Solving the Quadratic Assignment Problem with Cooperative Parallel Extremal Optimization

Abstract

Abstract. Several real-life applications can be stated in terms of the Quadratic Assignment Problem. Finding an optimal assignment is computationally very difficult, for many useful instances. We address this problem using a local search technique, based on Extremal Optimization and present experimental evidence that this approach is competitive. Moreover, cooperative parallel versions of our solver improve performance so much that large and hard instances can be solved quickly.

Weaving of Metaheuristics with Cooperative Parallelism

“…To evaluate the performance of our framework, we developed PHYSH-QAP 6 : a parallel hybrid solver for QAP which combines three metaheuristics: a Genetic Algorithm (GA) [7], a Robust Tabu Search (RoTS) [19] and an Extremal Optimization procedure (EO) [12]. PHYSH-QAP is built on top of PHYSH×10.…”

“…are transparently handled by CPLS. CPLS has been successfully used to tackle stable matching problems [15] and very difficult instances of the Quadratic Assignment Problem (QAP) [12]. We later extended CPLS to allow the user to run different metaheuristics in parallel.…”

On Integrating Population-Based Metaheuristics with Cooperative Parallelism

“…These methods are detailed in [18], [19]. We extend the CPLS model by having two independent pools of configurations inside the head node: the diversification pool (DivPool) and the intensification pool (IntPool).…”

“…For this evaluation we selected the 33 hardest instances of the QAPLIB benchmarks highlighted in [18], [19] 10 0.000 0.000 3.2 10 0.000 0.000 3.5 sko64 10 0.000 0.000 2.9 10 0.000 0.000 5.2 sko72 10 0.000 0.000 7.3 10 0.000 0.000 13.7 sko81 10 0.000 0.000 56.8 10 0.000 0.000 48.9 sko90 10 0.000 0.000 14.3 5 0.003 0.000 225.5 sko100a 10 0.000 0.000 43.7 8 0.003 0.000 163.6 sko100b 10 0.000 0.000 36.8 10 0.000 0.000 64.9 sko100c 10 0.000 0.000 57.4 10 0.000 0.000 98.9 sko100d 10 0.000 0.000 39. We first compare our prototype implementation (called GA-CPLS in the rest of this section) with ParEOTS, our reference.…”

“…This framework, available as an open source library written in the IBM X10 concurrent programming language, allows the programmer to tune the search process through an extensive set of parameters. This framework has been successfully used to tackle stable matching problems [17] and very difficult instances of the Quadratic Assignment Problem (QAP) [18].…”