Species-based Particle Swarm Optimizer enhanced by memory for dynamic optimization

•A new population updating method is proposed to enhance a representative algorithm, i.e. the Species-based Particle Swarm Optimization.•Experimental results show that the MSPSO is competitive on MPB, CMPB and DRGDB.•The effect of the memory size on the performance of the proposed algorithm is tested.

Both the species strategy and the memory scheme are efficient methods for addressing dynamic optimization problems. However, the combination of these two efficient techniques has scarcely been studied. Thus, this paper focuses on how to hybridize these two methods. In this paper, a new swarm updating method is proposed to enhance a representative species-based algorithm, i.e., SPSO (Species-based Particle Swarm Optimization), and the new algorithm is named MSPSO. MSPSO has two characteristics. First, the number of replaced particles in the current swarm is set adaptively according to the number of species. To not substantially destroy the exploitation capability of each species, no more than one particle in each species is replaced by the memory. Second, the retrieved memory particles are categorized according to their fitness values and their distances to the seed of the closest species. Aimed at enhancing the search in both promising areas and existing species, each category is processed by different operations. The MPB, Cyclic MPB and DRPBG are used to test the performance of MSPSO. Experimental results demonstrate that MSPSO is competitive for dynamic optimization problems.

Graphical abstractDescription of the states in both before updating and after updating.Figure gives an example to illustrate our algorithm. Part (a) gives the state of before updating. Part (b) explains the state of after updating. Assume there are five peaks in the search space, numbered 1–5 in Part (b). However, only four peaks are detected by the current population, numbered 1–4 in Part (a).Where, ⊕ denotes a replacer from the memory, Δ denotes a new generated particle around the replacer, and ⊗ denotes a replaced particle in the population. We can see that no more than one particle is replaced in each sub-population.Since ⊕ in peak 5 is better than the closest seed, i.e. the seed in sub-population 2, and its distance to the closest seed is larger than rs, the sub-population 5 is created to exploit this area.In sub-population 3, ⊕ is better than the closest seed, i.e. the seed in sub-population 3, and the distance between it to the closest seed is larger than 0.5 × rs and less than rs, so only one Δ is created around the ⊕.In sub-population 2, ⊕ is better than the closest seed, i.e. the seed in sub-population 2, but the distance between it to the closest seed is less than 0.5 × rs, so only ⊕ is added to this sub-population.There is one case that has not been described in this example. Here we suppose the replacer is not better than the worst particle in sub-population 1, so no replacement is conducted in this sub-population.Figure optionsDownload full-size imageDownload as PowerPoint slide