Incremental Algorithms for Local Search from Existential Second-Order Logic

Local search is a powerful and well-established method for solving hard combinatorial problems. Yet, until recently, it has provided very little user support, leading to time-consuming and error-prone implementation tasks. We introduce a scheme that, from a high-level description of a constraint in existential second-order logic with counting, automatically synthesises incremental penalty calculation algorithms. The performance of the scheme is demonstrated by solving real-life instances of a financial portfolio design problem that seem unsolvable in reasonable time by complete search.