Differential Evolution with Reversible Linear Transformations

Abstract

Differential evolution (DE) is a well-known type of evolutionary algorithms (EA). Similarly to other EA variants it can suffer from small populations and loose diversity too quickly. This paper presents a new approach to mitigate this issue: We propose to generate new candidate solutions by utilizing reversible linear transformation applied to a triplet of solutions from the population. In other words, the population is enlarged by using newly generated individuals without evaluating their fitness. We assess our methods on three problems: (i) benchmark function optimization, (ii) discovering parameter values of the gene repressilator system, (iii) learning neural networks. The empirical results indicate that the proposed approach outperforms vanilla DE and a version of DE with applying differential mutation three times on all testbeds.

Comparing lifetime learning methods for morphologically evolving robots

“…Reversible DE (RevDE) proposes a solution by applying a special set of linearly reversible transformation to produce a wide spread over search space when selecting new samples [20]. The algorithm works as follows: (1) initialize a population with λ-samples (2) evaluate the fitness over all λ-samples; (3) perform selection over the top samples to obtain genotype vector µ 1 ; (4) randomly shuffle µ 1 twice to obtain two additional vectors (µ 2 , µ 3 ), and create new samples with the following linear relations:…”

“…The number of evaluations per generation(λ-samples) is 3 times that of µ 1 which set to 10 (Table 1). Scaling factor F = 0.5 has shown to result in stable exploration/exploitation behaviour in RevDE, with a CR = 0.9 (from [20]).…”