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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.

Recently the literature of Simulation Optimization for solving stochastic constrained optimization problems has been substantially increasing. From the optimization perspective, the population based meta-heuristics algorithms, such as Differential Evolutionary (DE), has shown tremendous success in solving continuous constrained optimization problems. While from the simulation and stochastic perspectives, Monte-Carlo Simulation alongside Chance Constrained Programming (CCP), is one of the most successful combined approaches to handle constraint uncertainty, also called chance constraints. Risk levels are used in CCP to bound the stochastic constraints infeasibility. However, the determination of the risk levels is not precise and is based on subjective personal judgments; due to the lack of a scientific approach to determine their values especially in critical problems that require the minimum possible risk levels. Furthermore, reliability in such problems is a vital requirement, especially for studies under worst-case scenarios. Therefore, we propose a novel approach, called Two-stage simulation assisted Differential Evolutionary for Chance constrained programming algorithm (Two-stage DE-CCP), with two major contributions. The first contribution aims to obtain minimum boundaries for the chance constrains’ risk levels, by utilizing the meta-heuristics DE implicit capabilities with a two stages modification. While the second contribution proposed as a Reliable Chance Constrained Programming (RCCP) with a novel scheme for chance constraints’ feasibility checking, that is called Extreme Scenario Feasibility Checking (ESFC). This name reveals that ESFC aims to obtain more reliable solutions, through comparing the extreme/worst-case scenarios of the chance constraints. The proposed algorithm is applied under normal CCP feasibility checking and ESFC for RCCP, while a comparison between them is performed and an empirical Reliability ratio (Rr) is proposed. The experimental results on benchmark problems and real application show that the proposed algorithm is able to provide decision makers with the minimum possible risk levels. While a substantially high Rr is obtained from the proposed RCCP, as compared to traditional CCP.

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 Vehicle Routing Problem (VRP) is a complex and high-level set of routing problems. One of its important variants is the Dynamic Vehicle Routing Problem (DVRP) in which not all customers are known in advance, but are revealed as the system progresses. DVRP is a Dynamic Optimization Problem (DOP) that has become a challenging research topic in the past two decades. In DOPs, at least one part of the problem changes as time passes. For DVRP, customers change as a system progresses. Consequently, DVRP applications are seen to operate on a dynamic basis in various real-life systems. To date, a time-based evaluation approach has been used to evaluate periodic re-optimized DVRP systems, which are evaluated by solving while using a specific time budget. In this paper, we solve DVRP while using an enhanced Genetic Algorithm (GA) that tries to increase both diversity and the capability to escape from local optima. Also, we propose a fair weighted fitness evaluation approach as an alternative for the biased time-based approach, regardless of the specifications and power of the running system. The proposed enhanced GA outperformed the previously published algorithms based on both the time-based and weighted fitness evaluation approaches.

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.

Graphical abstractDisplay Omitted HighlightsAn optimization algorithm is introduced based on a partial evaluation policy.The population are evaluated based on a random sequence of constraints.The search using multiple constraint sequences offers the potential to reach different regions of the search space. Differential evolution (DE) refers to a class of population based stochastic optimization algorithms. In order to solve practical problems involving constraints, such algorithms are typically coupled with a constraint handling scheme. Such constraints often emerge out of user requirements, physical laws, statutory requirements, resource limitations etc and are routinely evaluated using computationally expensive analysis i.e., solvers relying on finite element methods, computational fluid dynamics, computational electromagnetics etc. In this paper, we introduce a novel scheme of constraint handling, wherein every solution is assigned a random sequence of constraints and the evaluation process is aborted whenever a constraint is violated. The solutions are sorted based on two measures i.e., the number of satisfied constraints and the violation measure. The number of satisfied constraints takes precedence over the amount of violation. We illustrate the performance of the proposed scheme and compare it with other state of the art constraint handling methods using a common framework based on differential evolution. The results are compared using CEC-2006, CEC-2010 and CEC-2011 test functions with inequality constraints. The results clearly highlight two key aspects (a) the ability to identify feasible solutions earlier than other constraint handling schemes and (b) potential savings in computational cost offered by the proposed strategy.

Measure the performance of SAMO-GA on a diverse set of constrained problems.Extend the idea of training and testing with EAs for solving COPs.The mean square error measure is used to quantify the results.The results provide interesting insights and a new way of choosing parameters. Over the last two decades, many different evolutionary algorithms (EAs) have been introduced for solving constrained optimization problems (COPs). Due to the variability of the characteristics in different COPs, no single algorithm performs consistently over a range of practical problems. To design and refine an algorithm, numerous trial-and-error runs are often performed in order to choose a suitable search operator and the parameters. However, even by trial-and-error, one may not find an appropriate search operator and parameters. In this paper, we have applied the concept of training and testing with a self-adaptive multi-operator based evolutionary algorithm to find suitable parameters. The training and testing sets are decided based on the mathematical properties of 60 problems from two well-known specialized benchmark test sets. The experimental results provide interesting insights and a new way of choosing parameters.

The job scheduling problem (JSP) belongs to the well-known combinatorial optimization domain. After scheduling, if a machine maintenance issue affects the scheduled processing of jobs, the delivery of jobs must be delayed. In this paper, we have first proposed a Hybrid Evolutionary Algorithm (HyEA) for solving JSPs. We have then analyzed the effect of machine maintenance, whether preventive or breakdown, on the job scheduling. For the breakdown maintenance case, it is required to revise the algorithm to incorporate a rescheduling option after the breakdown occurs. The algorithm has been tested by solving a number of benchmark problems and thence comparing them with the existing algorithms. The experimental results provide a better understanding of job scheduling and the necessary rescheduling operations under process interruption.

Over the last few decades, many different evolutionary algorithms have been introduced for solving constrained optimization problems. However, due to the variability of problem characteristics, no single algorithm performs consistently over a range of problems. In this paper, instead of introducing another such algorithm, we propose an evolutionary framework that utilizes existing knowledge to make logical changes for better performance. The algorithmic aspects considered here are: the way of using search operators, dealing with feasibility, setting parameters, and refining solutions. The combined impact of such modifications is significant as has been shown by solving two sets of test problems: (i) a set of 24 test problems that were used for the CEC2006 constrained optimization competition and (ii) a second set of 36 test instances introduced for the CEC2010 constrained optimization competition. The results demonstrate that the proposed algorithm shows better performance in comparison to the state-of-the-art algorithms.