Parallel Strategies Selection

Abstract

We consider the problem of selecting the best variable-value strategy for solving a given problem in constraint programming. We show that the recent Embarrassingly Parallel Search method (EPS) can be used for this purpose. EPS proposes to solve a problem by decomposing it in a lot of subproblems and to give them on-demand to workers which run in parallel. Our method uses a part of these subproblems as a simple sample as defined in statistics for comparing some strategies in order to select the most promising one that will be used for solving the remaining subproblems. For each subproblem of the sample, the parallelism helps us to control the running time of the strategies because it gives us the possibility to introduce timeouts by stopping a strategy when it requires more than twice the time of the best one. Thus, we can deal with the great disparity in solving times for the strategies. The selections we made are based on the Wilcoxon signed rank tests because no assumption has to be made on the distribution of the solving times and because these tests can deal with the censored data that we obtain after introducing timeouts. The experiments we performed on a set of classical benchmarks for satisfaction and optimization problems show that our method obtain good performance by selecting almost all the time the best variable-value strategy and by almost never choosing a variable-value strategy which is dramatically slower than the best one. Our method also outperforms the portfolio approach consisting in running some strategies in parallel and is competitive with the multi armed bandit framework.

Learning Robust Search Strategies Using a Bandit-Based Approach

“…Recently, parallel strategies selection (PSS) was shown to be a promising approach for selecting search heuristics (Palmieri, Régin, and Schaus 2016). PSS is quite different from online or supervised learning based methods.…”

“…Bachiri et al (Bachiri et al 2015) propose to learn the rewards of nodes and use the rewards to guide the search to backtrack to certain nodes. A recent work on adaptive search heuristics is the parallel strategies selection (PSS) approach (Palmieri, Régin, and Schaus 2016). PSS first decomposes the CSP into a large number sub-problems.…”

A review of literature on parallel constraint solving

“…Results for decision problems are not presented. Palmieri et al (2016) also use the Embarrassingly Parallel Search decomposition for heuristic selection, as an alternative to portfolios. They perform the decomposition, use parallelism to try many variations of variable and value-ordering heuristics on a small subset of the decomposed subproblems, and then select the most promising choice for the remainder of the search.…”

Combining Reinforcement Learning and Constraint Programming for Combinatorial Optimization

“…Naturally, well-designed heuristics are more likely to discover promising solutions, whereas bad heuristics may bring the search into a fruitless subpart of the solution space. In general, the choice of an appropriate branching strategy is non-trivial and their design is a hot topic in the CP community [42,19,34].…”