Hierarchical optimization by spatial-temporal indictor in multi-scale decision pyramid for constrained large-scale multi-objective problems

Abstract

Most existing constrained multi-objective evolutionary algorithms (CMOEAs) are not so efficient when handling constrained large-scale multi-objective problems (CLSMOPs). To overcome CLSMOPs, a hierarchical optimization, based on the spatial–temporal indictor in the decision pyramid (HOSTI-DP), is proposed to determine the dynamic trade-off between feasible and infeasible solutions in the effectively shrunken searching area. The decision pyramid consists of multiple decision spaces with a set of descending numbers of variables; it is initially constructed to speed up the solution convergence by the layer-by-layer dimensionality reduction and increase the population diversity based on the accumulation of these layers. The spatial–temporal indictor considers both the optimization stage (time) and the hierarchy structure of the decision pyramid (space) and it is designed to restrain the prematurely feasible solutions and find the promising infeasible solutions. Finally, the hierarchical optimization strategy, which applies the spatial–temporal indicator to the evolutionary algorithms in every layer of the decision pyramid and dynamically arranging the proportion among them, is designed for comprehensive balance of objectives, constraints, and computational complexity. Nine representative and state-of-the-art CMOEAs have been compared with the HOSTI-DP to demonstrate its effectiveness through comparative experiments on CLSMOPs with equality and inequality constraints and 1000 decision variables. Experimental results show that HOSTI-DP can significantly improve the performance of these CMOEAs.