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There are a lot of multi-objective optimization problems (MOPs) in the real world, and many multi-objective evolutionary algorithms (MOEAs) have been presented to solve MOPs. However, obtaining non-dominated solutions that trade off convergence and diversity remains a major challenge for a MOEA. To solve this problem, this paper designs an efficient multi-objective sine cosine algorithm based on a competitive mechanism (CMOSCA). In the CMOSCA, the ranking relies on non-dominated sorting, and the crowding distance rank is utilized to choose the outstanding agents, which are employed to guide the evolution of the SCA. Furthermore, a competitive mechanism stemming from the shift-based density estimation approach is adopted to devise a new position updating operator for creating offspring agents. In each competition, two agents are randomly selected from the outstanding agents, and the winner of the competition is integrated into the position update scheme of the SCA. The performance of our proposed CMOSCA was first verified on three benchmark suites (i.e., DTLZ, WFG, and ZDT) with diversity characteristics and compared with several MOEAs. The experimental results indicated that the CMOSCA can obtain a Pareto-optimal front with better convergence and diversity. Finally, the CMOSCA was applied to deal with several engineering design problems taken from the literature, and the statistical results demonstrated that the CMOSCA is an efficient and effective approach for engineering design problems. [ABSTRACT FROM AUTHOR]

This article introduces an efficient surrogate-assisted bi-swarm evolutionary algorithm (SABEA) with hybrid and ensemble strategies for computationally expensive optimization problems. In SABEA, the evolutionary swarm is randomly partitioned into two sub-swarms to maintain diversity of the population. One sub-swarm evolves using the differential evolution (DE) and the other one evolves using teaching-learning-based optimization (TLBO). The proposed SABEA has strong exploration and exploitation capabilities by taking advantages of these two powerful algorithms. Besides, both the global and the local surrogate models cooperate effectively in the proposed SABEA for estimating the fitness value. The global model is established with all samples in the database for global search, and the local model is created with training samples around the current swarm for local search. In addition, a restart mechanism and two model management schemes, namely the individual-based and generation-based, are effectively integrated in the proposed algorithm to make SABEA more strong. Twenty benchmark functions and the tension/compression spring design problem are employed to assess the proposed SABEA. Comprehensive experimental results demonstrate that our proposed SABEA has superior performance comparing with several state-of-the-art competing algorithms on most of the test problems with low, medium and high dimensions. [ABSTRACT FROM AUTHOR]

With the increase of the objective dimension of optimization problems, the effect of comparing individuals through Pareto dominance relation drops sharply. While some algorithms enhance Pareto dominance via diversity preservation strategies, performance indicators, and reference vectors, many of them encounter difficulties in balancing the convergence and diversity of populations. Therefore, this paper proposes a subspace segmentation based co-evolutionary algorithm for balancing convergence and diversity in many-objective optimization. First, the decision space is divided into a convergence subspace and a diversity subspace, which are searched in the early and late stages to improve the population convergence and diversity, respectively. Second, a capacity adaptively adjusted archive is used to retain elite individuals with better convergence in the population, which is further used to mate with the population. Moreover, an indicator with penalty factor is proposed to retain the boundary individuals so as to maintain the population diversity. Comparing with 6 advanced many-objective evolutionary algorithms on 63 benchmark cases, the proposed algorithm obtains smallest IGD on 36 benchmark cases, the experimental results show that the proposed algorithm can balance convergence and diversity well and has exhibit competitiveness. [ABSTRACT FROM AUTHOR]

A large number of evolutionary algorithms have been introduced for multi-objective optimization problems in the past two decades. However, the compromise of convergence and diversity of the non-dominated solutions is still the main difficult problem faced by optimization algorithms. To handle this problem, an efficient competitive mechanism based multi-objective differential evolution algorithm (CMODE) is designed in this work. In CMODE, the rank based on the non-dominated sorting and crowding distance is first adopted to create the leader set, which is utilized to lead the evolution of the differential evolution (DE) algorithm. Then, a competitive mechanism using the shift-based density estimation (SDE) strategy is employed to design a new mutation operation for producing offspring, where the SDE strategy is beneficial to balance convergence and diversity. Meanwhile, two variants of the CMODE using the angle competitive mechanism and the Euclidean distance competitive mechanism are proposed. The experimental results on three test suites show that the proposed CMODE performs better than six state-of-the-art multi-objective optimization algorithms on most of the twenty benchmark functions in terms of hypervolume and inverted generation distance. Furthermore, the proposed CMODE is applied to the feature selection problem. The comparison results on feature selection also demonstrate the efficiency of our proposed CMODE. • An efficient competitive mechanism based multi-objective differential evolution algorithm (CMODE) is proposed. • Two variants of the CMODE using the angle competitive mechanism and Euclidean distance competitive mechanism are proposed. • The performance of our proposed CMODE is comprehensively assessed by comparing with six popular MOEAs on twenty benchmarks. • The proposed CMODE is applied to the feature selection problem. [ABSTRACT FROM AUTHOR]

Many real-world engineering optimization problems usually need a lot of time for function evaluations or have massive decision variables. It is still a big challenge to address these problems effectively. Recently, surrogate-assisted meta-heuristic algorithms have drawn increasing attention, and have shown their potential to deal with such expensive complex optimization problems. In this study, a surrogate-assisted quasi-affine transformation evolutionary (SA-QUATRE) algorithm is proposed to further enhance the optimization efficiency and effectiveness. In SA-QUATRE, the global and the local surrogate models are effectively combined for fitness estimation. The global surrogate model is built based on all data in the database for global exploration. While, the local surrogate model is constructed with a predefined number of top best samples for local exploitation. Meanwhile, both the generation- and individual-based evolution controls as well as a top best restart strategy are incorporated in the global and the local searches. To enhance the exploration and the exploitation capabilities, the global search uses the mean of the population to be evaluated with the expensive real fitness function, while the local search chooses the individual with the best fitness according to the surrogate for real evaluation. The proposed SA-QUATRE is compared with five state-of-the-art optimization approaches over seven commonly used benchmark functions with dimensions varying from 10 to 100. Moreover, the proposed SA-QUATRE is also applied to solve the tension/compression spring design problem. The experimental results show that SA-QUATRE is promising for optimizing computationally expensive problems. [ABSTRACT FROM AUTHOR]