Recently, mobile edge computing (MEC) technology has been integrated with wireless blockchain networks to improve the computational capabilities of Internet of Things devices during the mining process. Jointly, optimizing miner selection (discrete) and resource allocation (continuous) in MEC-integrated blockchain networks is a challenging mixed-variable, NP-hard problem. Although several algorithms have been presented in the literature to solve it, they still suffer from low-quality results due to either slow convergence speed, local optima stagnation, or both, especially for small or medium problem sizes. To address this, we propose a transfer-function-guided encoding (TFE) framework that introduces a principled link between continuous metaheuristic search and discrete miner-operator control. Specifically, each individual maintains one discrete control variable determining insertion, deletion, or replacement of a miner and two continuous controls representing transmission power and computing resource allocation. Continuous metaheuristic outputs are converted to discrete decisions through families of S-shaped and V-shaped transfer functions, providing tunable exploration–exploitation balance and probabilistic control over operator selection. This mechanism is integrated with several state-of-the-art algorithms. Extensive experiments on MEC-blockchain networks with m ∈ [ 50 , 1000 ] miners demonstrate that TFE consistently accelerates convergence and improves system profit for small–medium scales, with HNOA-TFE achieving the best overall performance. The numerical results show that the hybrid nutcracker optimization algorithm with the TFE mechanism is effective across most problem instances. Also, the comparative study with recent MEC/blockchain resource-allocation and vehicular-edge benchmarks shows the robustness and scalability of the proposed method.

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.

We present a modified planning-assisted swarm shepherding method to effectively control multi-robot (sheepdogs) when herding a swarm of reactive agents (sheep) towards a goal and in environments with obstacles. Given a highly-dispersed sheep swarm, a mission planner based on Ant Colony Optimisation and A * is designed and developed to support the shepherding task. To apply the swarm shepherding method to real robots, a multi-layer environmental modelling method is proposed to construct customised environment maps for sheep and sheepdogs according to their physical characteristics. Then, a lookahead - based sub-goal selection method is presented for herding the sheep swarm to follow the A * optimised reference path. Furthermore, a circle-based method for selecting feasible driving/collecting points while avoiding obstacles is designed. Experiments are conducted in numerical simulation environments to compare the proposed method with the state-of-the-art planning-assisted shepherding method, followed by testing in the robot simulation platform CoppeliaSim to demonstrate the effectiveness of the proposed method.

Shepherding is a nature-inspired swarm guidance approach, where one or more sheepdogs act as actuators to guide a swarm towards a goal area. In the real-world, swarm guidance occurs in unknown environments. Context unfolds as the controller agent, the sheepdog, continues to discover new states, causing the state space to unfold during a mission due to the partial observability of the state space by each sheepdog. These individualised experiences could get shared among the shepherds to improve situation awareness. Our prior work introduced an approach to share interpretable knowledge between two agents. In this paper, we extend the two-agent interpretable knowledge fusion algorithm to multi-agent settings; allowing multiple sheepdogs to share their knowledge in an interpretable manner. When an agent receives knowledge from another agent, it decides on whether to integrate this new knowledge with what it already knows, leading to an increase in the size and space complexity of an agent's knowledge base. We propose a modular neural network society of mind architecture to store, update and manipulate the knowledge base of an agent. The architecture stores sub-networks and associate them with situations. When an agent is faced with a state, a gate controller decides based on the situation facing the agent which sub-networks are best suited to make decisions. The contribution is validated on a general classification task utilising the full-state-space for a swarm guidance shepherding problem. When compared to baseline methods, the proposed knowledge transfer algorithm improves generalisation, reduces catastrophic forgetting, and produces smaller models with faster adaptation.

This paper investigates a swarm shepherding problem which aims to herd multiple sub-swarm of robot agents (sheep) in a large-scale cluttered environment to a specific goal area using multiple distance-constrained robots (sheepdogs) located at different depots. We propose to formulate this challenging problem as a Multi-depot, Distance-constrained Close-Open Mixed Vehicle Routing Problem (MDCOMVRP). We also design a Two-phase Ant Colony Optimisation to address it by decomposing MDCOMVRP into a Multi-depot Open Vehicle Routing Problem (MOVRP) and a split problem. In the first phase, the Max-Min Ant System algorithm is employed to find open routes for all robots by transforming the MOVRP into a standard Travelling Salesman Problem using the proposed transformation method. In the second phase, a Modified Split algorithm is presented to construct a set of close or open distance-constrained routes, which are further optimised by the 2-opt local search method to generate the optimised sequence for each sheepdog robot to collect/drive sheep sub-swarms. Experiments are conducted to demonstrate that the proposed algorithm can solve MDCOMVRP successfully and assist the robots to complete the swarm shepherding mission efficiently.

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.

Within applications of swarm control, failing to maintain cohesion amongst the agents may lead to mission failure. We study the effect of limited sensing range of swarming agents when guided by a shepherd. A connectivity-aware approach is proposed to enhance the cohesion of the swarm. We combine a graph-based model of the flock with particle swarm optimization (assisted by DBSCAN) to improve the shepherd's performance in herding sheep (swarm members). The approach is evaluated using multiple initial swarm configurations. Simulation results on swarm sizes of 50 and 100 agents show up to 50% reduction in the task completion time and an average improvement of 25% in the success rate for low density sheep initialization scenarios and competitive results for the higher density scenarios.

The Resource-Constrained Project Scheduling Problem (RCPSP) is an NP-hard optimisation problem that can be found in many real-world applications. Considerable research effort has been put into overcoming the difficulties in solving the RCPSP by proposing innovative heuristics, meta-heuristics and their hybridisation. However, finding optimal solutions is still not guaranteed. It is known that quantum-inspired metaheuristics can improve population diversity and the quality of solutions but little has been published on adapting them to solving RCPSPs. Here, we examine the performance of a Quantum-Inspired Differential Evolution (QIDE) algorithm in solving such problems. The proposed QIDE uses a quantum population that is initialised using the rotation quantum gate and quantum superposition in the continuous domain, and then evolved using the differential-evolution operators. A local search is also adopted to accelerate convergence. The performance of the QIDE algorithm was tested by solving problems with 30 and 60 activities from the PSPLIB benchmark datasets. The QIDE algorithm outperformed another quantum-based particle swarm algorithm and some other meta-heuristics.

Controlling a large swarm of agents is a challenging task. Shepherding refers to an active field of research that seeks to address this challenge by using a control agent (sheepdog), which guides a swarm (sheep) towards a goal. Traditional shepherding involves switching between two main behaviours: driving the swarm towards the goal, and collecting stray sheep back to the flock. Evidently, the movement of the agents are dependent on their sensed information. Therefore, effectively controlling a swarm is even more challenging when sensor information or communication channels are unreliable. In this paper, we propose a shepherding methodology to achieve efficient swarm control in the presence of noise in the sensed information. The proposed approach consists of a new resting behaviour and a neural network-based reinforcement learning model. The neural network is used to learn shepherding policies using the new resting behaviour, where the objective is to optimise the frequency of sheep-to-dog interactions with varying levels of noise. The proposed approach is validated through simulations. Numerical experiments show that the proposed approach results in a more effective and stable performance compared to some conventional shepherding models from the literature.

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.

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.

In recent years, several multi-method and multi-operator-based algorithms have been proposed for solving optimization problems. Generally, their performance is better than other algorithms that based on a single operator and/or algorithm. However, they do not perform consistently well over all the problems tested in the literature. In this paper, we propose an improved optimization algorithm that uses the benefits of multiple differential evolution operators, with more emphasis placed on the best-performing operator. The performance of the proposed algorithm is tested by solving 10 problems with 5, 10, 15 and 20 dimensions taken from CEC2020 competition on single objective bound constrained optimization, with its results outperforming both single operator-based and different state-of-the-art algorithms.

Recently, many deferential evolution-based algorithms have been developed to solve constrained optimization problems. The performance of these methods outperforms the performance of single operator and/or algorithm-based ones. However, they do not perform consistently for all the problems tested in the literature. Also, the process of using the appropriate selection of algorithms and operators may be time-consuming since their designs are undertaken mainly through trial and error. In this paper, we propose an improved optimization algorithm that uses the benefits of multiple deferential evolution operators, with the best one is emphasized based on the quality and diversity of the population. The performance of the proposed algorithm is tested by solving 57 real-world constrained problems with different dimensions, number of equality and equality constraints, with its results showing a high success rate and that it outperformed different state-of-the-art 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.

In the shepherding problem, an external agent (the shepherd) attempts to influence the behavior of a swarm of agents (the sheep) by steering them towards a goal that is known to the shepherd but not the sheep. The problem offers a level of abstraction for Human-Swarm Interaction, where the human is able to shepherd the swarm towards a goal. Similarly, a smart robot could act as a shepherd to replace biological shepherds with ground or air vehicles. In both cases, it is important to preserve the energy of the shepherd by modulating the shepherd's influence vector on the sheep. Therefore, in this paper, we design a force modulation function for the shepherd agent to optimize the energy used by the agent and systematically study the effect of modulating the force of the influence vector on task success and energy used. The problem is further investigated using a bi-objective optimization formulation, where the energy used by the shepherd as well as the time of completion of the task are minimized, subject to a threshold of success rate. The findings demonstrate the coupling between contextual information used by the shepherd to modulate its influence vector and the effectiveness and efficiency of shepherd to complete the task.

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.

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.

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.

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.

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.

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.

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 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.