Computational complexity of discrete optimization problems

Recent developments in the theory of computational complexity as applied to combinatorial problems have revealed the existence of a large class of so-called NP-complete problems, either all or none of which are solvable in polynomial time. Since many infamous combinatorial problems have been proved to be NP-complete, the latter alternative seems far more likely. In that sense, NP-completeness of a problem justifies the use of enumerative optimization methods and of approximation algorithms. In this paper we give an informal introduction to the theory of NP-completeness and derive some fundamental results, in the hope of stimulating further use of this valuable analytical tooI

Perspectives on parallel computing

Operations research is one problem domain that is likely to benefit from advances in parallel computing. We briefly review what has been achieved in recent years and try to sketch what may be expected in the near future. We argue that the lack of uniformity in available architectures is the main obstacle for the breakthrough of parallel computing. Also, formal techniques will have to be developed for the design and implementation of efficient parallel algorithms, and more realism will be required in theoretical models of parallel computation

Optimization and approximation in deterministic sequencing and scheduling : a survey

The theory of deterministic sequencing and scheduling has expanded rapidly during the past years. In this paper we survey the state of the art with respect to optimization and approximation algorithms and interpret these in terms of computational complexity theory. Special cases considered are single machine scheduling, identical, uniform and unrelated parallel machine scheduling, and open shop, flow shop and job shop scheduling. We indicate some problems for future research and include a selective bibliography

A stochastic method for global optimization

A stochastic method for global optimization is described and evaluated. The method involves a combination of sampling, clustering and local search, and terminates with a range of confidence intervals on the value of the global optimum. Computational results on standard test functions are included as well