Comparing Solution Combination Techniques in Scatter Search for Quadratic Unconstrained Binary Optimization

Abstract

Quadratic Unconstrained Binary Optimization (QUBO) has emerged as a vital unifying model for combinatorial optimization problems, and (meta-)heuristic approaches are commonly used to solve them due to their NP-hard nature. Scatter Search (SS), a population-based metaheuristic framework, is one such method that has shown promising results for QUBO problems. Generating new solutions from more promising ones is a crucial operation in SS. Path Relinking (PR) based SS has been previously used to solve challenging QUBO problems with high-quality solutions. This paper introduces two new variants of the SS algorithm. The first is the (Multi) Uniform Crossover (MUC) based SS while the second is the Univariate Marginal Distribution Algorithm (UMDA) based SS. MUC and UMDA are well-known operators in Genetic Algorithms and Estimation of Distribution Algorithms respectively. When compared to the existing PR based SS, this work shows that more promising results can be achieved when the newly proposed MUC and UMDA-based SS are applied to QUBO formulations of the Quadratic Knapsack Problem (QKP) instances.