A dual-population differential evolution with coevolution for constrained optimization

Mission Planning for Energy-Efficient Passive UAV Radar Imaging System Based on Substage Division Collaborative Search

In our earlier study, an energy-efficient passive UAV radar imaging system was formulated, which comprehensively analyzed the system performance. In this article, based on the evaluator set, a mission planning framework for the underlying energy-efficient passive UAV radar imaging system is proposed to achieve optimized mission performance for a given remote sensing task. First, the mission planning problem is defined in the context of the proposed synthetic aperture radar (SAR) system and a general framework is outlined, including mission specification, illuminator selection, and path planning. It is found that the performance of the system is highly dependent upon the flight path adopted by the UAV platform in a 3-D terrain environment, which offers the potential of optimizing the mission performance by adjusting the UAV path. Then, the path planning problem is modeled as a single-objective optimization problem with multiple constraints. Path planning can be divided into two substages based on different mission orientations and low mutual correlation. Based on this property, a path planning method, called substage division collaborative search (Sub-DiCoS), is proposed. The problem is divided into two subproblems with the corresponding decision space and subpopulation, which significantly relax the constraints for each subproblem and facilitates the search for feasible solutions. Then, differential evolution and the whole-stage best guidance technique are devised to cooperatively lead the subpopulations to search for the best solution. Finally, simulations are presented to demonstrate the effectiveness of the proposed Sub-DiCoS method. The result of the mission planning method can be used to guide the UAV platform to safely travel through a 3-D rough terrain in an energy-efficient manner and achieve optimized SAR imaging and communication performance during the flight.

Balancing Objective Optimization and Constraint Satisfaction in Constrained Evolutionary Multiobjective Optimization

Both objective optimization and constraint satisfaction are crucial for solving constrained multiobjective optimization problems, but the existing evolutionary algorithms encounter difficulties in striking a good balance between them when tackling complex feasible regions. To address this issue, this article proposes a two-stage evolutionary algorithm, which adjusts the fitness evaluation strategies during the evolutionary process to adaptively balance objective optimization and constraint satisfaction. The proposed algorithm can switch between the two stages according to the status of the current population, enabling the population to cross the infeasible region and reach the feasible regions in one stage, and to spread along the feasible boundaries in the other stage. Experimental studies on four benchmark suites and three real-world applications demonstrate the superiority of the proposed algorithm over the state-of-the-art algorithms, especially on problems with complex feasible regions.

Evolutionary Optimization Under Uncertainty: The Strategies to Handle Varied Constraints for Fluid Catalytic Cracking Operation

This article studies an operational optimization problem of the fluid catalytic cracking (FCC) unit under uncertainty. The objective of this problem is to quickly reoptimize the operating variables that control the operational condition of the FCC unit when fossil fuel yield constraints or prices change. To solve this problem, based on the challenges caused by the varied constraints, we establish a mathematical model and propose a fast adaptive differential evolution algorithm with an adaptive mutation strategy, a parameter adaptation strategy, a repaired strategy, and an enhanced strategy. In the proposed algorithm, we integrate the status information of each solution into the mutation strategy and parameter adaptation scheme to search for the best solution in the irregular feasible region of the operating variables. In addition, a repaired strategy is proposed to repair the infeasible operating variables with unknown bounds, and an enhanced strategy is presented to further improve the objective function value of the best solution. The experimental results on ten test scenarios with different fossil fuel yield constraints and prices demonstrate the robustness of the proposed algorithm for optimizing the operating variables of the FCC unit under uncertainty.

Solving knapsack problems using a binary gaining sharing knowledge-based optimization algorithm

This article proposes a novel binary version of recently developed Gaining Sharing knowledge-based optimization algorithm (GSK) to solve binary optimization problems. GSK algorithm is based on the concept of how humans acquire and share knowledge during their life span. A binary version of GSK named novel binary Gaining Sharing knowledge-based optimization algorithm (NBGSK) depends on mainly two binary stages: binary junior gaining sharing stage and binary senior gaining sharing stage with knowledge factor 1. These two stages enable NBGSK for exploring and exploitation of the search space efficiently and effectively to solve problems in binary space. Moreover, to enhance the performance of NBGSK and prevent the solutions from trapping into local optima, NBGSK with population size reduction (PR-NBGSK) is introduced. It decreases the population size gradually with a linear function. The proposed NBGSK and PR-NBGSK applied to set of knapsack instances with small and large dimensions, which shows that NBGSK and PR-NBGSK are more efficient and effective in terms of convergence, robustness, and accuracy.

Dual-Subpopulation as reciprocal optional external archives for differential evolution

Differential Evolution (DE) is powerful for global optimization problems. Among DE algorithms, JADE and its variants, whose mutation strategy is DE/current-to-pbest/1 with optional archive, have good performance. A significant feature of the above mutation strategy is that one individual for difference operation comes from the union of the optional external archive and the population. In existing DE algorithms based on the mutation strategy—JADE and its variants, individuals eliminated from the population are send to the archive. In this paper, we propose a scheme for managing the optional external archive. According to our scheme, two subpopulations are maintained in the population. Each of them regards the other as the archive. In experiments, our scheme is applied in JADE and two of its variants—SHADE and L-SHADE. Experimental results show that our scheme can enhance JADE and its variants. Moreover, it can be seen that L-SHADE with our scheme performs significantly better than four DE algorithms, CoBiDE, MPEDE, EDEV, and MLCCDE.

Cooperative Differential Evolution Framework for Constrained Multiobjective Optimization

This paper presents a cooperative differential evolution framework (CCMODE) for constrained multiobjective optimization, and two instantiations of the CCMODE framework are implemented. The proposed framework has (M+1) populations, including M subpopulations for constrained single-objective optimization and an archive population for constrained M -objective optimization. Each subpopulation performs its own constrained single-objective differential evolution to optimize the assigned constrained single-objective optimization problem. For the archive population, the constraint handling techniques (CHTs) are modified for constrained multiobjective optimization. The proposed framework takes the advantage of existing effective constrained single-objective optimization algorithms, and extends them to deal with constrained multiobjective optimization problems. In two instantiations, two CHTs are implemented in CCMODE framework, respectively. Experiment results on several sets of benchmark problems with two, three, and many objectives show that the proposed algorithm is better than existing state-of-the-art constrained multiobjective evolutionary algorithms. The effectiveness of the subpopulations is also discussed.

Improving Metaheuristic Algorithms With Information Feedback Models

In most metaheuristic algorithms, the updating process fails to make use of information available from individuals in previous iterations. If this useful information could be exploited fully and used in the later optimization process, the quality of the succeeding solutions would be improved significantly. This paper presents our method for reusing the valuable information available from previous individuals to guide later search. In our approach, previous useful information was fed back to the updating process. We proposed six information feedback models. In these models, individuals from previous iterations were selected in either a fixed or random manner. Their useful information was incorporated into the updating process. Accordingly, an individual at the current iteration was updated based on the basic algorithm plus some selected previous individuals by using a simple fitness weighting method. By incorporating six different information feedback models into ten metaheuristic algorithms, this approach provided a number of variants of the basic algorithms. We demonstrated experimentally that the variants outperformed the basic algorithms significantly on 14 standard test functions and 10 CEC 2011 real world problems, thereby, establishing the value of the information feedback models.

A New Differential Evolution Algorithm for Minimax Optimization in Robust Design

Minimax optimization, which is actively involved in numerous robust design problems, aims at pursuing the solutions with best worst-case performances. Although considerable research has been devoted to the development of minimax optimization algorithms, there still exist several fundamental limitations for existing approaches, e.g., restriction on problem types, excessively high computational cost, and low optimization efficiency. To address these issues, a minimax differential evolution algorithm is proposed in this paper. First, a novel bottom-boosting scheme enables the algorithm to identify the promising solutions in a reliable yet efficient manner. After that, a partial-regeneration strategy together with a new mutation operator contribute to an in-depth exploration over solution space. Finally, a proper integration of these newly proposed mechanisms leads to an algorithmic structure that can appropriately handle various types of problems. Empirical comparison with seven famous methods demonstrates the statistical superiority of the proposed algorithm. Successful applications in two open problems of robust design further validate the effectiveness of the new approach.

A Scalable Approach to Capacitated Arc Routing Problems Based on Hierarchical Decomposition

The capacitated arc routing problem (CARP) is a challenging optimization problem with lots of applications in the real world. Numerous approaches have been proposed to tackle this problem. Most of these methods, albeit showing good performance on CARP instances of small and median sizes, do not scale well to large-scale CARPs, e.g., taking at least a few hours to achieve a satisfactory solution on a CARP instance with thousands of tasks. In this paper, an efficient and scalable approach is proposed for CARPs. The key idea of the proposed approach is to hierarchically decompose the tasks involved in a CARP instance into subgroups and solve the induced subproblems recursively. The output of the subproblems at the lower layer in the hierarchy is treated as virtual tasks and new subproblems are formulated based on these virtual tasks using clustering techniques. By this means, the number of tasks (or virtual tasks) decreases rapidly from the bottom to the top layers of the hierarchy, and the sizes of all subproblems at each layer can be kept tractable even for very large-scale CARPs. Empirical studies are conducted on CARP instances with up to 3584 tasks, which are an order of magnitude larger than the number of tasks involved in all CARP instances investigated in the literature. The results show that the proposed approach significantly outperforms existing methods in terms of scalability. Since the proposed hierarchical decomposition scheme is designed to obtain a good permutation of tasks in a CARP instance, it may also be generalized to other hard optimization problems that can be formulated as permutation-based optimization problems.

A General Framework of Dynamic Constrained Multiobjective Evolutionary Algorithms for Constrained Optimization

A novel multiobjective technique is proposed for solving constrained optimization problems (COPs) in this paper. The method highlights three different perspectives: 1) a COP is converted into an equivalent dynamic constrained multiobjective optimization problem (DCMOP) with three objectives: a) the original objective; b) a constraint-violation objective; and c) a niche-count objective; 2) a method of gradually reducing the constraint boundary aims to handle the constraint difficulty; and 3) a method of gradually reducing the niche size aims to handle the multimodal difficulty. A general framework of the design of dynamic constrained multiobjective evolutionary algorithms is proposed for solving DCMOPs. Three popular types of multiobjective evolutionary algorithms, i.e., Pareto ranking-based, decomposition-based, and hype-volume indicator-based, are employed to instantiate the framework. The three instantiations are tested on two benchmark suites. Experimental results show that they perform better than or competitive to a set of state-of-the-art constraint optimizers, especially on problems with a large number of dimensions.

Adaptive Differential Evolution With Sorting Crossover Rate for Continuous Optimization Problems

Differential evolution (DE) is one of the best evolutionary algorithms (EAs). The effort of improving its performance has received great research attentions, such as adaptive DE (JADE). Based on the analysis on the aspects that may improve the performance of JADE, we introduce a modified JADE version with sorting crossover rate (CR). In JADE, CR values are generated based on mean value and Gaussian distribution. In the proposed algorithm, a smaller CR value is assigned to individual with better fitness value. Therefore, the components of the individuals, which have better fitness values, can appear in the offspring with higher possibility. In addition, the better offspring generated from last iteration are supposed to have better schemes, hence these schemes are preserved in next offspring generation procedure. This modified version is called as JADE algorithm with sorting CR (JADE_sort). The experiments results with several excellent algorithms show the effectiveness of JADE_sort.

Multiple Exponential Recombination for Differential Evolution

Differential evolution (DE) is a popular population-based metaheuristic approach for solving numerical optimization problems. In recent years, considerable research has been devoted to the development of new mutation strategies and parameter adaptation mechanisms. However, as one of the basic algorithmic components of DE, the crossover operation has not been sufficiently examined in existing works. Most of the main DE variants solely employ traditional binomial recombination, which has intrinsic limitations in handling dependent subsets of variables. To fill this research niche, we propose a multiple exponential recombination that inherits all the main advantages of existing crossover operators while possessing a stronger ability in managing dependent variables. Multiple segments of the involved solutions will be exchanged during the proposed operator. The properties of the new scheme are examined both theoretically and empirically. Experimental results demonstrate the robustness of the proposed operator in solving problems with unknown variable interrelations.