On the usefulness of linkage processing for solving MAX-SAT

Mixing of partial solutions is a key mechanism used for creating new solutions in many Genetic Algorithms (GAs). However, this mixing can be disruptive and generate improved solutions inefficiently. Exploring a problem's structure can help in establishing less disruptive operators, leading to more efficient mixing. One way of using a problem's structure is to consider variable linkage information. Once a proper linkage model for a problem is obtained, mixing becomes more efficient. This paper focuses on exploring different methods of building family of subsets (FOS) linkage models, which are then used with the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) to solve MAX-SAT problems. Individual algorithms from the GOMEA family are distinguished by how the FOS linkage models are constructed. The Linkage Tree Genetic Algorithm (LTGA) is a GOMEA instance which learns the linkage between problem variables by building a linkage tree in every generation. In this paper, we introduce SAT-GOMEA. This algorithm uses a predetermined FOS linkage model based on the SAT-problem's definition. Both algorithms use linkage information. We show that because of this information they are capable of performing significantly better than other algorithms from the GOMEA family which do not explore linkage. In a black-box (BBO) setting, LTGA performs well. We further study the use of linkage models outside of the typical BBO approach by examining the behavior of LTGA and the problem-specific SAT-GOMEA in a white-box setting, where more of the problem information is known. We show that with this white-box optimization (WBO) approach, exploring linkage information can still be beneficial. We further compare the performance of these algorithms with a selection of non-GOMEA based algorithms. From the BBO perspective, we compare LTGA with the well-known hBOA. In the WBO setting, many very efficient problem-specific local search (LS) algorithm exist. We specifically consider Walksat and GSAT and show that combining LS with LTGA or SAT-GOMEA increases their performance.