Optimization by Pairwise Linkage Detection, Incremental Linkage Set, and Restricted / Back Mixing: DSMGA-II

TL;DR

DSMGA-II is a new evolutionary algorithm that leverages pairwise linkage detection and an incremental linkage set to efficiently solve complex optimization problems by exploiting problem substructures.

Contribution

It introduces DSMGA-II, which combines pairwise linkage detection, incremental linkage sets, and restricted/back mixing for improved optimization performance.

Findings

Outperforms LT-GOMEA and hBOA in function evaluations

Effective on trap, NK-landscape, Ising spin-glass, and MAX-SAT problems

Demonstrates superior exploitation and exploration capabilities

Abstract

This paper proposes a new evolutionary algorithm, called DSMGA-II, to efficiently solve optimization problems via exploiting problem substructures. The proposed algorithm adopts pairwise linkage detection and stores the information in the form of dependency structure matrix (DSM). A new linkage model, called the incremental linkage set, is then constructed by using the DSM. Inspired by the idea of optimal mixing, the restricted mixing and the back mixing are proposed. The former aims at efficient exploration under certain constrains. The latter aims at exploitation by refining the DSM so as to reduce unnecessary evaluations. Experimental results show that DSMGA-II outperforms LT-GOMEA and hBOA in terms of number of function evaluations on the concatenated/folded/cyclic trap problems, NK-landscape problems with various degrees of overlapping, 2D Ising spin-glass problems, and MAX-SAT. The investigation of performance comparison with P3 is also included.