A hybrid metaheuristic approach to solving the UBQP problem

Abstract

This paper presents a hybrid metaheuristic approach (HMA) for solving the Unconstrained Binary Quadratic Programming (UBQP) problem. By incorporating a tabu search procedure into the framework of evolutionary algorithms, the proposed approach exhibits several distinguishing features, including a diversification-based combination operator and a distance-and-quality based replacement criterion for pool updating. The proposed algorithm is able to easily obtain the best-known solutions for 31 large random instances up to 7000 variables (which no previous algorithm has done) and find new best solutions for 3 of 9 instances derived from the set partitioning problem, demonstrating the efficacy of our proposed algorithm in terms of both solution quality and computational efficiency. Furthermore, some key elements and properties of the HMA algorithm are also analyzed.

Probabilistic GRASP-Tabu Search algorithms for the UBQP problem

“…Due to the fact that the exact methods become prohibitively expensive to apply for solving large instances, various metaheuristic algorithms have been extensively used to find high-quality solutions to large UBQP instances in an acceptable time. Some representative metaheuristic methods include local search heuristics [7], Simulated Annealing [4,18]; adaptive memory approaches based on Tabu Search [14,15,27,29]; population-based approaches such as Evolutionary Algorithms [5,21,25], Scatter Search [2] and Memetic Algorithms [22,26].…”

Combining Clustered Adaptive Multistart and Discrete Dynamic Convexized Method for the Max-Cut Problem

“…It is necessary to preserve the diversity of the elite solution set P. A number of strategies have been presented to control the diversity of the population in memetic algorithms [27,35,38]. [27,35,38] use a function to determine whether an offspring is added to the population or not. The function takes two factors into account: the quality of the solution and the diversity of the population after addition of the solution.…”

“…In this paper, we adopt an elite solution set updating strategy used in [27,38]. It takes both the quality and the diversity of the set P into account.…”

“…We adopt a quality-and-distance scoring function, which was originally proposed in [27], to decide whether a new solution x should be added to an elite solution set P or not.…”

“…Definition 4.5 Given a solution set Q ¼ fx 1 ; Á Á Á ; x q g and a solution x 6 2 Q, the quality-and-distance scoring function [27,38] where f ðxÞ is the objective function value, b is a parameter set to 0.6 according to [27,38], and e Að:Þ represents the normalized function:…”