Solving constrained multi-objective optimization problems (CMOPs) with various features and challenges via evolutionary algorithms is very popular. Existing methods usually adopt an additional helper problem to simplify and solve them by divide-and-conquer. This paper proposes a new multitasking framework for CMOPs, borrowing the idea of evolutionary multitasking optimization. The main contributions are i) a multitasking framework is proposed, where a CMOP is modeled as a multitasking optimization problem with three tasks. Then, it is solved by constraint-first, constraint-ignored, and constraint-relaxed multi-objective evolutionary algorithms; ii) a knowledge expression and a transfer strategy are devised to transfer the knowledge among the tasks; and iii) based on the proposed framework, a new two-stage algorithm is presented to solve CMOPs. The effectiveness of our approach is validated through experiments on four CMOP benchmark suites and 19 real-world CMOPs.

Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention. Various constrained multi-objective optimization evolutionary algorithms (CMOEAs) have been developed with the use of different algorithmic strategies, evolutionary operators, and constraint-handling techniques. The performance of CMOEAs may be heavily dependent on the operators used, however, it is usually difficult to select suitable operators for the problem at hand. Hence, improving operator selection is promising and necessary for CMOEAs. This work proposes an online operator selection framework assisted by Deep Reinforcement Learning. The dynamics of the population, including convergence, diversity, and feasibility, are regarded as the state; the candidate operators are considered as actions; and the improvement of the population state is treated as the reward. By using a Q-network to learn a policy to estimate the Q-values of all actions, the proposed approach can adaptively select an operator that maximizes the improvement of the population according to the current state and thereby improve the algorithmic performance. The framework is embedded into four popular CMOEAs and assessed on 42 benchmark problems. The experimental results reveal that the proposed Deep Reinforcement Learning-assisted operator selection significantly improves the performance of these CMOEAs and the resulting algorithm obtains better versatility compared to nine state-of-the-art CMOEAs.

Solving multi-objective optimization problems through meta-heuristic methods gets considerable attention. Based on the classical variation operators, several enhanced operators, as well as multi-objective optimization evolutionary algorithms, have been developed. Among these operators, the competitive swarm optimizer exhibits promising performance. However, it encounters difficulties when tackling constrained multi-objective optimization problems with large objective spaces or complex infeasible regions. In this paper, a competitive and cooperative swarm optimizer is proposed, which contains two particle update strategies: i) the competitive swarm optimizer provides faster convergence speed to accelerate the approximation of the Pareto front; and ii) the cooperative swarm optimizer suggests a mutual-learning strategy to enhance the ability to jump out of local feasible regions or local optima. We also present a new algorithm for constrained multi-objective optimization problems. The results on four benchmark suites with 47 instances demonstrate the superiority of our approach compared with other state-of-the-art methods. Additionally, its effectiveness on large scale constrained multi-objective optimization problems has also been verified.

Solving multimodal multi-objective optimization problems (MMOPs) via evolutionary algorithms receives increasing attention recently. Maintaining good diversity in both decision and objective spaces is essential to handling MMOPs. Unfortunately, most of the existing methods prefer convergence in the objective space, resulting in the elimination of poorly converged solutions that may be helpful to improve the diversity in the decision space. To overcome this drawback, we propose a coevolutionary algorithm to balance the convergence and the diversity in both objective and decision spaces to better solve MMOPs. In the proposed method, a convergence-first population aims at pursuing a solution set well distributed on both the Pareto front and Pareto set assisted by a convergence-relaxed population. Further, a novel objective relaxation technique is developed for the convergence–relaxed population, which can supplement Pareto set segments not detected by the convergence-first population. Additionally, the environmental selections, mating selection, and fitness evaluation strategies are customized to bring about the balance of convergence and diversity in both objective and decision spaces. Experimental studies on four MMOP benchmarks demonstrated the superiority of the proposed algorithm over six state-of-the-art methods tailored for MMOPs.

Solving constrained multi-objective optimization problems (CMOPs) is one of the most popular research topics in the multi-objective optimization community. Various approaches based on different algorithmic strategies have been proposed for benchmark CMOPs with different features and challenges. Although most of these algorithms employ one or more fixed strategies, determining the most suitable strategy is challenging and problem-dependent. This work presents a general multitasking framework comprising a main task for the original CMOP and an arbitrary number of auxiliary tasks based on different strategies for the auxiliary problems. Reinforcement learning techniques are utilized according to the population state to choose the most suitable auxiliary task during the evolutionary process. As instantiations, Q-Learning and Deep Q-Learning are successfully applied in the framework. Accordingly, two novel algorithms are developed to solve CMOPs. The results demonstrate the effectiveness of the proposed approaches on five benchmark CMOP test suites and real-world problems compared to 11 advanced methods.