A∗-based construction of decision diagrams for a prize-collecting scheduling problem

• A novel * -based compilation scheme for relaxed multi-valued decision diagrams. Considering a prize-collecting scheduling problem. Obtained diagrams provide stronger bounds than compiled by standard methods. Exploiting structural information of to construct restricted New state the art results obtained considered Decision (DDs) have proven be useful tools in combinatorial optimization. Relaxed DDs represent discrete relaxations problems, can encode essential compact form, and may yield strong dual bounds. We propose construction problem which subset elements has selected from ground set need sequenced. The proposed builds upon search guided fast-to-calculate problem-specific bound heuristic. In contrast traditional DD methods, new approach does not rely on correspondence layers variables. For kind problem, this implies that multiple nodes representing same at different avoided, consequently also many redundant isomorphic substructures. keeping compact, mechanism merging layer-independent way is suggested. our job sequencing experimental show substantially better while frequently being an order-of-magnitude smaller given about time. To obtain heuristic solution corresponding lower bound, we further based one, thereby exploiting already gained information. This outperforms standalone construction, basic constraint programming mixed integer linear approaches, variable neighborhood terms quality most benchmark instances.