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

Authors:
Diane E. Vaughan;Sheldon H. Jacobson;Shane N. Hall;Laura A. McLay
Affiliations:
Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA;Simulation and Optimization Laboratory, Department of Mechanical & Industrial Engineering, University of Illinois, 1206 West Green Street (MC-244), Urbana, Illinois 61801-2906, USA;Simulation and Optimization Laboratory, Department of Mechanical & Industrial Engineering, University of Illinois, 1206 West Green Street (MC-244), Urbana, Illinois 61801-2906, USA;Simulation and Optimization Laboratory, Department of Mechanical & Industrial Engineering, University of Illinois, 1206 West Green Street (MC-244), Urbana, Illinois 61801-2906, USA
Venue:
INFORMS Journal on Computing
Year:
2005

Citing 8
Cited 2

Threshold accepting: a general purpose optimization algorithm appearing superior to simulated annealing

Journal of Computational Physics
On the convergence of generalized hill climbing algorithms

Discrete Applied Mathematics
Local Search in Combinatorial Optimization

Local Search in Combinatorial Optimization
Tabu Search

Tabu Search
A class of convergent generalized hill climbing algorithms

Applied Mathematics and Computation
The complexity of theorem-proving procedures

STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Analyzing the Performance of Generalized Hill Climbing Algorithms

Journal of Heuristics
Global Optimization Performance Measures for Generalized Hill Climbing Algorithms

Journal of Global Optimization

Analyzing the performance of simultaneous generalized hill climbing algorithms

Computational Optimization and Applications
Optimal search strategies using simultaneous generalized hill climbing algorithms

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	0.00

Visualization

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.