A GPU-based iterated tabu search for solving the quadratic 3-dimensional assignment problem

Abstract

Abstract-The quadratic 3-dimensional assignment problem (Q3AP) is an extension of the well-known NP-hard quadratic assignment problem. It has been proved to be one of the most difficult combinatorial optimization problems. Local search (LS) algorithms are a class of heuristics which have been successfully applied to solve such hard optimization problem. These methods handle with a single solution iteratively improved by exploring its neighborhood in the solution space. In this paper, we propose an iterated tabu search for solving the Q3AP. The design of this algorithm is essentially based on a new large neighborhood structure. Indeed, in LS heuristics, designing operators to explore large promising regions of the search space may improve the quality of the obtained solutions. However, designing such neighborhood is at the expense of a highly computationally process. Therefore, the use of graphics processing units (GPUs) provides an efficient complementary way to speed up the search. The proposed GPU-based iterated tabu search has been experimented on 5 different Q3AP instances. The obtained results are convincing both in terms of efficiency, quality and robustness of the provided solutions at run time.Index Terms-Quadratic 3-dimensional assignment problem (Q3AP), GPU-based local search, metaheuristics on GPU, iterated tabu search on graphics processing units.

A comparative study of high-productivity high-performance programming languages for parallel metaheuristics

“…In [12] a GPU-based iterated tabu search (ITS) is proposed. The experimental results show that it is advantageous to use a very large neighborhood, containing O(n 4 ) neighbors obtained by simultaneous 2-exchange moves in both permutations π and σ.…”

“…if ∆max > 0 then applyMoveAndUpdateCost(s, m best , ∆max) We consider a local search that uses incremental evaluation of neighbor solutions and a large neighborhood that consists in jointly exchanging two positions in both permutation, as in [12]. Each move can be represented by four integers.…”

“…We compare the (parallel) performance, scalability, and productivity of three programming languages (Chapel, Python and Julia) for two metaheuristics (one trajectory-based and one population-based) applied to the quadratic 3-dimensional assignment problem (Q3AP). The Q3AP is used as a test-case because metaheuristic solution approaches are time-consuming [11] and parallel computing is highly recommended to tackle the problem [12,13,14]. Tar are designed to provide high-performance and a high-level of expressiveness simultaneously, so we chose these languages as a priori candidates to lie on a "Pareto front" of optimal trade-offs between performance and programmability.…”

Parallel metaheuristics: recent advances and new trends

“…Also, some new parallel algorithms have been proposed following the parallel moves strategy (or master/slave) for both population‐ and trajectory‐based metaheuristics, but these algorithms usually are classical ones adapted to be used in modern parallel platforms, mainly GPUs (Harding and Banzhaf, ; Van Luong et al., ; Tsutsui and Fujimoto, ), and they will be detailed in next sections.…”

Recent Advances on GPU Computing in Operations Research

“…2) Tabu Search: We note also that Luong et al have proposed a hybrid Tabu Search method for the 3-dimensional Quadratic Assignment Problem (QAP) in [39]. The basic TS algorithm runs on the CPU.…”