Constraint-directed search for all-interval series

Abstract

All-interval series is a standard benchmark problem for constraint satisfaction search. An all-interval series of size n is a permutation of integers [0, n) such that the differences between adjacent integers are a permutation of [1, n). Generating each such all-interval series of size n is an interesting challenge for constraint community. The problem is very difficult in terms of the size of the search space. Different approaches have been used to date to generate all the solutions of AIS but the search space that must be explored still remains huge. In this paper, we present a constraint-directed backtrackingbased tree search algorithm that performs efficient lazy checking rather than immediate constraint propagation. Moreover, we prove several key properties of all-interval series that help prune the search space significantly. The reduced search space essentially results into fewer backtracking. We also present scalable parallel versions of our algorithm that can exploit the advantage of having multi-core processors and even multiple computer systems. Our new algorithm generates all the solutions of size up to 27 while a satisfiability-based state-of-the-art approach generates all solutions up to size 24.

Constraint based local search for flowshops with sequence-dependent setup times

“…To that end, we have employed a constraint based local search approach in our proposed algorithm. Constraint based local search approach is a concept that recently attracts great attention for solving different combinatorial problems such as Golomb rulers (Polash et al, 2017a), all-interval series (Polash et al, 2017b), minimum spanning tree problem (Arbelaez et al, 2018), aircraft scheduling (Riahi et al, 2018a(Riahi et al, , 2019b, and customer order scheduling (Riahi et al, 2019a). Constraint based approaches transform the constraints into an objective function and use search algorithms to optimise the objective (Hentenryck and Michel, 2009).…”