There are usually multiple constraints in constrained multi-objective optimization. Those constraints reduce the feasible area of the constrained multi-objective optimization problems (CMOPs) and make it difficult for current multi-objective optimization algorithms (CMOEAs) to obtain satisfactory feasible solutions. In order to solve this problem, this paper studies the relationship between constraints, then obtains the priority between constraints according to the relationship between the Pareto Front (PF) of the single constraint and their common PF. Meanwhile, this paper proposes a multi-stage CMOEA and applies this priority, which can save computing resources while helping the algorithm converge. The proposed algorithm completely abandons the feasibility in the early stage to better explore the objective space, and obtains the priority of constraints according to the relationship; Then the algorithm evaluates a single constraint in the medium stage to further explore the objective space according to this priority, and abandons the evaluation of some less-important constraints according to the relationship to save the evaluation times; At the end stage of the algorithm, the feasibility will be fully considered to improve the quality of the solutions obtained in the first two stages, and finally get the solutions with good convergence, feasibility, and diversity. The results on five CMOP suites and three real-world CMOPs show that the algorithm proposed in this paper can have strong competitiveness in existing constrained multi-objective optimization.

In science and engineering, multi-objective optimization problems usually contain multiple complex constraints, which poses a significant challenge in obtaining the optimal solution. This paper aims to solve the challenges brought by multiple complex constraints. First, this paper analyzes the relationship between single constrained Pareto Front (SCPF) and their common Pareto Front sub-constrained Pareto Front (SubCPF). Next, we discussed the SCPF, SubCPF, and Unconstrainti Pareto Front (UPF)’s help to solve constraining Pareto Front (CPF). Then further discusses what kind of cooperation should be used between multiple populations constrained multi-objective optimization algorithm (CMOEA) to better deal with multi-constrained multi-objective optimization problems (mCMOPs). At the same time, based on the discussion in this paper, we propose a new multi-population CMOEA called MCCMO, which uses a new cooperation mechanism. MCCMO uses C+2 (C is the number of constraints) populations to find the UPF, SCPF, and SubCPF at an appropriate time. Furthermore, MCCMO uses the newly proposed Activation Dormancy Detection (ADD) to accelerate the optimization process and uses the proposed Combine Occasion Detection (COD) to find the appropriate time to find the SubCPF. The performance on 32 mCMOPs and real-world mCMOPs shows that our algorithm can obtain competitive solutions on MOPs with multiple constraints.

In large-scale multiobjective optimization, too many decision variables hinder the convergence search of evolutionary algorithms. Reducing the search range of the decision space will significantly alleviate this puzzle. With this in mind, this paper proposes a fuzzy decision variables framework for large-scale multiobjective optimization. The framework divides the entire evolutionary process into two main stages: fuzzy evolution and precise evolution. In fuzzy evolution, we blur the decision variables of the original solution to reduce the search range of the evolutionary algorithm in the decision space so that the evolutionary population can quickly converge. The degree of fuzzification gradually decreases with the evolutionary process. Once the population approximately converges, the framework will turn to precise evolution. In precise evolution, the actual decision variables of the solution are directly optimized to increase the diversity of the population so as to be closer to the true Pareto optimal front. Finally, this paper embeds some representative algorithms into the proposed framework and verifies the framework’s effectiveness through comparative experiments on various large-scale multiobjective problems with 500 to 5000 decision variables. Experimental results show that in large-scale multiobjective optimization, the framework proposed in this paper can significantly improve the performance and computational efficiency of multiobjective optimization algorithms.

In this article, we propose an evolutionary algorithm based on layered prediction (LP) and subspace-based diversity maintenance (SDM) for handling dynamic multiobjective optimization (DMO) environments. The LP strategy takes into account different levels of progress by different individuals in evolution and historical information to predict the population in the event of environmental changes for a prompt change response. The SDM strategy identifies gaps in population distribution and employs a gap-filling technique to increase population diversity. SDM further guides rational population reproduction with a subspace-based probability model to maintain the balance between population diversity and convergence in every generation of evolution regardless of environmental changes. The proposed algorithm has been extensively studied through comparison with five state-of-the-art algorithms on a variety of test problems, demonstrating its effectiveness in dealing with DMO problems.