Deep Reinforcement Learning (DRL)-based Dynamic Voltage Frequency Scaling (DVFS) has shown great promise for energy conservation in embedded systems. While many works were devoted to validating its efficacy or improving its performance, few discuss the feasibility of the DRL agent deployment for embedded computing. State-of-the-art approaches focus on the miniaturization of agents’ inferential networks, such as pruning and quantization, to minimize their energy and resource consumption. However, this spatial-based paradigm still proves inadequate for resource-stringent systems. In this paper, we address the feasibility from a temporal perspective, where FiDRL, a flexible invocation-based DRL model is proposed to judiciously invoke itself to minimize the overall system energy consumption, given that the DRL agent incurs non-negligible energy overhead during invocations. Our approach is three-fold: (1) FiDRL that extends DRL by incorporating the agent's invocation interval into the action space to achieve invocation flexibility; (2) a FiDRL-based DVFS approach for both inter- and intra-task scheduling that minimizes the overall execution energy consumption; and (3) a FiDRL-based DVFS platform design and an on/off-chip hybrid algorithm specialized for training the DRL agent for embedded systems. Experiment results show that FiDRL achieves 55.1% agent invocation cost reduction, under 23.3% overall energy reduction, compared to state-of-the-art approaches.

The Set-Union Knapsack Problem (SUKP) is a complex combinatorial optimisation problem with applications in resource allocation, portfolio selection, and logistics. This paper presents a parallel local search algorithm for solving SUKP on the Compute Unified Device Architecture (CUDA) platform in Graphics Processing Units (GPUs). The proposed method employs a compact algorithm that divides the search space into smaller regions. For diversity, each thread in a GPU block starts the search process from a different location in a region using a different initial solution. Each thread then searches the local optimum by utilising communication between individuals through a crossover operator exploiting the best solution within the GPU block. Through extensive experiments on a set of SUKP benchmark instances ranging in size from small to large, we demonstrate the effectiveness of the proposed algorithm in finding high-quality solutions within comparable time frames. Furthermore, a comparative performance analysis with the current state-of-the-art SUKP algorithms reveals the competitive advantage of the proposed method. The GPU-based parallel local search algorithm using uniform crossover is a valuable addition to the repertoire of algorithms addressing SUKP, highlighting its potential for practical applications in real-world decision-making scenarios.

Hyper-heuristics are general purpose search methods for solving computationally difficult problems. A selection hyper-heuristic is composed of two key components: a heuristic selection method and move acceptance criterion. Under an iterative single-point search framework, a solution is modified by selecting and applying a predefined low-level heuristic, with a decision then taken to accept or reject the resulting solution. Designing a selection hyper-heuristic is an extremely challenging task. In this study, we investigate computer-aided design of a selection hyper-heuristic for the open vehicle routing problem. A time delay neural network is used as an offline apprenticeship learning method. Our approach first observes the search behavior of multiple expert human-designed selection hyper-heuristics on a selected sample of training instances, before automatically generating a selection hyper-heuristic capable of solving unseen instances effectively. The proposed approach is tested on open vehicle routing problem instances of different sizes to examine the performance and generality of the selection hyper-heuristics generated. Improved performance is demonstrated over a set of well-known benchmarks from the literature when compared to using the existing expert systems directly.

Metaheuristics, providing high level guidelines for heuristic optimisation, have successfully been applied to many complex problems over the past decades. However, their performances often vary depending on the choice of the initial settings for their parameters and operators along with the characteristics of the given problem instance handled. Hence, there is a growing interest into designing adaptive search methods that automate the selection of efficient operators and setting of their parameters during the search process. In this study, an adaptive binary parallel evolutionary algorithm, referred to as ABPEA, is introduced for solving the uncapacitated facility location problem which is proven to be an NP-hard optimisation problem. The approach uses a unary and two other binary operators. A reinforcement learning mechanism is used for assigning credits to operators considering their recent impact on generating improved solutions to the problem instance in hand. An operator is selected adaptively with a greedy policy for perturbing a solution. The performance of the proposed approach is evaluated on a set of well-known benchmark instances using ORLib and M*, and its scaling capacity by running it with different starting points on an increasing number of threads. Parameters are adjusted to derive the best configuration of three different rewarding schemes, which are instant, average and extreme. A performance comparison to the other state-of-the-art algorithms illustrates the superiority of ABPEA. Moreover, ABPEA provides up to a factor of 3.9 times acceleration when compared to the sequential algorithm based on a single-operator.

Parameter tuning is a challenging and time-consuming task, crucial to obtaining improved metaheuristic performance. There is growing interest in cross-domain search methods, which consider a range of optimisation problems rather than being specialised for a single domain. Metaheuristics and hyper-heuristics are typically used as high-level cross-domain search methods, utilising problem-specific low-level heuristics for each problem domain to modify a solution. Such methods have a number of parameters to control their behaviour, whose initial settings can influence their search behaviour significantly. Previous methods in the literature either fix these parameters based on previous experience, or set them specifically for particular problem instances. There is a lack of extensive research investigating the tuning of these parameters systematically. In this paper, F-Race is deployed as an automated cross-domain parameter tuning approach. The parameters of a steady-state memetic algorithm and the low-level heuristics used by this algorithm are tuned across nine single-objective problem domains, using different training strategies and budgets to investigate whether F-Race is capable of effectively tuning parameters for cross-domain search. The empirical results show that the proposed methods manage to find good parameter settings, outperforming many methods from the literature, with different configurations identified as the best depending upon the training approach used.

Selection hyper-heuristics have emerged as high level general-purpose search methodologies that mix and control a set of low-level (meta)heuristics. Previous empirical studies over a range of single objective optimisation problems have shown that the number and type of low-level (meta)heuristics used are influential to the performance of selection hyper-heuristics. In addition, move acceptance strategies play an important role and can significantly affect the overall performance of a hyper-heuristic. In this paper, we introduce an adapted variant of an existing learning automata based multiobjective hyper-heuristic from the literature. We investigate the performance and generality level of the proposed method, and another learning automata based selection hyper-heuristic, operating over a search space of multiobjective evolutionary algorithms (MOEAs) across two well-known multiobjective optimisation benchmarks. The experimental results demonstrate that, regardless of the number and type of low-level metaheuristics available, the learning automata based hyper-heuristics outperform each constituent MOEA individually, and an online learning and random choice selection hyper-heuristic from the literature. This performance and generality is shown to be consistent across a number of different move acceptance strategies.

Blockchain technology and metaverse advancements allow people to create virtual personalities and spend time online. Integrating public transportation into the metaverse could improve services and collect user data. This article introduces a hybrid decision-making framework for prioritizing sustainable public transportation in Metaverse under q-rung orthopair fuzzy set (q-ROFS) context. In this regard, first, q-rung orthopair fuzzy (q-ROF) generalized Dombi weighted aggregation operators and their characteristics are developed to aggregate the q-ROF information. Second, a q-ROF information-based method using the removal effects of criteria and stepwise weight assessment ratio analysis models are proposed to find the objective and subjective weights of criteria, respectively. Then, a combined weighting model is taken to determine the final weights of the criteria. Third, the weighted sum product method is extended to q-ROFS context by considering the double normalization procedures, the proposed operators and integrated weighting model. This method has taken the advantages of two normalization processes and four utility measures that approve the effect of benefit and cost criteria by using weighted sum and weighted product models. Next, to demonstrate the practicality and effectiveness of the presented method, a case study of sustainable public transportation in metaverse is presented in the context of q-ROFSs. The findings of this article confirms that the proposed model can recommend more feasible performance while facing numerous influencing factors and input uncertainties, and thus, provides a wider range of applications.

This study presents an offline learning Simulated Annealing approach to generate a constructive hyper-heuristic evaluated through training and testing on a set of instances for solving the Job-Shop Scheduling problem. The generated hyperheuristic uses a range of state features to control a set of low-level constructive heuristics. A hyper-heuristic is represented in terms of a set of rules, where each rule contains a fixed set of values for the features in consideration and the low level heuristic to be invoked. At each constructive step, the `closest' rule is selected and then the corresponding constructive low level heuristic is applied. Our distance metric is the Euclidean distance between the values within the rule and the state features characterising the partial schedule along with the remaining jobs to be scheduled for the partial solution. In this paper, we study a set of features computed with various well-known metrics and different feature transformation methods for improving the characterization of the problem instances and solutions to Job-Shop Scheduling as a part of our approach. Eight different scenarios are evaluated on a set of randomly generated problem instances. Each scenario represents a distinct approach combining a different feature transformation applied during the training and testing phases. The empirical results show that transformations can improve the spread of feature values and the choice of the transformation methods is influential on the performance of the overall approach. A particular choice generates a slightly better performance when compared to the standard approach, which uses the original features at all times, indicating the potential of the proposed approach for the future studies.

Abstract This work tackles a rich vehicle routing problem (VRP) problem integrating a capacitated vehicle routing problem with time windows (CVRPTW), and a service technician routing and scheduling problem (STRSP) for delivering various equipment based on customers' requests, and the subsequent installation by a number of technicians. The main objective is to reduce the overall costs of hired resources, and the total transportation costs of trucks/technicians. The problem was the topic of the fourth edition of the VeRoLog Solver Challenge in cooperation with the ORTEC company. Our contribution to research is the development of a mathematical model for this problem and a novel hyper‐heuristic algorithm to solve the problem based on a population of solutions. Experimental results on two datasets of small and real‐world size revealed the success of the hyper‐heuristic approach in finding optimal solutions in a shorter computational time, when compared to our exact model. The results of the large size dataset were also compared to the results of the eight finalists in the competition and were found to be competitive, proving the potential of our developed hyper‐heuristic framework.

Hot spot identification problems are present across a wide range of areas, such as transportation, health care and energy. Hot spots are locations where a certain type of event occurs with high frequency. A recent big data approach is capable of identifying hot spots in a dynamic manner, through the processing of large volumes of sensor data arriving as a stream. However, the method may produce imprecise results due to its crisp interpretation of hot spot locations and reliance on a fixed hot spot radius value. This paper presents an initial approach to addressing this shortcoming through incorporating the concept of fuzzy hot spots into the process. Experimental results on large real-world transportation datasets demonstrate the improved way in which this approach handles uncertainty in the definition of hot spots, and highlight promising future research areas for further application of fuzzy systems to the hot spot identification problem.

Fuzzy systems mimic human reasoning and provide solutions to problems under uncertainty via `computing with words'. This particular strength of fuzzy systems is often discarded in some real world applications where the fuzzy sets are designed for control problems or created through training using historical data. This study explores the interpretability of fuzzy systems by generating `meaningful' fuzzy sets using a dictionary constructed by humans and fuzzy transfer learning. The inverted pendulum control problem is used as a case study. The empirical results show that intepretability of a fuzzy system is achievable even for this problem at the expense of a `slightly' reduced performance.

Metaheuristics, being tailored to each particular domain by experts, have been successfully applied to many computationally hard optimization problems. However, once implemented, their application to a new problem domain or a slight change in the problem description would often require additional expert intervention. There is a growing number of studies on reusable cross-domain search methodologies, such as selection hyper-heuristics, which are applicable to problem instances from various domains, requiring minimal expert intervention or even none. This paper introduces a new learning automata-based selection hyper-heuristic controlling a set of multiobjective metaheuristics. The approach operates above three well-known multiobjective evolutionary algorithms and mixes them, exploiting the strengths of each algorithm. The performance and behavior of two variants of the proposed selection hyper-heuristic, each utilizing a different initialization scheme are investigated across a range of unconstrained multiobjective mathematical benchmark functions from two different sets and the real-world problem of vehicle crashworthiness. The empirical results illustrate the effectiveness of our approach for cross-domain search, regardless of the initialization scheme, on those problems when compared to each individual multiobjective algorithm. Moreover, both variants perform significantly better than some previously proposed selection hyper-heuristics for multiobjective optimization, thus significantly enhancing the opportunities for improved multiobjective optimization.

Simulated Annealing is a well known local search metaheuristic used for solving computationally hard optimisation problems. Cross-domain search poses a higher level issue where a single solution method is used with minor, preferably no modification for solving characteristically different optimisation problems. The performance of a metaheuristic is often dependant on its initial parameter settings, hence detecting the best configuration, i.e. parameter tuning is crucial, which becomes a further challenge for cross-domain search. In this paper, we investigate the cross-domain search performance of Simulated Annealing via tuning for solving six problems, ranging from personnel scheduling to vehicle routing under a stochastic local search framework. The empirical results show that Simulated Annealing is extremely sensitive to the initial parameter settings leading to sub-standard performance when used as a single solution method for cross-domain search. Moreover, we demonstrate that cross-domain parameter tuning is inferior to domain-level tuning highlighting the requirements for adaptive parameter configurations when dealing with cross-domain search.

Multi-objective evolutionary algorithms (MOEAs) based on the concept of Pareto-dominance have been successfully applied to many real-world optimisation problems. Recently, research interest has shifted towards indicator-based methods to guide the search process towards a good set of trade-off solutions. One commonly used approach of this nature is the indicator-based evolutionary algorithm (IBEA). In this study, we highlight the solution distribution issues within IBEA and propose a modification of the original approach by embedding an additional Pareto-dominance based component for selection. The improved performance of the proposed modified IBEA (mIBEA) is empirically demonstrated on the well-known DTLZ set of benchmark functions. Our results show that mIBEA achieves comparable or better hypervolume indicator values and epsilon approximation values in the vast majority of our cases (13 out of 14 under the same default settings) on DTLZ1-7. The modification also results in an over 8-fold speed-up for larger populations.

A selection hyper-heuristic is a search method that controls a prefixed set of low-level heuristics for solving a given computationally difficult problem. This study investigates a learning-via demonstrations approach generating a selection hyper-heuristic for Open Vehicle Routing Problem (OVRP). As a chosen `expert' hyper-heuristic is run on a small set of training problem instances, data is collected to learn from the expert regarding how to decide which low-level heuristic to select and apply to the solution in hand during the search process. In this study, a Time Delay Neural Network (TDNN) is used to extract hidden patterns within the collected data in the form of a classifier, i.e an `apprentice' hyper-heuristic, which is then used to solve the `unseen' problem instances. Firstly, the parameters of TDNN are tuned using Taguchi orthogonal array as a design of experiments method. Then the influence of extending and enriching the information collected from the expert and fed into TDNN is explored on the behaviour of the generated apprentice hyper-heuristic. The empirical results show that the use of distance between solutions as an additional information collected from the expert generates an apprentice which outperforms the expert algorithm on a benchmark of OVRP instances.

Supplier selection and inventory planning are critical and challenging tasks in Supply Chain Management. There are many studies on both topics and many solution techniques have been proposed dealing with each problem separately. In this study, we present a two-stage integrated approach to the supplier selection and inventory planning. In the first stage, suppliers are ranked based on various criteria, including cost, delivery, service and product quality using Interval Type-2 Fuzzy Sets (IT2FS)s. In the following stage, an inventory model is created. Then, an Multi-objective Evolutionary Algorithm (MOEA) is utilised simultaneously minimising the conflicting objectives of supply chain operation cost and supplier risk. We evaluated the performance of three MOEAs with tuned parameter settings, namely NSGA-II, SPEA2 and IBEA on a total of twenty four synthetic and real world problem instances. The empirical results show that in the overall, NSGA-II is the best performing MOEA producing high quality trade-off solutions to the integrated problem of supplier selection and inventory planning.

Memetic algorithms, which hybridise evolutionary algorithms with local search, are well-known metaheuristics for solving combinatorial optimisation problems. A common issue with the application of a memetic algorithm is determining the best initial setting for the algorithmic parameters, but these can greatly influence its overall performance. Unlike traditional studies where parameters are tuned for a particular problem domain, in this study we do tuning that is applicable to cross-domain search. We extend previous work by tuning the parameters of a steady state memetic algorithm via a ‘design of experiments’ approach and provide surprising empirical results across nine problem domains, using a cross-domain heuristic search tool, namely HyFlex. The parameter tuning results show that tuning has value for cross-domain search. As a side gain, the results suggest that the crossover operators should not be used and, more interestingly, that single point based search should be preferred over a population based search, turning the overall approach into an iterated local search algorithm. The use of the improved parameter settings greatly enhanced the cross-domain performance of the algorithm, converting it from a poor performer in previous work to one of the stronger competitors.

There is a growing number of studies on general purpose metaheuristics that are directly applicable to multiple domains. Parameter setting is a particular issue considering that many of such search methods come with a set of parameters to be configured. Fuzzy logic has been used extensively in control applications and is known for its ability to handle uncertainty. In this study, we investigate the potential of using fuzzy systems to control the parameter settings of a threshold accepting (TA) metaheuristic for improving the overall effectiveness of a cross-domain approach. We have evaluated the performance of various general purpose local search metaheuristics which mix multiple heuristics at random and apply the TA metaheuristic with fixed threshold, crisp (non-fuzzy) rule-based control of the threshold and various fuzzy systems controlling the threshold. The empirical results show that the approach using the TA with crisp rule-based control performs the best across six problem domains from a benchmark.

In this study we use Genetic Programming (GP) as an offline hyper-heuristic to evolve a mutation operator for Evolutionary Programming. This is done using the Gaussian and uniform distributions as the terminal set, and arithmetic operators as the function set. The mutation operators are automatically designed for a specific function class. The contribution of this paper is to show that a GP can not only automatically design a mutation operator for Evolutionary Programming (EP) on functions generated from a specific function class, but also can design more general mutation operators on functions generated from groups of function classes. In addition, the automatically designed mutation operators also show good performance on new functions generated from a specific function class or a group of function classes.

Hyper-heuristics are high-level methodologies for solving complex problems that operate on a search space of heuristics. In a selection hyper-heuristic framework, a heuristic is chosen from an existing set of low-level heuristics and applied to the current solution to produce a new solution at each point in the search. The use of crossover low-level heuristics is possible in an increasing number of general-purpose hyper-heuristic tools such as HyFlex and Hyperion. However, little work has been undertaken to assess how best to utilise it. Since a single-point search hyper-heuristic operates on a single candidate solution, and two candidate solutions are required for crossover, a mechanism is required to control the choice of the other solution. The frameworks we propose maintain a list of potential solutions for use in crossover. We investigate the use of such lists at two conceptual levels. First, crossover is controlled at the hyper-heuristic level where no problem-specific information is required. Second, it is controlled at the problem domain level where problem-specific information is used to produce good-quality solutions to use in crossover. A number of selection hyper-heuristics are compared using these frameworks over three benchmark libraries with varying properties for an NP-hard optimisation problem: the multidimensional 0-1 knapsack problem. It is shown that allowing crossover to be managed at the domain level outperforms managing crossover at the hyper-heuristic level in this problem domain.

Hyper-heuristics are search methodologies which operate at a higher level of abstraction than traditional search and optimisation techniques. Rather than operating on a search space of solutions directly, a hyper-heuristic searches a space of low-level heuristics or heuristic components. An iterative selection hyper-heuristic operates on a single solution, selecting and applying a low-level heuristic at each step before deciding whether to accept the resulting solution. Crossover low-level heuristics are often included in modern selection hyper-heuristic frameworks, however as they require multiple solutions to operate, a strategy is required to manage potential solutions to use as input. In this paper we investigate the use of crossover control schemes within two existing selection hyper-heuristics and observe the difference in performance when the method for managing potential solutions for crossover is modified. Firstly, we use the crossover control scheme of AdapHH, the winner of an international competition in heuristic search, in a Modified Choice Function - All Moves selection hyper-heuristic. Secondly, we replace the crossover control scheme within AdapHH with another method taken from the literature. We observe that the performance of selection hyper-heuristics using crossover lowlevel heuristics is not independent of the choice of strategy for managing input solutions to these operators.

Hyper-heuristics are a class of high-level search methodologies which operate on a search space of low-level heuristics or components, rather than on solutions directly. Traditional iterative selection hyper-heuristics rely on two key components, a heuristic selection method and a move acceptance criterion. Choice Function heuristic selection scores heuristics based on a combination of three measures, selecting the heuristic with the highest score. Modified Choice Function heuristic selection is a variant of the Choice Function which emphasises intensification over diversification within the heuristic search process. Previous work has shown that improved results are possible in some problem domains when using Modified Choice Function heuristic selection over the classic Choice Function, however in most of these cases crossover low-level heuristics (operators) are omitted. In this paper, we introduce crossover low-level heuristics into a Modified Choice Function selection hyper-heuristic and present results over six problem domains. It is observed that although on average there is an increase in performance when using crossover low-level heuristics, the benefit of using crossover can vary on a per-domain or per-instance basis.

Selection of an appropriate supplier is a crucial and challenging task in the effective management of a supply chain. Also, appropriate inventory management is critical to the success of a supply chain operation. In recent years, there has been a growing interest in the area of selection of an appropriate vendor and creating good inventory planning using supplier selection information. In this paper, we consider both of these tasks in a two-stage approach employing Interval Type-2 Fuzzy Sets (IT2FS) and Simulated Annealing (SA). In the first stage, the supplier selection problem is solved by using IT2FS for ranking the suppliers. We present an inventory model incorporating information from the first stage that captures the influence of supplier risk on the total cost of supply chain operation. In the second stage, SA is used for solving the inventory planning problem based on this model improving on both supply chain operation cost and supplier risk. In this study, we evaluated our approach using different scenarios and scalarisation techniques for SA to handle two objectives, simultaneously.

Mutation in a Genetic Algorithm is the key variation operator adjusting the genetic diversity in a population throughout the evolutionary process. Often, a fixed mutation probability is used to perturb the value of a gene. In this study, we describe a novel data science approach to adaptively generate the mutation probability for each locus. The trail of high quality candidate solutions obtained during the search process is represented as a 3rd order tensor. Factorizing that tensor captures the common pattern between those solutions, identifying the degree of mutation which is likely to yield improvement at each locus. An online bin packing problem is used as an initial case study to investigate the proposed approach for generating locus dependent mutation probabilities. The empirical results show that the tensor approach improves the performance of a standard Genetic Algorithm on almost all classes of instances, significantly.

doi:10.1093/comjnl/bxt130 Comp J 2014;57(3): 469–479 Descriptions of LLH3 and LLH9 are amended as follows: LLH3: Select largest sum(or close to largest) of row, column or diagonal and smallest sum (or close to smallest) of row, column or diagonal and swap the largest element from the first with smallest in the second. LLH9: Select the row with the largest sum(or close to largest) and another rowwith the lowest sum(or close to smallest) and swap each entry with a probability of 0.5. Then, do the same for columns. The authors apologise for this error.

A square matrix of distinct numbers in which every row, column and both diagonals have the same total is referred to as a magic square. Constructing a magic square of a given order is considered a difficult computational problem, particularly when additional constraints are imposed. Hyper-heuristics are emerging high-level search methodologies that explore the space of heuristics for solving a given problem. In this study, we present a range of effective selection hyper-heuristics mixing perturbative low-level heuristics for constructing the constrained version of magic squares. The results show that selection hyper-heuristics, even the non-learning ones deliver an outstanding performance, beating the best-known heuristic solution on average.

Variable ordering has been a recurrent topic of study in the field of constraint satisfaction because of its impact in the cost of the search. Various variable ordering heuristics have been proposed to help guiding the search under different situations. One important direction of the study about variable ordering is the use of distinct heuristics as the search progresses to reduce the cost of the search. Even though the idea of combining heuristics goes back to the 60's, only a few works that study which heuristics to use and how they interact with each other have been described. In this investigation, we analyse the interactions of four important variable ordering heuristics by combining them through hyper-heuristics that decide the heuristic to apply based on the depth of the nodes in the search tree. The paper does not include any specific model for generating such hyperheuristics; instead, it presents an analysis of the changes in the cost when different heuristics are applied during the search by using one simple hyper-heuristic representation. The results show that selectively applying distinct heuristics as the search progresses may lead to important reductions in the cost of the search with respect to the performance of the same heuristics used in isolation.

There is a growing body of work in the field of hyper-heuristics. Hyper-heuristics are high level search methodologies that operate on the space of heuristics to solve hard computational problems. A frequently used hyper-heuristic framework mixes a predefined set of low level heuristics during the search process. While most of the work on such selection hyper-heuristics in the literature are empirical, we analyse the runtime of hyper-heuristics rigorously. Our initial analysis shows that mixing heuristics could lead to exponentially faster search than individual (deterministically chosen) heuristics on chosen problems. Both mixing of variation operators and mixing of acceptance criteria are investigated on some selected problems. It is shown that mixing operators is only efficient with the right mixing distribution (parameter setting). Additionally, some of the existing adaptation mechanisms for mixing operators are also evaluated.

Hyper-heuristics enable us to selectively apply the most suitable low-level heuristic depending on the properties of the problem at hand. They can be used for solving Constraint Satisfaction Problems (CSP) in different ways considering the variety of hyper-heuristics and low-level heuristics. A particular approach which has been receiving attention in the recent years is based on variable ordering using hyper-heuristics. A hyper-heuristic decides the next variable to process using a set of predefined heuristics considering the features that describe the instance at a given point during the search in this framework. This study explores an approach in which each hyper-heuristic is represented as a set of vectors mapping instance features to heuristics for variable ordering. The results suggest that the proposed approach is able to combine the strengths of different heuristics and compensate for their weaknesses performing better than each heuristic in isolation across a range of instances.

Online bin-packing is a well-known problem in which immediate decisions must be made about the placement of items with various sizes into fixed capacity bins. The associated decisions can be based on an index policy in which each decision option is independently given a value and the highest value choice is selected. In this paper, we represent such heuristics for online bin packing as a simple matrix of scores. We then use a genetic algorithm to search for matrices giving good performance. This might be regarded as parameter tuning of the packing heuristic but in which a fine-grained representation is used and so the number of parameters is much larger than in standard parameter tuning. The evolved matrices perform better than the standard heuristics. They also reveal interesting structures and so have impact on questions of how heuristic score functions should be represented and what structure they might be expected to exhibit.

Hyper-heuristics are high level search methodologies that operate over a set of heuristics which operate directly on the problem domain. In one of the hyper-heuristic frameworks, the goal is automating the process of selecting a human-designed low level heuristic at each step to construct a solution for a given problem. Constraint Satisfaction Problems (CSP) are well know NP complete problems. In this study, behaviours of two variable ordering heuristics Max-Conflicts (MXC) and Saturation Degree (SD) with respect to various combinations of constraint density and tightness values are investigated in depth over a set of random CSP instances. The empirical results show that the performance of these two heuristics are somewhat complementary and they vary for changing constraint density and tightness value pairs. The outcome is used to design three hyper-heuristics using MXC and SD as low level heuristics to construct a solution for unseen CSP instances. It has been observed that these hyper-heuristics improve the performance of individual low level heuristics even further in terms of mean consistency checks for some CSP instances.

A hyperheuristic is a high level problem solving methodology that performs a search over the space generated by a set of low level heuristics. One of the hyperheuristic frameworks is based on a single point search containing two main stages: heuristic selection and move acceptance. Most of the existing move acceptance methods compare a new solution, generated after applying a heuristic, against a current solution in order to decide whether to reject it or replace the current one. Late acceptance strategy is presented as a promising local search methodology based on a novel move acceptance mechanism. This method performs a comparison between the new candidate solution and a previous solution that is generated L steps earlier. In this study, the performance of a set of hyper-heuristics utilising different heuristic selection methods combined with the late acceptance strategy are investigated over an examination timetabling problem. The results illustrate the potential of this approach as a hyperheuristic component. The hyper-heuristic formed by combining a random heuristic selection with late acceptance strategy improves on the best results obtained in a previous study.

Timetabling problems are constraint optimization problems proven to be NP-complete. Furthermore, evaluation of violations is costly, and there is no common data format for representing timetabling problem instances. In this paper, a framework for designing memetic algorithms (MAs) to solve timetabling problems is described and a tool, named final exam scheduler (FES) is introduced. FES is the first tool that accepts timetabling markup language (TTML) documents as input. It utilizes an MA with an adaptive violation directed hierarchical hill climbing method for solving examination timetabling problem instances. Experimental results on a set of benchmark data indicate the success of MA.

Determining the optimum data distribution, degree of parallelism and the communication structure on distributed memory machines for a given algorithm is not a straightforward task. Assuming that a parallel algorithm consists of consecutive stages, a genetic algorithm is proposed to find the best number of processors and the best data distribution method to be used for each stage of the parallel algorithm. Steady state genetic algorithm is compared with transgenerational genetic algorithm using different crossover operators. Performance is evaluated in terms of the total execution time of the program including communication and computation times. A computation intensive, a communication intensive and a mixed implementation are utilized in the experiments. The performance of GA provides satisfactory results for these illustrative examples.

Course timetabling problems are real world constraint optimization problems that are often coped with educational institutions, such as universities or high schools. In this paper, we present a variety of new operators that can be also applied in evolutionary algorithms for other timetabling problems, such as, exam timetabling. Operators include violation directed mutations, crossovers, and a successful violation directed hierarchical hill climbing method. Tests are performed on a small portion of a real data and results are promising.

A new optimization method has been proposed by J. Kennedy and R.C. Eberhart (1997; 1995), called Particle Swarm Optimization (PSO). This approach combines social psychology principles and evolutionary computation. It has been applied successfully to nonlinear function optimization and neural network training. Preliminary formal analyses showed that a particle in a simple one-dimensional PSO system follows a path defined by a sinusoidal wave, randomly deciding on both its amplitude and frequency (Y. Shi and R. Eberhart, 1998). The paper takes the next step, generalizing to obtain closed form equations for trajectories of particles in a multi-dimensional search space.

Shape recognition is a challenging task when images contain overlapping, noisy, occluded, partial shapes. This paper addresses the task of matching input shapes with model shapes described in terms of features such as line segments and angles. The quality of matching is gauged using a measure derived from attributed shape grammars. We apply genetic algorithms to the partial shape-matching task. Preliminary results, using model shapes with 6 to 70 features each, are extremely encouraging.