关键词: 约束多目标优化, 进化算法, 梯度下降, 多阶段搜索

Abstract:

Constrained Multi-Objective Evolutionary Algorithms （CMOEAs） are metaheuristics tailored for solving constrained multi-objective optimization problems. These algorithms use population-based stochastic search paradigms， striking balance between objectives and constrains on various optimization problems. However， they do not take advantage of gradient information of the functions， exhibiting slow convergence speed on complex problems. Nevertheless， the introduction of gradients is not trivial， as the calculation of the gradients of all the objectives and constraints are computationally expensive， and the conflicts between objectives and constraints make it difficult to determine the gradient directions. Therefore， an optimization algorithm combining evolutionary computation and Gradient Descent （GD） was proposed， namely CMOEA with Multiple Stages assisted by Gradients （CMOEA-MSG）. It consists of two stages： at the first stage， helper problems were constructed and either the gradients of objectives or the gradients of constraints were calculated， which were used to update solutions and drive the population to quickly converge towards feasible regions； at the second stage， the constraint-first principle was utilized to solve the original problem， so as to ensure the feasibility and diversity of the population. Compared with peer algorithms on LIR-CMOP， MW and DAS-CMOP test sets， CMOEA-MSG is verified to be more effective for solving constrained multi-objective optimization problems.

Key words: constrained multi-objective optimization, Evolutionary Algorithm (EA), Gradient Descent (GD), multi-stage search