Trial vector generation strategies and control parameters have a significant influence on the performance of differential evolution (DE). This paper studies whether the performance of DE can be improved by combining several effective trial vector generation strategies with some suitable control parameter settings. A novel method, called composite DE (CoDE), has been proposed in this paper. This method uses three trial vector generation strategies and three control parameter settings. It randomly combines them to generate trial vectors. CoDE has been tested on all the CEC2005 contest test instances. Experimental results show that CoDE is very competitive.

Constrained multiobjective optimization problems (CMOPs) are frequently encountered in real-world applications, which usually involve constraints in both the decision and objective spaces. However, current artificial CMOPs never consider constraints in the decision space (i.e., decision constraints) and constraints in the objective space (i.e., objective constraints) at the same time. As a result, they have a limited capability to simulate practical scenes. To remedy this issue, a set of CMOPs, named DOC, is constructed in this paper. It is the first attempt to consider both the decision and objective constraints simultaneously in the design of artificial CMOPs. Specifically, in DOC, various decision constraints (e.g., inequality constraints, equality constraints, linear constraints, and nonlinear constraints) are collected from real-world applications, thus making the feasible region in the decision space have different properties (e.g., nonlinear, extremely small, and multimodal). On the other hand, some simple and controllable objective constraints are devised to reduce the feasible region in the objective space and to make the Pareto front have diverse characteristics (e.g., continuous, discrete, mixed, and degenerate). As a whole, DOC poses a great challenge for a constrained multiobjective evolutionary algorithm (CMOEA) to obtain a set of well-distributed and well-converged feasible solutions. In order to enhance current CMOEAs’ performance on DOC, a simple and efficient two-phase framework, named ToP, is proposed in this paper. In ToP, the first phase is implemented to find the promising feasible area by transforming a CMOP into a constrained single-objective optimization problem. Then in the second phase, a specific CMOEA is executed to obtain the final solutions. ToP is applied to four state-of-the-art CMOEAs, and the experimental results suggest that it is quite effective.

For solving constrained multiobjective optimization problems (CMOPs), many algorithms have been proposed in the evolutionary computation research community during the past two decades. Generally, the effectiveness of an algorithm for CMOPs is evaluated by artificial test problems. However, after a brief review of current artificial test problems, we have found that they are not well-designed and fail to reflect the characteristics of real-world applications (e.g., small feasibility ratio). Thus, in this paper, we firstly propose a new constraint construction method to facilitate the systematic design of test problems. Then, on the basis of this method, we design a new test suite consisting of 14 instances, which covers diverse characteristics extracted from real-world CMOPs and can be divided into four types. Considering that the comprehensive performance comparisons among constraint-handing techniques (CHTs) remain scarce, we choose several representative CHTs and compare their performance on our test suite. The performance comparisons identify the strengths and weaknesses of different CHTs on different types of CMOPs and provide guidelines on how to select/design a CHT in a specific scenario.

A considerable number of constrained optimization evolutionary algorithms (COEAs) have been proposed due to increasing interest in solving constrained optimization problems (COPs) by evolutionary algorithms (EAs). In this paper, we first review existing COEAs. Then, a novel EA for constrained optimization is presented. In the process of population evolution, our algorithm is based on multiobjective optimization techniques, i.e., an individual in the parent population may be replaced if it is dominated by a nondominated individual in the offspring population. In addition, three models of a population-based algorithm-generator and an infeasible solution archiving and replacement mechanism are introduced. Furthermore, the simplex crossover is used as a recombination operator to enrich the exploration and exploitation abilities of the approach proposed. The new approach is tested on 13 well-known benchmark functions, and the empirical evidence suggests that it is robust, efficient, and generic when handling linear/nonlinear equality/inequality constraints. Compared with some other state-of-the-art algorithms, our algorithm remarkably outperforms them in terms of the best, mean, and worst objective function values and the standard deviations. It is noteworthy that our algorithm does not require the transformation of equality constraints into inequality constraints