An improved estimation of distribution algorithm for multi-objective optimization problems with mixed-variable

Multi-objective evolutionary algorithms face many challenges in optimizing mixed-variable multi-objective problems, such as quantization error, low search efficiency of discontinuous discrete variables, and difficulty in coding non-integer discrete variables. To overcome these challenges, this paper proposes a mixed-variable multi-objective evolutionary algorithm based on estimation of distribution algorithm (MVMO-EDA). Compared with traditional multi-objective evolutionary algorithms, MVMO-EDA has the following improvements: (1) instead of crossover and mutation, statistics and sampling are used to generate offspring, which can avoid the quantization error caused by crossover and mutation operations; (2) using index coding for discrete variables to improve the search efficiency; and (3) a scalable histogram probability distribution model and two crowding distance-based diversity maintenance strategies are used to improve the global optimization ability. The performance of the proposed MVMO-EDA is evaluated on the modified ZDT and DTLZ benchmark sets with mixed-variable, and the results show that MVMO-EDA has a competitive performance both in convergence and diversity.