Lazy Modeling of Variants of Token Swapping Problem and Multi-agent Path Finding through Combination of Satisfiability Modulo Theories and Conflict-based Search
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We address item relocation problems in graphs in this paper. We assume items placed in vertices of an undirected graph with at most one item per vertex. Items can be moved across edges while various constraints depending on the type of relocation problem must be satisfied. We introduce a general problem formulation that encompasses known types of item relocation problems such as multi-agent path finding (MAPF) and token swapping (TSWAP). In this formulation we express two new types of relocation problems derived from token swapping that we call token rotation (TROT) and token permutation (TPERM). Our solving approach for item relocation combines satisfiability modulo theory (SMT) with conflict-based search (CBS). We interpret CBS in the SMT framework where we start with the basic model and refine the model with a collision resolution constraint whenever a collision between items occurs in the current solution. The key difference between the standard CBS and our SMT-based modification of CBS (SMT-CBS) is that the standard CBS branches the search to resolve the collision while in SMT-CBS we iteratively add a single disjunctive collision resolution constraint. Experimental evaluation on several benchmarks shows that the SMT-CBS algorithm significantly outperforms the standard CBS. We also compared SMT-CBS with a modification of the SAT-based MDD-SAT solver that uses an eager modeling of item relocation in which all potential collisions are eliminated by constrains in advance. Experiments show that lazy approach in SMT-CBS produce fewer constraint than MDD-SAT and also achieves faster solving run-times.
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