Combinatorial optimization

Abstract

Bin packing, routing, scheduling, layout, and network design are generic examples of combinatorial optimization problems that often arise in computer engineering and decision support. Unfortunately, almost all interesting generic classes of combinatorial optimization problems are N P -hard. The scale at which these problems arise in applications and the explosive exponential complexity of the search spaces preclude the use of simplistic enumeration and search techniques. Despite the worst-case intractability of combinatorial optimization, in practice we are able to solve many large problems and often with offthe-shelf software. Effective software for combinatorial optimization is usually problem specific and based on sophisticated algorithms that combine approximation methods with search schemes and that exploit mathematical (and not just syntactic) structure in the problem at hand.