Simultaneous Generalized Hill-Climbing Algorithms for Addressing Sets of Discrete Optimization Problems

Abstract

This paper introduces simultaneous generalized hill-climbing (SGHC) algorithms as a framework for simultaneously addressing a set of related discrete optimization problems using heuristics. Many well-known heuristics can be embedded within the SGHC algorithm framework, including simulated annealing, pure local search, and threshold accepting (among others). SGHC algorithms probabilistically move between a set of related discrete optimization problems during their execution according to a problem probability mass function. When an SGHC algorithm moves between discrete optimization problems, information gained while optimizing the current problem is used to set the initial solution in the subsequent problem. The information used is determined by the practitioner for the particular set of problems under study. However, effective strategies are often apparent based on the problem description. SGHC algorithms are motivated by a discrete manufacturing process design optimization problem (that is used throughout the paper to illustrate the concepts needed to implement a SGHC algorithm). This paper discusses effective strategies for three examples of sets of related discrete optimization problems (a set of traveling salesman problems, a set of permutation flow shop problems, and a set of MAX 3-satisfiability problems). Computational results using the SGHC algorithm for randomly generated problems for two of these examples are presented. For comparison purposes, the associated generalized hill-climbing (GHC) algorithms are applied to the individual discrete optimization problems in the sets. These computational results suggest that near-optimal solutions can be reached more effectively and efficiently using SGHC algorithms.