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Many-objective problems refer to the optimization problems containing more than three conflicting objectives. To obtain a representative set of well-distributed non-dominated solutions close to Pareto front in the objective space remains a challenging problem. Many papers have proposed different Multi-Objective Evolutionary Algorithms to solve the lack of the convergence and diversity in many-objective problems. One of the more promising approaches uses a set of reference points to discriminate the solutions and guide the search process. However, this approach was incorporated mainly in Multi-Objective Evolutionary Algorithms, and there are just some few promising adaptations of Particle Swarm Optimization approaches for effectively tackling many-objective problems regarding convergence and diversity. Thus, this paper proposes a practical and efficient Many-Objective Particle Swarm Optimization algorithm for solving many-objective problems. Our proposal uses a set of reference points dynamically determined according to the search process, allowing the algorithm to converge to the Pareto front, but maintaining the diversity of the Pareto front. Our experimental results demonstrate superior or similar performance when compared to other state-of-art algorithms. [ABSTRACT FROM AUTHOR]

Abstract As a new evolutionary computation method, the structure of backtracking search optimization algorithm (BSA) is simple and the exploration capability of it is strong. However, the global performance of the BSA is significantly affected by mutation strategies and control parameters. Designing appropriate mutation strategies and control parameters is important to improve the global performance of the BSA. In this paper, an adaptive BSA with knowledge learning (KLBSA) is developed to improve the global performance of the BSA. In the method, an adaptive control parameter based on the global and local information of the swarms in the current iteration is designed to adjust the search step length of individuals, which helps to balance the exploration and exploitation abilities of the algorithm. Moreover, a new mutation strategy based on the guidance of different information is designed to improve the optimization ability of the algorithm. In addition, a multi-population strategy is implemented to thoroughly improve the searching ability of the algorithm for different searching areas. To this end, experiments on three groups of benchmark functions and three real-world problems are implemented to verify the performance of the proposed KLBSA algorithm. The results indicate that the proposed algorithm performs competitively and effectively when compared to some other evolutionary algorithms. [ABSTRACT FROM AUTHOR]

Abstract: Several variants of the particle swarm optimization (PSO) algorithm have been proposed in recent past to tackle the multi-objective optimization (MO) problems based on the concept of Pareto optimality. Although a plethora of significant research articles have so far been published on analysis of the stability and convergence properties of PSO as a single-objective optimizer, till date, to the best of our knowledge, no such analysis exists for the multi-objective PSO (MOPSO) algorithms. This paper presents a first, simple analysis of the general Pareto-based MOPSO and finds conditions on its most important control parameters (the inertia factor and acceleration coefficients) that govern the convergence behavior of the algorithm to the optimal Pareto front in the objective function space. Computer simulations over benchmark MO problems have also been provided to substantiate the theoretical derivations. [Copyright &y& Elsevier]