A convergence and diversity guided leader selection strategy for many-objective particle swarm optimization

Recently, particle swarm optimizer (PSO) is extended to solve many-objective optimization problems (MaOPs) and becomes a hot research topic in the field of evolutionary computation. Particularly, the leader particle selection (LPS) and the search direction used in a velocity update strategy are two crucial factors in PSOs. However, the LPS strategies for most existing PSOs are not so efficient in high-dimensional objective space, mainly due to the lack of convergence pressure or loss of diversity. In order to address these two issues and improve the performance of PSO in high-dimensional objective space, this paper proposes a convergence and diversity guided leader selection strategy for PSO, denoted as CDLS, in which different leader particles are adaptively selected for each particle based on its corresponding situation of convergence and diversity. In this way, a good tradeoff between the convergence and diversity can be achieved by CDLS. To verify the effectiveness of CDLS, it is embedded into the PSO search process of three well-known PSOs. Furthermore, a new variant of PSO combining with the CDLS strategy, namely PSO/CDLS, is also presented. The experimental results validate the superiority of our proposed CDLS strategy and the effectiveness of PSO/CDLS, when solving numerous MaOPs with regular and irregular Pareto fronts (PFs)

A self-organizing weighted optimization based framework for large-scale multi-objective optimization

The solving of large-scale multi-objective optimization problem (LSMOP) has become a hot research topic in evolutionary computation. To better solve this problem, this paper proposes a self-organizing weighted optimization based framework, denoted S-WOF, for addressing LSMOPs. Compared to the original framework, there are two main improvements in our work. Firstly, S-WOF simplifies the evolutionary stage into one stage, in which the evaluating numbers of weighted based optimization and normal optimization approaches are adaptively adjusted based on the current evolutionary state. Specifically, regarding the evaluating number for weighted based optimization (i.e., t1), it is larger when the population is in the exploitation state, which aims to accelerate the convergence speed, while t1 is diminishing when the population is switching to the exploration state, in which more attentions are put on the diversity maintenance. On the other hand, regarding the evaluating number for original optimization (i.e., t2), which shows an opposite trend to t1, it is small during the exploitation stage but gradually increases later. In this way, a dynamic trade-off between convergence and diversity is achieved in S-WOF. Secondly, to further improve the search ability in the large-scale decision space, an efficient competitive swarm optimizer (CSO) is implemented in S-WOF, which shows efficiency for solving LSMOPs. Finally, the experimental results have validated the superiority of S-WOF over several state-of-the-art large-scale evolutionary algorithms

Sampling Reference Points on the Pareto Fronts of Benchmark Multi-Objective Optimization Problems

The effectiveness of evolutionary algorithms have been verified on multi-objective optimization, and a large number of multi-objective evolutionary algorithms have been proposed during the last two decades. To quantitatively compare the performance of different algorithms, a set of uniformly distributed reference points sampled on the Pareto fronts of benchmark problems are needed in the calculation of most performance metrics. However, not much work has been done to investigate the method for sampling reference points on Pareto fronts, even though it is not an easy task for many Pareto fronts with irregular shapes. More recently, an evolutionary multi-objective optimization platform was proposed by us, called PlatEMO, which can automatically generate reference points on each Pareto front and use them to calculate the performance metric values. In this paper, we report the reference point sampling methods used in PlatEMO for different types of Pareto fronts. Experimental results show that the reference points generated by the proposed sampling methods can evaluate the performance of algorithms more accurately than randomly sampled reference points

Sampling Reference Points on the Pareto Fronts of Benchmark Multi-Objective Optimization Problems

Tian Y, Xiang X, Zhang X, Cheng R, Jin Y. Sampling Reference Points on the Pareto Fronts of Benchmark Multi-Objective Optimization Problems. In: 2018 IEEE Congress on Evolutionary Computation (CEC). IEEE; 2018: 1-6.The effectiveness of evolutionary algorithms have been verified on multi-objective optimization, and a large number of multi-objective evolutionary algorithms have been proposed during the last two decades. To quantitatively compare the performance of different algorithms, a set of uniformly distributed reference points sampled on the Pareto fronts of benchmark problems are needed in the calculation of many performance metrics. However, not much work has been done to investigate the method for sampling reference points on Pareto fronts, even though it is not an easy task for many Pareto fronts with irregular shapes. More recently, an evolutionary multi-objective optimization platform was proposed by us, called PlatEMO, which can automatically generate reference points on each Pareto front and use them to calculate the performance metric values. In this paper, we report the reference point sampling methods used in PlatEMO for different types of Pareto fronts. Experimental results show that the reference points generated by the proposed sampling methods can evaluate the performance of algorithms more accurately than randomly sampled reference points