical oil production planning optimization problem. For oil wells with insufficient reservoir pressure, gas is usually injected to artificially lift oil, a practice commonly referred to as enhanced oil recovery (EOR). The total gas that can be used for oil extraction is constrained by daily availability limits. The oil extracted from each well is known to be a nonlinear function of the gas injected into the well and varies between wells. The problem is to identify the optimal amount of gas that needs to be injected into each well to maximize the amount of oil extracted subject to the constraint on the total daily gas availability. The problem has long been of practical interest to all major oil exploration companies as it has the potential to derive large financial benefit. In this paper, an infeasibility driven evolutionary algorithm is used to solve a 56 well reservoir problem which demonstrates its efficiency in solving constrained optimization problems. Furthermore, a multi-objective formulation of the problem is posed and solved using a number of algorithms, which eliminates the need for solving the (single objective) problem on a regular basis. Lastly, a modified single objective formulation of the problem is also proposed, which aims to maximize the profit instead of the quantity of oil. It is shown that even with a lesser amount of oil extracted, more economic benefits can be achieved through the modified formulation.

Many real-world optimization problems are difficult to solve as they do not possess the nice mathematical properties required by the exact algorithms. Evolutionary algorithms are proven to be appropriate for such problems. In this paper, we propose an improved differential evolution algorithm that uses a mix of different mutation operators. In addition, the algorithm is empowered by a covariance adaptation matrix evolution strategy algorithm as a local search. To judge the performance of the algorithm, we have solved well-known benchmark as well as a variety of real-world optimization problems. The real-life problems were taken from different sources and disciplines. According to the results obtained, the algorithm shows a superior performance in comparison with other algorithms that also solved these problems.

Bringing the 2012 IEEE World Congress on Computational Intelligence (IEEE-WCCI 2012) for the first time to Australia has been a fulfilling journey of joy and honour. This premier event of the IEEE Computational Intelligence Society (IEEE-CIS) brings together three flagship conferences of the society in even years. It consisted of these conferences: the International Joint Conference on Neural Networks (IJCNN 2012), the IEEE International Conference on Fuzzy Systems (FUZZIEEE 2012) and the 2012 IEEE Congress on Evolutionary Computation (IEEE CEC 2012). This document presents the technical papers from the IEEE CEC 2012 conference, which had 758 submissions, of which, 482 were accepted.

This paper proposes an efficient, adaptive constraint handling approach that can be used within the class of evolutionary multi-objective optimization (EMO) algorithms. The proposed constraint handling approach is presented within the framework of one of the most successful algorithms i.e. multi-objective evolutionary algorithm based on decomposition (MOEA/D) [1]. The constraint handling mechanism adaptively decides on the violation threshold for comparison. The violation threshold is based on the type of constraints, size of the feasible space and the search outcome. Such a process intrinsically treats constraint violation and objective function values separately and adds a selection pressure, wherein infeasible solutions with violations less than the identified threshold are considered at par with feasible solutions. As illustrated, the constraint handling scheme extends the current capability of MOEA/D to deal with constraints. The performance of the algorithm is illustrated using 10 commonly studied benchmark problems and a real-world constraint optimization problem, and compared with the results obtained using yet another commonly used form i.e. Nondominated Sorting Genetic Algorithm (NSGA-II).

During the last two decades, a considerable number of particle swarm variants have been introduced. However, no single variant consistently performed well over a range of test problems with different mathematical properties. In this paper, a memetic multi-topology particle swarm optimizer (MMTPSO) is introduced for solving constrained optimization problems. MMTPSO utilizes the strengths of two different particle swarm topologies and during the evolution process the algorithm is designed to emphasize the best performing topology. Moreover, to increase the convergence pattern of the proposed algorithm, a local search algorithm is periodically used. MMTPSO shows a superior performance to its independent variants, as well as other state-of-the-art algorithms, by solving 13 well-known test problems.

Over the last few decades, a considerable number of Differential Evolution (DE) algorithms have been proposed with excellent performance on mathematical benchmarks. However, like any other optimization algorithm, the success of DE is highly dependent on its search operators and control parameters. Although a considerable number of investigations have been carried out for parameter selection, it is seen as a tedious task. In this paper, we propose a DE algorithm that uses an adaptive mechanism to select the best performing combination of parameters (amplification factor, crossover rate and the population size) during the course of a single run. The performance of the algorithm is analyzed on a set of 24 constrained optimization test problems. The results demonstrate that the proposed algorithm not only saves the computational time, but also shows better performance over the state-of-the-art algorithms.

Over the last few decades, real world constrained optimization has become an important research topic in the evolutionary computation field. The Economic Load Dispatch is one of the well-known complex practical problems. The problem is usually represented by a non-convex constrained optimization model. In this paper, we propose to use an ensemble of three different Constraint Consensus (CC) methods within the Differential Evolution algorithm to solve the Economic Load Dispatch problem. During the evolution process, an adaptive mechanism is used to assign the infeasible solutions to each CC method with the emphasis on the best performing one. The experimental results show that the proposed algorithm is not only able to reach the 100% feasibility ratio, but that it is also able to obtain better solutions in comparison to the state-of-the-art algorithms.

Large scale optimization problems are very challenging problems. Most of the recently developed optimization algorithms lose their efficiency when the dimensionality of the problems increases. Decomposing a large scale problem into smaller subproblems overcomes this drawback. However, if the large scale optimization problem contains dependent variables, they should be grouped into one subproblem to avoid a decrease in performance. In this paper, the Dependency Identification with Memetic Algorithm (DIMA) model is proposed for solving large scale optimization problems. The Dependency Identification (DI) technique identifies the best arrangement to group the dependent variables into smaller scale subproblems. These subproblems are then evolved using a Memetic Algorithm (MA) with a proposed self-directed Local Search (LS). As the subproblems of a nonseparable large scale problem may contain interdependent variables, the proposed model, DIMA, uses an Information Exchange Mechanism to maintain one value for all the instances of any independent variable in the different subproblems. A newly designed test suite of problems has been developed to evaluate the performance of DIMA. The first evaluation shows that the DI technique is competitive to other decomposition techniques in the literature in terms of consuming less computational resources and better performance. Another evaluation shows that DI makes the optimization of a decomposed large scale problem using DIMA as powerful as the optimization of a complete large scale problem using MA. This makes DIMA a promising optimization model for optimization problems which can be 10 times larger (or more) than the large scale optimization problems under consideration in this paper.

In this paper, we have proposed a progressive alignment method using a genetic algorithm for multiple sequence alignment, named GAPAM. We have introduced two new mechanisms to generate an initial population: the first mechanism is to generate guide trees with randomly selected sequences and the second is shuffling the sequences inside such trees. Two different genetic operators have been implemented with GAPAM. To test the performance of our algorithm, we have compared it with existing well-known methods, such as PRRP, CLUSTALX, DIALIGN, HMMT, SB_PIMA, ML_PIMA, MULTALIGN, and PILEUP8, and also other methods, based on genetic algorithms (GA), such as SAGA, MSA-GA, and RBT-GA, by solving a number of benchmark datasets from BAliBase 2.0. To make a fairer comparison with the GA based algorithms such as MSA-GA and RBT-GA, we have performed further experiments covering all the datasets reported by those two algorithms. The experimental results showed that GAPAM achieved better solutions than the others for most of the cases, and also revealed that the overall performance of the proposed method outperformed the other methods mentioned above.

Real world optimization problems are challenging as they often involve a large number of variables and highly nonlinear constraints and objective functions. While a number of efficient optimization algorithms and numerous mathematical benchmark test functions have been introduced in recent years, the performance of such algorithms have rarely been studied across a range of real world optimization problems. In this paper, we introduce an improved adaptive differential evolution (DE) algorithm and report its performance on the newly proposed real world optimization problems. The proposed differential evolution algorithm incorporates adaptive parameter control strategies; a center based differential exponential crossover and hybridization with local search to improve its efficiency. While comprehensive results of other algorithms on the test problems are unavailable at this stage, our preliminary comparison with published results indicates promising performance of the proposed DE across the range of problems.

To solve two-dimensional (2D) rectangular packing problems, we introduce a new spatial method based on the discretization of the container into a grid of cells with predefined resolution. Before an item is added, grid cells are checked whether they can accommodate the item. If an appropriate empty cell cluster is found, the item is added and moved towards the bottom-left corner of the container. This placement and sliding method is supplemented by a heuristic that orders the items according to descending size. Order and rotation of items can be improved by hybridizing the heuristic with a genetic algorithm (GA) in which a population of order-rotation chromosomes is evolved. The method is tested on 47 benchmark problems and compared to other methods in the literature. This shows that it is fast and performs very well in finding close to optimal problem solutions. Particularly for large problem sizes, it outperforms some of the currently leading methods, such as heuristic recursive (HR). The hybridization with the GA meta-heuristic results in further performance improvements.

Over the last two decades, many Genetic Algorithms have been introduced for solving Constrained Optimization Problems (COPs). Due to the variability of the characteristics in different COPs, none of these algorithms performs consistently over a range of problems. In this paper, we introduce a Genetic Algorithm with a new multi-parent crossover for solving a variety of COPs. The proposed algorithm also uses a randomized operator instead of mutation and maintains an archive of good solutions. The algorithm has been tested by solving the 36 test instances, introduced in the CEC2010 constrained optimization competition session. The results show that the proposed algorithm performs better than the state-of-the-art algorithms.

Over the last two decades, many Genetic Algorithms have been introduced for solving optimization problems. Due to the variability of the characteristics in different optimization problems, none of these algorithms performs consistently over a range of problems. In this paper, we introduce a GA with a new multi-parent crossover for solving a variety of optimization problems. The proposed algorithm also uses both a randomized operator as mutation and maintains an archive of good solutions. The algorithm has been applied to solve the set of real world problems proposed for the IEEE-CEC2011 evolutionary algorithm competition.

Over the last two decades, many Differential Evolution (DE) strategies have been introduced for solving Optimization Problems. Due to the variability of the characteristics in optimization problems, no single DE algorithm performs consistently over a range of problems. In this paper, for a better coverage of problem characteristics, we introduce a DE algorithm framework that uses multiple search operators in each generation. The appropriate mix of the search operators, for any given problem, is determined adaptively. The proposed algorithm has been applied to solve the set of real world numerical optimization problems introduced for a special session of CEC2011.

Due to the variability of the characteristics of different Constrained Optimization Problems, no single Differential Evolution strategy, with no single constraint handling technique, performs consistently over a range of problems. In this paper, for a better coverage of the problem characteristics, we introduce a DE algorithm that uses multiple search operators and constraint handling techniques. In the proposed algorithm, initially each individual is assigned a random combination of operators. After a certain number of generations, the improvement made by each combination is recorded, and the best combination is then assigned to more and more individuals, while each of the other individuals are assigned a random combination. To accelerate the convergence of the proposed algorithm, a local search procedure is also applied to selected individuals. The algorithm has been tested by solving 18 test problems, with 10D and 30D. The results showed that the proposed algorithm is superior to state of the art algorithms.

Solving a Constrained Optimization Problem (COP) is much more challenging than its unconstrained counterpart. In solving COPs, the feasibility of a solution is a prime condition that requires the conversion of one or more infeasible individuals to feasible individuals. In this paper, to encourage the effective movement of infeasible individuals towards a feasible region, we introduce a Constraint Consensus (CC) method within the Differential Evolution (DE) algorithm for solving COPs. The algorithm has been tested by solving 13 well-known benchmark problems. The experimental results show that the solutions are competitive, if not better, as compared to the state of the art algorithms.

BACKGROUND: Many Bioinformatics studies begin with a multiple sequence alignment as the foundation for their research. This is because multiple sequence alignment can be a useful technique for studying molecular evolution and analyzing sequence structure relationships. RESULTS: In this paper, we have proposed a Vertical Decomposition with Genetic Algorithm (VDGA) for Multiple Sequence Alignment (MSA). In VDGA, we divide the sequences vertically into two or more subsequences, and then solve them individually using a guide tree approach. Finally, we combine all the subsequences to generate a new multiple sequence alignment. This technique is applied on the solutions of the initial generation and of each child generation within VDGA. We have used two mechanisms to generate an initial population in this research: the first mechanism is to generate guide trees with randomly selected sequences and the second is shuffling the sequences inside such trees. Two different genetic operators have been implemented with VDGA. To test the performance of our algorithm, we have compared it with existing well-known methods, namely PRRP, CLUSTALX, DIALIGN, HMMT, SB_PIMA, ML_PIMA, MULTALIGN, and PILEUP8, and also other methods, based on Genetic Algorithms (GA), such as SAGA, MSA-GA and RBT-GA, by solving a number of benchmark datasets from BAliBase 2.0. CONCLUSIONS: The experimental results showed that the VDGA with three vertical divisions was the most successful variant for most of the test cases in comparison to other divisions considered with VDGA. The experimental results also confirmed that VDGA outperformed the other methods considered in this research.

The job scheduling problem (JSP) is considered as one of the complex combinatorial optimization problems. In this paper, we have developed a hybrid Genetic Algorithm (HGA), which improves the performance of GAs when solving JSPs. We have also modified the developed algorithm to study JSPs under the machine unavailability condition. We have considered two types of machine unavailability. Firstly, where the unavailability information is available in advance (predictive) and, secondly, where the information is known after a real breakdown (reactive). We have shown that the revised schedule is mostly able to recover if the disruptions occur during the early stages of a schedule.

Multiple sequence alignment is one of the most important issues in molecular biology as it plays an important role such as in life saving drug design. In this paper, we divide given sequences into two or more subsequences and then combine them together in order to find better multiple sequence alignments by applying a new GA based approach to the combined sequences. We also introduce new ways of generating an initial population and of applying the genetic operators. We have carried out experiments for the BAliBASE benchmark database using the sum of pair objective function with the PAM250 score matrix. To evaluate our proposed approach, we have compared with well known methods such as T-Coffee, MUSCLE, MAFFT and ProbCons. The experimental results show that better multiple sequence alignments may be obtained with higher number of divisions, however the computation time increases with the number of decompositions. The overall performance of the proposed Decomposition with GA (DGA) method is better than the existing methods and the GA method (without decompositions).

Over the last two decades several methods have been proposed for handling functional constraints while solving nonlinear optimization problems using Evolutionary Algorithms (EA). However EAs have inherent difficulty in dealing with equality constraints. This paper presents an Agent-based Memetic Algorithm (AMA) for solving nonlinear optimization problems with equality constraints. A new learning process for agents is introduced specifically for handling the equality constraints in the evolutionary process. The basic concept is to reach a point on the equality constraint from its current position by the selected individual agents. The proposed algorithm is tested on a set of standard benchmark problems. The preliminary results show that the proposed technique works very well on those benchmark problems.

The Job-Shop Scheduling Problem (JSSP) is considered as one of the difficult combinatorial optimization problems and treated as a member of NP-complete problem class. In this paper, we consider JSSPs with an objective of minimizing makespan while satisfying a number of hard constraints. First, we develop a genetic algorithm (GA) based approach for solving JSSPs. We then introduce a number of priority rules such as partial reordering, gap reduction and restricted swapping to improve the performance of the GA. We run the GA incorporating these rules in a number of different ways. We solve 40 benchmark problems and compared their results with that of a number of well-known algorithms. We obtain optimal solutions for 27 problems, and the overall performance of our algorithms is quite encouraging.

Scenarios are pen-pictures of plausible futures, used for strategic planning. The aim of this investigation is to expand the horizon of scenario-based planning through computational models that are able to aid the analyst in the planning process. The investigation builds upon the advances of Information and Communication Technology (ICT) to create a novel, flexible and customizable computational capability-based planning methodology that is practical and theoretically sound. We will show how evolutionary computation, in particular evolutionary multi-objective optimization, can play a central role - both as an optimizer and as a source for innovation.

The hurdles in solving Constrained Optimization Problems (COP) arise from the challenge of searching a huge variable space in order to locate feasible points with acceptable solution quality. It becomes even more challenging when the feasible space is very tiny compare to the search space. Usually, the quality of the initial solutions influences the performance of the algorithm in solving such problems. In this paper, we discuss an Evolutionary Agent System (EAS) for solving COPs. In EAS, we treat each individual in the population as an agent. To enhance the performance of EAS for solving COPs with tiny feasible space, we propose a Search Space Reduction Technique (SSRT) as an initial step of our algorithm. SSRT directs the selected infeasible agents in the initial population to move towards the feasible space. The performance of the proposed algorithm is tested on a number of test problems and a real world case problem. The experimental results show that SSRT not only improves the solution quality but also speed up the processing time of the algorithm.

Capability planning problems are pervasive throughout many areas of human interest with prominent examples found in defense and security. Planning provides a unique context for optimization that has not been explored in great detail and involves a number of interesting challenges which are distinct from traditional optimization research. Planning problems demand solutions that can satisfy a number of competing objectives on multiple scales related to robustness, adaptiveness, risk, etc. The scenario method is a key approach for planning. Scenarios can be defined for long-term as well as short-term plans. This paper introduces computational scenario-based planning problems and proposes ways to accommodate strategic positioning within the tactical planning domain. We demonstrate the methodology in a resource planning problem that is solved with a multi-objective evolutionary algorithm. Our discussion and results highlight the fact that scenario-based planning is naturally framed within a multi-objective setting. However, the conflicting objectives occur on different system levels rather than within a single system alone. This paper also contends that planning problems are of vital interest in many human endeavors and that Evolutionary Computation may be well positioned for this problem domain.

Large scale constrained optimization problem solving is a challenging research topic in the optimization and computational intelligence domain. This paper examines the possible division of computational tasks, into smaller interacting components, in order to effectively solve constrained optimization problems in the continuous domain. In dividing the tasks, we propose problem decomposition, and the use of GAs as the solution approach. In this paper, we consider problems with block angular structure with or without overlapping variables. We decompose not only the problem but also the chromosome as suitable for different components of the problem. We also design a communication process for exchanging information between the components. The research shows an approach of dividing computation tasks, required in solving large scale optimization problems, which can be processed in parallel machines. A number of test problems have been solved to demonstrate the use of the proposed approach. The results are very encouraging.

The quality of individuals in the initial population influences the performance of evolutionary algorithms, especially when the feasible region of the constrained optimization problems is very tiny in comparison to the entire search space. Too much diversity of the population may cost huge processing time; on the other hand the algorithms may trap into local optima for lack of diversity. This paper proposes a simple method to improve the quality of randomly generated initial solutions by sacrificing very little in diversity of the population. We introduce the method of search space reduction technique (SSRT) which is tested using four different existing EAs by solving a number of state-of-the-art test problems and a real world case problem. The experimental results show SSRT improves the solution qualities as well as speeding up the performance of the algorithm.

Over the last decade, significant progress has been made in understanding complex biological systems, however, there have been few attempts at incorporating this knowledge into nature inspired optimization algorithms. In this paper, we present a first attempt at incorporating some of the basic structural properties of complex biological systems which are believed to be necessary preconditions for system qualities such as robustness. In particular, we focus on two important conditions missing in evolutionary algorithm populations; a self-organized definition of locality and interaction epistasis. We demonstrate that these two features, when combined, provide algorithm behaviors not observed in the canonical evolutionary algorithm (EA) or in EAs with structured populations such as the cellular genetic algorithm. The most noticeable change in algorithm behavior is an unprecedented capacity for sustainable coexistence of genetically distinct individuals within a single population. This capacity for sustained genetic diversity is not imposed on the population but instead emerges as a natural consequence of the dynamics of the system.

The Job-Shop Scheduling Problem (JSSP) is one of the most critical combinatorial optimization problems. The objective of JSSP in this research is to minimize the makespan. In this paper, we propose two Genetic Algorithm (GA) based approaches for solving JSSP. Firstly, we design a simple heuristic to reduce the completion time of jobs on the bottleneck machines that we call the reducing bottleneck technique (RBT). This heuristic was implemented in conjunction with a GA. Secondly; we propose to fill any possible gaps left in the simple GA solutions by the tasks that are scheduled later. We call this process the gap-utilization technique (GUT). With GUT, we also apply a swapping technique that deals only with the bottleneck job. We study 35 test problems with known solutions, using the existing GA and our proposed two algorithms. We obtain optimal solutions for 23 problems, and the solutions are very close for the rest.

Machine layout and material flow between machines are crucial considerations for improving productivity in any manufacturing environment. The machine layout and the operations assignment problems are both known to be NP hard problems. In this paper, we introduce a new combined machine layout and operations assignment problem. We propose an evolutionary algorithm to solve the combined machine layout and operations assignment problem. The effectiveness of our approach is demonstrated through numerical examples.

In recent years, memetic algorithms (MAs) have been proposed to enhance the performance of evolutionary algorithms by incorporating local search techniques with evolutionary algorithms' global search ability, and applied successfully to solve different type of optimization problems. This paper proposes a new memetic algorithm and then introduces an agent-based memetic algorithm (AMA), for the first time, to further enhance the ability of MA in solving constrained optimization problems. In a lattice-like environment, each of the agents represents a candidate solution of the problem. The agents are able to sense and act on the society, and their performances i.e. fitness of the solution improves through co-evolutionary adaptation of society with the individual learning of the agents. The proposed algorithm is tested on 13 benchmark problems and the experimental results show promising performance.

In this paper, we discuss a practical oil production problem from a petroleum field. A field typically consists of a number of oil wells and to extract oil from these wells, gas is usually injected which is referred as gas-lift. The total gas used for the oil extraction is constrained by daily availability limits. The oil extracted from each well is known to be a nonlinear function of the gas injected into a well and varies between wells. The problem is to identify the optimal amount of gas that needs to be injected into each well to maximize the amount of oil extracted subject to the constraint mentioned earlier on a daily basis. The problem has long been of practical interest to all major oil exploration companies as it has a potential of deriving large financial benefits. Considering the complexity of the problem, we have used an evolutionary algorithm to solve the production planning problem. The multiobjective formulation is attractive as it eliminates the need to solve such problems on a daily basis while maintaining the quality of solutions. Our results show significant improvement over the existing practices.

In this paper, the issue of adapting probabilities for Evolutionary Algorithm (EA) search operators is revisited. A framework is devised for distinguishing between measurements of performance and the interpretation of those measurements for purposes of adaptation. Several examples of measurements and statistical interpretations are provided. Probability value adaptation is tested using an EA with 10 search operators against 10 test problems with results indicating that both the type of measurement and its statistical interpretation play significant roles in EA performance. We also find that selecting operators based on the prevalence of outliers rather than on average performance is able to provide considerable improvements to adaptive methods and soundly outperforms the non-adaptive case.

In this paper, a new method for assigning credit to search operators is presented. Starting with the principle of optimizing search bias, search operators are selected based on an ability to create solutions that are historically linked to future generations. Using a novel framework for defining performance measurements, distributing credit for performance, and the statistical interpretation of this credit, a new adaptive method is developed and shown to outperform a variety of adaptive and non-adaptive competitors.

Red teaming is the process of studying a problem by anticipating adversary behaviors. When done in simulations, the behavior space is divided into two groups; one controlled by the red team which represents the set of adversary behaviors or bad guys, while the other is controlled by the blue team which represents the set of defenders or good guys. Through red teaming, analysts can learn about the future by forward prediction of scenarios. More recently, defense has been looking at evolutionary computation methods in red teaming. The fitness function in these systems is highly stochastic, where a single configuration can result in multiple different outcomes. Operational, tactical and strategic decisions can be made based on the findings of the evolutionary method in use. Therefore, there is an urgent need for understanding the nature of these problems and the role of the stochastic fitness to gain insight into the possible performance of different methods. This paper presents a first attempt at characterizing the search space difficulties in red teaming to shed light on the expected performance of the evolutionary method in stochastic environments.

The paper presents a genetic algorithm with fuzzy logic controller for determining opportunistic replacement policy for deteriorating components of an equipment or system. An opportunistic replacement model has been formulated by considering the dynamics of the decision process of such a policy. In order to reduce the computational burden involving complete enumeration of all possible policies, genetic algorithm has been used to find near optimal solution by maximizing net benefit to be gained from an opportunistic replacement. A fuzzy logic controller has been used to automatically adjust the fine-tuning structure of genetic algorithm parameters. The performance of the model and the solution procedure has been evaluated for a number of case problems, which clearly demonstrates that the proposed method is very effective.

Evolutionary algorithms (EAs) has attracted increasing attention in recent years, as powerfully computational technique, for solving many complex real-world problems. The successful application of evolutionary algorithms to optimization problems is dependent on the methods and parameters used for the algorithm. In this paper, we investigate the effect of population sizes on the quality of solutions to be obtained, the computational time required and the size of search spaces of the problems under consideration. We select a two-stage transportation problem as a test case and also use a well known conventional optimization technique to compare the solutions. The numerical results are analyzed and the interesting findings are discussed.

Support vector machine (SVM) has appeared as a powerful tool for forecasting forex market and demonstrated better performance over other methods, e.g., neural network or ARIMA based model. SVM-based forecasting model necessitates the selection of appropriate kernel function and values of free parameters: regularization parameter and /spl epsiv/-insensitive loss function. We investigate the effect of different kernel functions, namely, linear, polynomial, radial basis and spline on prediction error measured by several widely used performance metrics. The effect of regularization parameter is also studied. The prediction of six different foreign currency exchange rates against Australian dollar has been performed and analyzed. Some interesting results are presented.

Evolutionary Computation (EC) has attracted increasing attention in recent years, as powerful computational techniques, for solving many complex real-world problems. The Operations Research (OR)/Optimization community is divided on the acceptability of these techniques. One group accepts these techniques as potential heuristics for solving complex problems and the other rejects them on the basis of their weak mathematical foundations. In this paper, we discuss the reasons for using EC in optimization. A brief review of Evolutionary Algorithms (EAs) and their applications is provided. We also investigate the use of EAs for solving a two-stage transportation problem by designing a new algorithm. The computational results are analyzed and compared with conventional optimization techniques.

The use of evolutionary algorithms (EAs) to solve problems with multiple objectives (known as multi-objective optimization problems (MOPs)) has attracted much attention. Being population based approaches, EAs offer a means to find a group of Pareto-optimal solutions in a single run. Differential evolution (DE) is an EA that was developed to handle optimization problems over continuous domains. The objective of this paper is to introduce a novel Pareto-frontier differential evolution (PDE) algorithm to solve MOPs. The solutions provided by the proposed algorithm for two standard test problems, outperform the Strength Pareto Evolutionary Algorithm, one of the state-of-the-art evolutionary algorithms for solving MOPs.