An Empirical Study of Multi-Point Constructive Search for Constraint Satisfaction

Multi-Point Constructive Search (MPCS) is a constructive search technique which borrows the idea from local search of being guided by multiple viewpoints. MPCS consists of a series of resource-limited backtracking searches: each starting from an empty solution or guided by one of a set of high quality, “elite” solutions encountered earlier in the search. This paper focuses on MPCS as applied to constraint satisfaction problems where elite solution quality is measured by the number of assigned variables in a partial solution. We systematically study different parameter settings including the size of the elite set, the probability of using an elite solution for guidance, and the use of chronological backtracking or limited discrepancy search. Experiments are performed on three constraint satisfaction problems: quasigroup-with-holes, magic squares, and multi-dimensional knapsack problems. Our results indicate that MPCS significantly out-performs both randomized restart and standard backtracking search on quasigroup-withholes, performs about the same as randomized restart on the other problems, and is much worse than chronological on the multi-dimensional knapsack problems. The observed differences on two such similar problems (quasigroup-with-holes and magic square) suggests that these problems are a good testbed for future work to understand the reasons underlying the performance of MPCS.