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The covariance matrix self-adaptation evolution strategy with repelling subpopulations (RS-CMSA-ES) is one of the most successful multimodal optimization 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 multimodal optimization 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 multimodal optimization in previous years. Besides, this study extends RS-CMSA-ESII to dynamic multimodal optimization and compares it with a few recently proposed methods on the modified moving peak benchmark functions.

Prediction methods are useful tools for dynamic multiobjective optimization (DMO), especially if the changes roughly follow some patterns. Multi-model prediction methods, in particular, may capture different types of change patterns; however, they should address two issues. First, they should define a similarity measure that can correctly find the corresponding Pareto-optimal solutions in two successive time steps. Second, they should be reasonably robust to input errors. This study introduces a new information-sharing strategy to improve the robustness of multi-model prediction methods in which each prediction model utilizes some information from the individual models of adjacent solutions. An adaptive scheme based on the relative distribution of population members is also proposed to utilize this information properly. The efficacy of this strategy in improving the robustness of the multi-model prediction method is demonstrated. Furthermore, this study introduces a similarity metric and thoroughly analyzes it alongside some of the commonly used similarity metrics for DMO. A weighted pointwise prediction method (WPPM) for DMO is then developed using the formulated information-sharing strategy and the proposed variable-based similarity metric. WPPM is compared with other well-known prediction methods on the CEC2018 test suite for DMO, with the numerical results revealing the superiority of WPPM.

Future Force Design (FFD) is a strategic planning activity that decides the programming of defence capability options. This is a complex problem faced by the Australian Department of Defence (DoD) and requires the simultaneous selection and scheduling of projects. Specifically, this is a NP-hard problem known as the Project Portfolio Selection and Scheduling Problem (PPSSP). While the PPSSP is a complex problem itself, its complexity is further increased when coupled with the additional characteristics that arise in the context of defence-oriented planning, such as long planning periods and complex operational constraints. As a result, many previous studies examined only a small number of projects over a short planning period and are largely unsuitable for the scale required in the defence sector. To address this issue, two primary contributions are made in this paper. Firstly, this study describes a complex practical PPSSP, inspired by the FFD process, and develops a corresponding mathematical model. Problem instances are derived from real-world, publicly-available defence data. Secondly, to address instances of the problem, two existing meta-heuristics are considered and a hybrid, multi-population approach is proposed. Results are compared against those attained by a commercial exact solver and indicate that there is no statistically significant difference in performance between the proposed multi-population approach and the exact solver. A key benefit of the proposed meta-heuristic approach is that its run time is not significantly influenced by the complexity of the problem instance. Additionally, many interesting practical insights regarding the solution of selection and scheduling problems are uncovered.

Finding the optimum solution for open-pit mine scheduling problems (OPMSPs) is a well-known challenging problem in the mining industry. The existing methodologies for solving large-scale OPMSPs are mostly limited to conventional optimization approaches and heuristics. However, due to the problem’s complexity, represented by high-dimensionality, and hard and soft constraints, the current approaches face challenges in finding good quality solutions with a reasonable computational cost. As an alternative approach, in this paper, we propose an evolutionary approach, based on differential evolution, with three important features: to deal with high-dimensionality, based on the extraction status of each block, we reduce the number of decision variables (blocks) over the planning horizon; to deal with the complex constrained landscape, we develop a repair mechanism that guarantees feasibility and to enhance the algorithm’s performance, we incorporate a local search technique. The experimental results on well-known mine deposits, with up to 112, 687 blocks show that the algorithm has the edge over existing methods to obtain better solutions.

In many real-world decision problems, there are specific objective, decision variables, conditions, data and/or parameters that may vary over time. When these problems are solved through an optimization process, they are generally known as dynamic optimization. Dynamic optimization is a challenging research topic as the optimal solution usually moves with any change in the problem environment. In locating the optimal point in any optimization problems, the effectiveness of the search process is influenced by the nature of the problem landscape. In order to improve the effectiveness of the search process, in this article, a new approach is developed by integrating a landscape-based strategy with appropriately designed evolutionary algorithms for solving dynamic problems. The proposed approach is named as Landscape Influenced Dynamic Optimization Algorithm (LIDOA). LIDOA checks the similarity before and after the changed environment which is then used as an input to guide the evolutionary search process. The dynamic benchmark functions from IEEE-CEC2009 are solved using LIDOA. LIDOA was able to enhance the performance of the evolutionary algorithms in their adaptation to dynamic changes, which in turn enhanced their ability to attain better results.

Sheepdogs smartly herd a flock of sheep and guide them towards a goal. A single dog can herd a few hundred sheep in easy to navigate environments. Understanding the interaction space between the sheepdogs, sheep and the environment is important due to the possibility of transferring this knowledge to solve practical swarm robotics problems. This interaction space is a complex mesh of influencing factors. We scrutinize this interaction space to identify areas where the complexity of the herding problem changes from low (easy to solve) to high (harder to solve or becoming unsolvable) complexity. In particular, we study reactive models for shepherding, whereby agents respond directly to stimuli in the environments by fusing the set of force vectors influencing their behaviour. We present an enhanced shepherding model with higher success rate than its predecessor. We investigate four key factors that influence the complexity of the problem: the relative speed between the sheepdog and sheep, the spatial configuration of the sheep at the start of the task, the number of sheepdogs, and the density of obstacles in the environment. We discovered a phase transition in shepherding resulting from the interaction between the number of sheepdogs and obstacles. The phase transition occurs as the density of obstacles range from 0.2% for a single shepherding agent to 5% for 10 shepherding agents. During this phase transition, the problem changes from being an easy problem where the flock gets collected quickly, to a hard one where the overall herding task becomes utterly not achievable using reactive approaches.

The solution of large-scale optimization problems is the key to many decision-making processes in practice. However, it is a challenging research topic when considered both the quality of solutions and the required computational time. One of the popular approaches for these problems is to divide the problems into a number of smaller sub-problems, that are then solved separately with an exchange of some information using the cooperative co-evolution (CC) concept. However, the characteristics of sub-components could be different, and their contributions to the overall performance can also be different while solving the problem. In the CC approach, it usually applies one optimizer and allocates equal computational budget to all sub-components. In this article, a new algorithm is proposed with the use of multiple optimizers, along with a need-based allocation of computational budget for the sub-components. In the proposed algorithm, a group of optimizers cooperate in an effective way to evolve the sub-components, depending on heuristic fuzzy rules. The performance of our proposed algorithm was evaluated by solving a number of large-scale global optimization benchmark functions. The empirical results show that the proposed algorithm outperforms equal allocation CC, a single selection characteristic, a single candidate optimizer and state-of-the-art algorithms.

The problem of designing an effective future defense force is quite complex and challenging. One methodology that is often employed in this domain is portfolio optimization, whereby the objective is to select a diverse set of assets that maximize the return on investment. In the defense context, the return on investment is often measured in terms of the capabilities that the investments will provide. While the field of portfolio optimization is well established, applications in the defense sector pose unique challenges not seen in other application domains. However, the literature regarding portfolio optimization for defense applications is rather sparse. To this end, this paper provides a structured review of recent applications and identifies a number of areas that warrant further investigation.

Although several multi-operator and multi-method approaches for solving optimization problems have been proposed, their performances are not consistent for a wide range of optimization problems. Also, the task of ensuring the appropriate selection of algorithms and operators may be inefficient since their designs are undertaken mainly through trial and error. This research proposes an improved optimization framework that uses the benefits of multiple algorithms, namely, a multi-operator differential evolution algorithm and a co-variance matrix adaptation evolution strategy. In the former, reinforcement learning is used to automatically choose the best differential evolution operator. To judge the performance of the proposed framework, three benchmark sets of bound-constrained optimization problems (73 problems) with 10, 30 and 50 dimensions are solved. Further, the proposed algorithm has been tested by solving optimization problems with 100 dimensions taken from CEC2014 and CEC2017 benchmark problems. A real-world application data set has also been solved. Several experiments are designed to analyze the effects of different components of the proposed framework, with the best variant compared with a number of state-of-the-art algorithms. The experimental results show that the proposed algorithm is able to outperform all the others considered.

Although multi-objective evolutionary subspace clustering approaches have shown promise in handling high-dimensional datasets, their performance is restricted by two main drawbacks. First, their local search strategies have not been well investigated. Second, while exploring the search space, they neglect the useful knowledge from previously solved problems. To tackle these issues, this paper proposes a transfer learning-assisted multi-objective evolutionary clustering framework with decomposition. Firstly, we provide a decomposition-based local search strategy. To capture a comprehensive data structure, this strategy updates the weights of features by considering both the within-class compactness and between-class separation, and spontaneously balances the two properties . Secondly, we develop a knowledge transfer strategy. By transferring search experience from a previously solved clustering problem , the strategy improves the search efficiency, consequently enhances the clustering accuracy of the current problem. It has a closed-form solution and can transfer knowledge across both homogeneous and heterogeneous problems from either different or the same domains. Finally, we conduct an extensive experimental study on the framework by comparing with six representative subspace clustering approaches on a wide range of benchmarks and real-world applications. Results demonstrate the superiority of our framework.

Many real-world decision problems consider more than one objective. These objectives usually conflict with each other. In the problem environments, many data and parameters are usually uncertain at the time of planning. So multi-objective optimization combined with uncertainty is a challenging research topic. To deal with the basic search process in such problems, in this paper, a new approach has been proposed that combines multiple population based algorithms under a single algorithm structure. To deal with the uncertainty, a dynamic scenario-based approach is developed and integrated with the search process, in which the number of scenarios is dynamically set during the solution process. This is a new way of solving multi-objective optimization problems under uncertainty. To judge the performance of the proposed approach, we have solved a set of standard test problems without uncertainty and a number of practical problems with uncertainty. The practical problems are the well-known dynamic economic and emission dispatch problems, with different combinations of energy sources. The experimental studies demonstrated that the proposed approach performs better than other well-known algorithms compared in this paper.

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.

The commonly used methodology for the simulation of dynamic problems formulates them as intervals of static problems, in which the change occurs between two successive intervals. This study proposes a more practically sound formulation of steadily changing dynamic problems, a class of dynamic problems in which the problem landscape continuously, but smoothly, changes over time. The new formulation provides more flexibility for a dynamic optimizer to choose the trade-off between the change frequency and the change severity while the change rate is prescribed by the actual problem. Besides, this study introduces a novel performance indicator for dynamic optimization methods. Unlike conventional ones, this indicator considers the real-time change in the actual problem during a time step and the period in which the best solution should be implemented. The practical importance of this formulation and the proposed performance indicator are studied on a few carefully designed controlled experiments. Subsequently, more comprehensive numerical simulations are performed to investigate the dependency of the optimal change frequency on the employed prediction method and test problem.

Given a set of candidate projects, selecting and scheduling an optimal subset of the projects is a complex problem faced by many organizations. This problem is referred to as the Project Portfolio Selection and Scheduling Problem (PPSSP) and is known to be NP-hard. In the defence sector, the PPSSP arises as a sub-process of Future Force Design (FFD), which is a strategic planning task that assists in the decision making process for future defence force capability programming. The PPSSP faced in the defence context has its own set of challenges above and beyond those typical of the problem. As such, this study investigates a formulation of the PPSSP inspired by the FFD process in the context of the Australian Department of Defence (DoD). Given the NP-hard nature of the problem, four metaheuristics are examined on large-scale synthetic data sets. Three different solution representations are examined and results are compared against solutions provided by a commercial exact solver. Results indicate that there is no observed significant difference in total portfolio value attained by the proposed meta-heuristic approaches and the commercial solver, thereby justifying their usage in this domain.

Shepherding involves herding a swarm of agents (\emph{sheep}) by another a control agent (\emph{sheepdog}) towards a goal. Multiple approaches have been documented in the literature to model this behaviour. In this paper, we present a modification to a well-known shepherding approach, and show, via simulation, that this modification improves shepherding efficacy. We then argue that given complexity arising from obstacles laden environments, path planning approaches could further enhance this model. To validate this hypothesis, we present a 2-stage evolutionary-based path planning algorithm for shepherding a swarm of agents in 2D environments. In the first stage, the algorithm attempts to find the best path for the sheepdog to move from its initial location to a strategic driving location behind the sheep. In the second stage, it calculates and optimises a path for the sheep. It does so by using \emph{way points} on that path as the sequential sub-goals for the sheepdog to aim towards. The proposed algorithm is evaluated in obstacle laden environments via simulation with further improvements achieved.

Shepherding is a biologically inspired swarm control methodology based on the herding of sheep by sheepdogs. The approach is applicable not only to sheep herding, but also to the guidance of one group of agents (eg.robots) by another. The pertinent research questions involve modeling the dynamics of the sheep and sheep-dog agent behaviours, in order to fully understand the sources of complexity in the problem and improve shepherding performance. To this end, we examine an existing model by Strombom et al. and present a preliminary study towards improving it.

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.

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

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.

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 real-life 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.

Large-scale optimization is the key to many practical decision processes. To deal with the dimensional issue in such problems, many approaches incorporate a divide-and-conquer strategy. Among them, cooperative coevolution approaches have recently gained popularity. Depending on the problem’s structure, the decomposition of any large problem, into a number of smaller sub-problems, may leave some variables common in more than one sub-problem. Such a decomposition may have a negative effect on the quality of the final solution of an optimization problem. In this paper, we have proposed an algorithm that incorporates a novel decomposition method, where the objective of decomposition is to minimize the number of common variables between sub-problems, achieved by exploiting a variable interaction matrix developed from the problem. So the algorithm works as a two-stage approach, where the first stage is the problem decomposition, and the second stage is to find the solutions of the problem. The performance of our proposed algorithm is assessed by solving different sets of large-scale non-separable benchmark functions with up to 2,905 variables. The experimental results provide important insights into the efficiency of the proposed decomposition method, which in turn improves the performance of the optimization process.

Storm-induced saltwater intrusion (SISWI) often starts with (i) overtopping/breaching of a coastal barrier followed by (ii) hinterland inundation and (iii) subsequent vertical seawater intrusion behind the barrier. Though these three processes are naturally successive, they are often analysed separately. However, the necessity of considering these processes as fully coupled has been increasingly recognised. This study, therefore, addresses the modelling of these processes in an integrated approach. The previous related studies are examined and four coupling scenarios are proposed. Thus, a new modelling scenario, utilising the model XBeach for simulating overtopping/breaching and subsequent flooding and SEAWAT for simulating the SISWI, is chosen for application to a case study in northern Germany. Moreover, the study addresses the mitigation of SISWI using a subsurface drainage network. The simulation results illustrate the high efficiency of such drainage in shortening the remediation time as well as in limiting salt intrusion to the deeper freshwater aquifers.

Resource-constrained project scheduling problems (RCPSPs) represent an important class of practical problems. Over the years, many optimization algorithms for solving them have been proposed, with their performances evaluated using well-established test instances with various levels of complexity. While it is desirable to obtain a high-quality solution and fast rate of convergence from an optimization algorithm, no single one performs well across the entire space of instances. Furthermore, even for a given algorithm, the optimal choice of its operators and control parameters may vary from one problem to another. To deal with this issue, we present a generic framework for solving RCPSPs in which various meta-heuristics, each with multiple search operators, are self-adaptively used during the search process and more emphasis is placed on the better-performing algorithms, and their underlying search operators. To further improve the rate of convergence and introduce good-quality solutions into the population earlier, a local search approach is introduced. The experimental results clearly indicate the capability of the proposed algorithm to attain high-quality results using a small population. Compared with several state-of-the-art algorithms, the proposed one delivers the best solutions for problems with 30 and 60 activities, and is very competitive for those involving 120 activities.

A large number of differential evolution algorithms has been proposed in recent years, many of which have been used to solve mainly unconstrained problems. However, similar to other evolutionary algorithms, their performances are highly dependent on their search operators and control parameters. Although many investigations have been conducted to ensure appropriate choices of these operators and parameters, the task is recognized as tedious. In this research, a differential evolution algorithm, which includes a new mechanism for automatically selecting the best combinations of parameters (amplification factor, crossover rate, and population size) as well as search operators, is developed. Instead of choosing discrete values for the amplification factor and crossover rate from a given set of values, this study adaptively selects them from some given continuous ranges and, furthermore, proposes a new methodology for handling constraints. 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.

Graphical abstractDisplay Omitted HighlightsProblem: Project portfolio optimization under multiple planning scenarios.Approach: Optimizing simulation using many objective optimization and Q-learning.Application: Defence capability project portfolio or program optimisation.Outcomes: Portfolio selection with minimum cost and risks across scenarios over time. Capability-based planning (CBP) is a strategy focused planning framework that facilitates organizations to systematically develop capacity to achieve their business objectives in highly uncertain, dynamic and competitive environments. Capability programming is an integral part of CBP which requires selecting a portfolio of capability projects for execution, referred as a capability program, such that the overall strategic risk facing the planning organization across a number of projected future operating scenarios is minimized while maintaining the most economical choice. It is a challenging optimization problem that requires handling a number of dynamic constraints and objectives that vary throughout the entire planning horizon. An optimizing simulation approach is presented in this paper that combines an evolutionary multi-objective optimization algorithm with a reinforcement learning technique to generate capability programs which optimize strategic risks and program costs across multiple planning scenarios as well as over a rolling planning horizon. The role of the optimization algorithm in this approach is to search for the non-dominated capability programs at each decision point by minimizing the strategic risks associated with individual capability projects across a number of planning scenarios as well as the total cost of the program. The reinforcement learning algorithm, on the other hand, searches horizontally within the set of non-dominated programs to minimize capability risks and costs over the entire planning horizon. The methodology is evaluated on a test problem generated based on the data distributions in an Australian Defence Capability Plan and the performance is compared with two myopic heuristic methods.

The reproduction of seventeen laboratory tests for dune erosion by the surf-beat mode of the two-dimensional horizontal (2DH) model XBeach for storm wave conditions showed that the model overestimates the erosion and thus the deposition volumes. This overestimation becomes particularly significant for very large overtopping rates on coastal barriers, which are commonly induced by extreme storm surges. In this paper, the recent model improvements to overcome this problem are first summarised. Moreover, two physical reasons for these overestimations are identified: (i) the wave nonlinearity effect on sediment transport, which is described in XBeach by a calibration factor for the time-averaged flow depending on the wave skewness and asymmetry and (ii) the considerable excess of the actual shear stress required to initiate the sediment particle motion as compared to that predicted by the common Shields curve. To improve the prediction capability of XBeach in terms of erosion and overwash volumes, two new improvements, related to the two aforementioned reasons for the overestimation, are introduced and implemented in the model. The improved XBeach model is then tested for dune erosion, for barrier breaching as well as for a barrier island erosion and overwash under an extreme storm surge event. The results showed a very good prediction capability of the improved model. Particularly, the second model improvement opens the way toward further model improvements to account for spatially varying soil resistance, which is crucial for reliable prediction of a barrier breaching.

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.

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.

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.

A reinitialization approach is an effective way of generalizing a static multi-objective optimization method to a dynamic one. It is usually comprised of a prediction operator for predicting the approximate location(s) of the optimal solution(s) and a variation operator for enhancing the diversity of the reinitialized solution(s) after a change. While many recent studies have focused on prediction methods, the importance of the variation operator has usually been overlooked. This study systematically explores the effects of the accuracy of the prediction method employed as well as the frequency and severity of the change on the optimal strength of the variation used for reinitialization. Subsequently, it introduces an adaptive variation operator for dynamic multi-objective optimization which can learn the optimal variation strength on-the-fly. To develop this method, firstly, a heredity measure for evolutionary algorithms is formulated to quantify the contribution of each reinitialized solution to the optimization process by measuring the presence of its traits in the final population. Some carefully designed descriptive simulations are performed to explore the capability of the proposed method to learn the optimal variation strength and its sensitivity to the change severity, initial variation strength, and accuracy of the employed prediction method. Finally, the performance of this variation operator on 42 dynamic multi-objective test problems is compared with those of five other popular ones, with numerical comparisons revealing its superior learning capability.

A competitive energy market with strategic consumers and suppliers is discussed.The game based bidding problem of a competitive energy market is formulated as a bi-level optimization problem.Two co-evolutionary solution approaches based on two evolutionary algorithms for the bidding problem are proposed.Three competitive and non-competitive energy markets with four different scenarios are solved.The performances of the proposed approaches are found superior to existing ones. Determining optimal bidding strategies in a competitive electricity market to maximize the profit of each bidder is a challenging economic game problem. In this paper, it is formulated as a bi-level optimization problem in which, in the lower level, the communitys social welfare is maximized by solving a power flow problem while, in the upper level, the profits of individual bidders are maximized. In this bidders game, instead of using a set of discrete strategies as is usual, we consider continuous functions as strategies. To solve the upper-level problem, two co-evolutionary approaches are proposed and, for the lower level, an interior point algorithm is applied. Three IEEE benchmark problems in four different scenarios are solved and their results compared with those obtained from two conventional approaches and the literature which indicate that the proposed approaches have some merit regarding quality and efficiency.

To achieve optimal generation from a number of mixed power plants by minimizing the operational cost while meeting the electricity demand is a challenging optimization problem. When the system involves uncertain renewable energy, the problem has become harder with its operated generators may suffer a technical problem of ramp-rate violations during the periodic implementation in subsequent days. In this paper, a scenario-based dynamic economic dispatch model is proposed for periodically implementing its resources on successive days with uncertain wind speed and load demand. A set of scenarios is generated based on realistic data to characterize the random nature of load demand and wind forecast errors. In order to solve the uncertain dispatch problems, a self-adaptive differential evolution and real-coded genetic algorithm with a new heuristic are proposed. The heuristic is used to enhance the convergence rate by ensuring feasible load allocations for a given hour under the uncertain behavior of wind speed and load demand. The proposed frameworks are successfully applied to two deterministic and uncertain DED benchmarks, and their simulation results are compared with each other and state-of-the-art algorithms which reveal that the proposed method has merit in terms of solution quality and reliability.

The dynamic economic dispatch problem is a high-dimensional complex constrained optimization problem that determines the optimal generation from a number of generating units by minimizing the fuel cost. Over the last few decades, a number of solution approaches, including evolutionary algorithms, have been developed to solve this problem. However, the performance of evolutionary algorithms is highly dependent on a number of factors, such as the control parameters, diversity of the population, and constraint-handling procedure used. In this paper, a self-adaptive differential evolution and a real-coded genetic algorithm are proposed to solve the dynamic dispatch problem. In the algorithm design, a new heuristic technique is introduced to guide infeasible solutions towards the feasible space. Moreover, a constraint-handling mechanism, a dynamic relaxation for equality constraints, and a diversity mechanism are applied to improve the performance of the algorithms. The effectiveness of the proposed approaches is demonstrated on a number of dynamic economic dispatch problems for a cycle of 24 h. Their simulation results are compared with each other and state-of-the-art algorithms, which reveals that the proposed method has merit in terms of solution quality and reliability.

In Resource Constrained Project Scheduling Problems (RCPSPs), it is usually assumed that the activity durations are known and integers. This assumption helps to conveniently develop a standard mathematical model, using discrete time steps. However, in reality, activity durations may not only be integer, and they may not be known with certainty at the time of project planning. The consideration of real-valued activity durations would increase the complexity in modelling of RCPSPs. In this paper, we consider that activity duration can be either integer or real-valued or both, and they are uncertain. To solve the optimization problem with uncertainty, scenario-based approaches are a popular choice. However, such a solution method is computationally very expensive. Therefore, in this research, we propose a simulation assisted evolutionary framework, that consists of two multi-operator based EAs and two heuristics to deal with the optimization process, and a simulation approach to deal with the uncertainty components. In the simulation, a range of problem instances is evaluated that are generated based on uncertain durations. The framework also proposes a new strategy to reduce the number of simulation runs. In the approach, the solution representation is different from the one required in the mathematical programming approach for RCPSP, and it does not require any discretization of the time periods. More than 1600 test problems, including some industrial problems, with up to 120 activities, have been solved using this proposed approach and the results have been compared with a set of state-of-the-art algorithms. The results obtained by the proposed approach were found to be of acceptable quality with a significant reduction of computational time.

The Multi-Mode Resource Constrained Project Scheduling Problem (MMRCPSP) is a challenging NP-hard optimization problem, that schedules activities under a set of resource constraints. Although, over the last few decades, different solution approaches have been proposed, no single algorithm has consistently been the best for a wide range of MMRCPSPs. In this paper, we have proposed an effective hybrid algorithm, in which two multi-operator evolutionary algorithms perform sequentially under two sub-populations, with their sizes dynamically adapted based on their performance during the evolutionary process. In addition, two heuristics are proposed, the first one is based on a linear programming approach with an aim to obtain feasible modes, while the second one is based on a modified forward and backward justification approach with an aim of obtaining feasible schedules. Also, a classification technique is used to determine the complexity of a given problem, based on its resource’s availability. The proposed approach is tested by solving a wide-range of multi-mode resource-constrained project scheduling problems, including available larger test problems, with the results revealing that the proposed method outperforms well-known algorithms.

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.

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.

During the last two decades, dealing with big data problems has become a major issue for many industries. Although, in recent years, differential evolution has been successful in solving many complex optimization problems, there has been research gaps on using it to solve big data problems. As a real-time big data problem may not be known in advance, determining the appropriate differential evolution operators and parameters to use is a combinatorial optimization problem. Therefore, in this paper, a general differential evolution framework is proposed, in which the most suitable differential evolution algorithm for a problem on hand is adaptively configured. A local search is also employed to increase the exploitation capability of the proposed algorithm. The algorithm is tested on the 2015 big data optimization competition problems (six single objective problems and six multi-objective problems). The results show the superiority of the proposed algorithm to several state-of-the-art algorithms.

In this paper, we introduce a mathematical framework that allows the designer to consider more of the proposed ideas and options in conceptual design phase into the design process. The proposed model allows for dynamical relationship between the system’s high-level requirements and the detailed design parameters, where an optimization engine can optimize over the design parameters and variables for a given range in the requirement. This is done by proposing an input/output block structure named recursive design modular (RDM). The output of RDM is the functions that the system supposes to perform at particular level. The input of RDM is the design parameters that control the required behaviour through a set of mapping or transformation.

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.

In this paper, a new differential evolution framework is proposed. In it, the best-performing differential evolution mutation strategy, from a given set, is dynamically determined based on a problem’s landscape, as well as the performance history of each operator. The performance of the proposed algorithm has been tested on a set of 30 unconstrained single objective real-parameter optimization problems. The experimental results show that the proposed algorithm is capable of producing good solutions that are clearly better than those obtained from a set of considered state-of-the-art algorithms.

In this paper, a traditional genetic algorithm with an integer representation is developed to search suitable variable arrangements for decomposition problems into a Cooperative-Coevolution framework for large-scale constrained optimization problems. The function evaluation is based on the Variable Interaction Identification for Constrained Optimization Problems (VIIC), that detects interactions among variables in large-scale problems. The new algorithm is capable of getting variable arrangements where the number of subgroups, as well as variables in each subgroup, are not fixed as in traditional decomposition methods. The proposed method is compared against VIIC with neighborhood strategy (VIICN). Those algorithms are tested on a novel benchmark for large scale constrained problems with 100, 500 and 1000 dimensions. The numerical results indicate that the proposed method outperforms VIICN, with the computational time is greatly reduced, which makes DVIIC a viable method for solving large-scale constrained optimization problems.

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.

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.

Scheduling of wind-thermal electrical generators is a challenging constrained optimization problem, where the main goal is to find the optimal allocation of output power among various available generators to serve the system load. Over the last few decades, a large number of solution approaches, including evolutionary algorithms, have been developed to solve this problem. However, these approaches are usually ineffective and time consuming. In this paper, we apply two variants of genetic algorithm GA for solving the problem where the first variant is to optimize the allocation and the second one is to rank the generators for allocation. The proposed algorithm is applied to a recent wind-thermal benchmark that comprises five thermal and 160 wind farms. The model includes a stochastic nature of wind energy and gas emission effects of thermal plants. The simulation results show that the proposed method is superior to those results of different variants of GA and the state-of-the-art algorithms.

The resource constrained project scheduling problem is considered as a complex scheduling problem. In order to solve this NP-hard problem, an efficient differential evolution DE algorithm is proposed in this paper. In the algorithm, improved mutation and crossover operators are introduced with an aim to maintain feasibility for generated individuals and hence being able to converge quickly to the optimal solutions. The algorithm is tested on a set of well-known project scheduling problem library PSPLIB, with instances of 30, 60, 90 and 120 activities. The proposed DE is shown to have superior performance in terms of lower average deviations from the optimal solutions compared to some of the state-of-the-art algorithms.

Differential evolution has shown success in solving different optimization problems. However, its performance depends on the control parameters and search operators. Different from existing approaches, in this paper, a new framework which dynamically configures the appropriate choices of operators and parameters is introduced, in which the success of a search operator is linked to the proper combination of control parameters scaling factor and crossover rate. Also, an adaptation of the population size is adopted. The performance of the proposed 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.

Breaching of coastal barriers is a three-dimensional process induced by complex interactions between hydrodynamics, sediment transport and soil avalanching processes. Although numerous coastal barriers are breached every year in many coastal countries, causing dramatic inundations of the nearshore areas, the understanding of the processes and interactions associated with both breaching and subsequent flood propagation is still poor. This might explain why their combined modelling and prediction has not yet been sufficiently addressed. Consequently, barrier breaching and subsequent inundation are still often modelled separately, thus ignoring the strong interaction between breaching and flooding. However, the combined modelling of such strongly coupled processes is crucial. Since the open-source model system “XBeach” consists, among others, of a nonlinear shallow water solver coupled with a morphodynamic model, also including a soil avalanching module, it has the potential to simulate both breaching and subsequent flood propagation together. Indeed, the mutual interactions between hydrodynamics and morphodynamics (including soil avalanching) are properly accounted for. This paper, therefore, aims to examine the applicability of XBeach for modelling coastal barrier breaching and inundation modelling in combination, instead of the current approaches, which address the modelling of each of these two processes separately. The performance of XBeach, in terms of inundation modelling, is assessed through comparisons of the results from this model system (i) with the results from common 1D and 2D flood propagation models and (ii) with observations for barrier breaching and subsequent inundation from a real case study. Besides providing an improved understanding of the breaching process, the results of this study demonstrate a new promising application of XBeach and its potential for calculating time-varying inland discharges, as well as for combined modelling of both dune breaching and subsequent flood propagation in coastal zones.