A Multi-population Helper and Equivalent Objective Differential Evolution Algorithm

The helper and equivalent objective method is to convert a constrained optimisation problem into an optimisation problem consisting of helper and equivalent objectives with only boundary constraints, then to solve the converted problem by a decomposition-based evolutionary algorithm. Based on this method, an algorithm called HECO-DE was designed which outperformed the state-of-art evolutionary algorithms in IEEE CEC 2018 constrained optimisation competition. However, it is observed that its computation time increases quickly as the dimension of the decision space. A potential solution to this problem is to divide a population into several subpopulations and run them separately for parallel processing. This paper considers a multi-population implementation of HECO-DE called HECOD-Em, which splits a population into three sub-populations. Objective decomposition in each subpopulation is assigned with different weights. This leads to different searches directions. A process of regularly sorting all individuals is employed for individual exchange among subpopulations. HECO-DEm is compared with HECO-DE and algorithms in IEEE CEC 2018 constrained optimisation competition. Experiment results show that its overall performance is the same as HECO-DE and better than other algorithms. Compared with HECO-DE, the multi-population version performs slightly better on 50 and 100 dimensional functions. Furthermore, HECO-DEm has great potential in parallel processing.