Abstract
NP-hard combinatorial optimization problems are pivotal in science and business. There exists a variety of approaches for solving such problems, but for problems with complex constraints and objective functions, local search algorithms scale the best. Such algorithms usually assume that finding a non-optimal solution with no other requirements is easy. However, what if it is NP-hard? In such case, a SAT solver can be used for finding the initial solution, but how can one continue solving the optimization problem? We offer a generic methodology, called Local Search with SAT Oracle (LSSO), to solve such problems. LSSO facilitates implementation of advanced local search methods, such as variable neighbourhood search, hill climbing and iterated local search, while using a SAT solver as an oracle. We have successfully applied our approach to solve a critical industrial problem of cell placement and productized our solution at Intel.
Highlights
Real-life combinatorial optimization problems are pivotal in science, operations research, engineering, economics, and business [11, 13, 20, 21, 23].Loosely speaking, an instance of a combinatorial optimization problem deals with the minimization of an objective function over a finite set, subject to feasibility constraints
We focus on solving any problem, which can be expressed as a constraint optimization program (COP) [2]
This work presents a new methodology for solving a wide class of combinatorial optimization problems, which can be expressed as a Constraint Optimization Program, shown in Def. 1
Summary
Real-life combinatorial optimization problems are pivotal in science, operations research, engineering, economics, and business [11, 13, 20, 21, 23]. For such problems, various algorithmic strategies have been devised, including complete methods, such as branchand-bound and dynamic programming, and incomplete methods, such as greedy algorithms and local search. Local search algorithms stand out from the rest in that they impose relatively mild constraints on the type of the problem to be addressed, providing a wide scope of applicability. They seem to scale better with input size relative to complete algorithms [24]. A key advantage of our approach is that it can handle problems with complex constraints and objective functions
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