Adaptive Memory Tabu Search for Binary Quadratic Programs

Abstract

Recent studies have demonstrated the effectiveness of applying adaptive memory tabu search procedures to combinatorial optimization problems. In this paper we describe the development and use of such an approach to solve binary quadratic programs. Computational experience is reported, showing that the approach optimally solves the most difficult problems reported in the literature. For challenging problems of limited size, which are capable of being approached by exact procedures, we find optimal solutions considerably faster than the best reported exact method. Moreover, we demonstrate that our approach is significantly more efficient and yields better solutions than the best heuristic method reported to date. Finally, we give outcomes for larger problems that are considerably more challenging than any currently reported in the literature.Integer Programming, Heuristics, Nonlinear Optimization

A Study of Multi-parent Crossover Operators in a Memetic Algorithm

“…Our tabu search procedure uses a neighborhood defined by the simple one-flip move, which consists of changing (flipping) the value of a single variable x i to its complementary value 1 − x i . The implementation of this neighborhood uses a fast incremental evaluation technique [9] to calculate the cost (move value) of transitioning to each neighboring solution.…”

Diversification-driven tabu search for unconstrained binary quadratic problems

“…Some representative examples include local search based approaches such as Simulated Annealing (Alkhamis et al (1998); Beasley (1998); Katayama and Narihisa (2001)) and Tabu Search (Glover et al (1998); Beasley (1998); Palubeckis (2004Palubeckis ( , 2006), populationbased approaches such as Evolutionary Algorithms (Lodi et al (1999); Merz and Freisleben (1999); Katayama et al (2000); Borgulya (2005)), Scatter Search (Amini et al (1999)) and Memetic Algorithms (Merz and Katayama (2004)). …”

“…One of the first adaptive memory TS algorithms for the UBQP (Glover et al (1998)), for instance, has since been used to solve applications arising in a wide variety of settings, as a demonstration of the value of the UBQP model and the ability to solve such applications successfully. More recently, Palubeckis (2004) has explored several multistart TS strategies and has achieved very good results on large problem instances.…”

A Unified Framework for Modeling and Solving Combinatorial Optimization Problems: A Tutorial

“…(4) All instances of UQP solved in this tutorial were solved using the tabu search method described in [GKAA99,GKA98].…”

“…In the work reported here, we used a basic tabu search method due to Glover, Kochenberger, and Alidaee [GL97,GKAA99,GKA98]. A brief overview of the approach is given below.…”