A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming

Abstract

The conventional Unconstrained Binary Quadratic Programming (UBQP) problem is known to be a unified modeling and solution framework for many combinatorial optimization problems. This paper extends the single-objective UBQP to the multiobjective case (mUBQP) where multiple objectives are to be optimized simultaneously. We propose a hybrid metaheuristic which combines an elitist evolutionary multiobjective optimization algorithm and a state-of-the-art single-objective tabu search procedure by using an achievement scalarizing function. Finally, we define a formal model to generate mUBQP instances and validate the performance of the proposed approach in obtaining competitive results on large-size mUBQP instances with two and three objectives.

Using Parallel Strategies to Speed up Pareto Local Search

“…Many MCOPs are challenging because of their NP-hardness and their intractability [5]. This is the case of the mUBQP problem considered in the paper [9]. …”

“…In this paper, the neighborhood structure is taken as the 1-bit-flip, which is directly related to a Hamming distance 1. In this paper, we only consider mUBQP instances from [9] with m = 2 objectives. Notice that PLS has been shown to provide a high-quality Pareto set approximation for those instances, and is actually a core building block of the state-of-the-art [10].…”

“…Drugan and Thierens [3] discuss different neighborhood exploration strategies and restart strategies for PLS. At last, for the mUBQP problem, Liefooghe et al [9,10] conduct an experimental analysis on the characteristics of small-size instances and the performances of some metaheuristics, including PLS, on larger instances. …”

Experiments on Local Search for Bi-objective Unconstrained Binary Quadratic Programming

“…Furthermore, a number of NP-hard combinatorial optimization problems can be recast as UBQP problems, such as graph coloring, max-cut, set packing, set partitioning, or maximum clique, among others [11]. The singleobjective UBQP problem has received a growing interest in recent years [9,11], and a multi-objective extension of UBQP has been proposed recently [12].…”

“…However, as for many problems from multi-objective combinatorial optimization, the biobjective UBQP problem raises several difficulties for heuristics design. In particular, the number of optimal solutions can be very large [12], and determining whether a candidate solution is optimal is NP-complete, even in the singleobjective case [8]. For these reasons, we design and experiment with multiobjective stochastic local search algorithms, and measure their efficiency and their effectiveness on instances with different dimensions and correlation degrees between the objective function values.…”