Parallel Local Search for the Costas Array Problem

Abstract

Abstract-The Costas Array Problem is a highly combinatorial problem linked to radar applications. We present in this paper its detailed modeling and solving by Adaptive Search, a constraint-based local search method. Experiments have been done on both sequential and parallel hardware up to several hundreds of cores. Performance evaluation of the sequential version shows results outperforming previous implementations, while the parallel version shows nearly linear speedups up to 8,192 cores.

A Parametric Framework for Cooperative Parallel Local Search

“…We solve the instances using 8, 16, 24 and 32 cores. The results show quasi-linear speed-ups for the CAP instance, in accordance with [8]. However, for MSP and AIP the speed-up tends to flatten out when increasing the number of cores.…”

“…The idea is to use isolated sequential Local Search solver instances dividing the search space of the problem through different random starting points [24]. This approach has been successfully used in constraint programming problems reaching good performance [2,7,8].…”

“…Previous work on independent multi-walk local search in a massively parallel context [2,7,8] achieves good but not ideal parallel speedups. On structured constraint-based problems such as (large instances of) Magic Square or AllInterval, independent multiple-walk parallelization does not yield linear speedups, reaching for instance a speedup factor of "only" 50-70 for 256 cores.…”

“…On structured constraint-based problems such as (large instances of) Magic Square or AllInterval, independent multiple-walk parallelization does not yield linear speedups, reaching for instance a speedup factor of "only" 50-70 for 256 cores. However on the Costas Array Problem, the speedup can be linear, even up to 8000 cores [8]. On a more theoretical level, it can be shown that the parallel behavior depends on the sequential runtime distribution of the problem: for problems admitting an exponential distribution, the speedup can be linear, while if the runtime distribution is shifted-exponential or (shifted) lognormal, then there is a bound on the speedup (which will be the asymptotic limit when the number of cores goes to infinity), see [23] for a detailed analysis of these phenomena.…”

Sequential and Parallel Restart Policies for Constraint-Based Local Search

“…For this purpose, we study the behavior of a constraint-based local search method applied to a few Constraint Satisfaction Problems (CSP). This method is quite efficient to solve hard combinatorial problems and has been extended with a simple parallel scheme [8], [9].…”