ELSEVIER European Journal of Operational Research 83 (1995) 253-270 EUROPEAN JOURNAL OF OPERATIONAL RESEARCH Some thoughts on combinatorial optimisation M.H. Bjorndal a,., A. Caprara b P.I. Cowling c, F. Della Croce d H. Lourenqo e, F. Malucelli f, A.J. Orman g, D. Pisinger h, C. Rego i, j.j. Salazar J a Norwegian School of Economics and Business Administration, Bergen, Norway b DEIS, Universit~ di Bologna, Bologna, Italy c Service de Math~matiques de la Gestion, Universit~ Libre de Bruxelles, Brussels, Belgium d DAI, Politecnico di Torino, Torino, Italy e Departamento de Estatlstica e Inl;estigaq~o Operacional, Universidade de Lisboa, Lisbon, Portugal f Dipartimento di Informatica, Universit?t di Pisa, Pisa, Italy g Faculty of Mathematical Studies, University of Southampton, Southampton, UK h Department of Computer Science, University of Copenhagen, Copenhagen, Denmark i DI, Universidade Portucalense, Porto, Portugal J DE10C, Universidad de La Laguna, Tenerife, Spain Abstract A group of young researchers from the ESI X summer school, HEC, Jouy-en-Josas 1994, give their personal views on the current status of, and prospects for, Combinatorial Optimisation. Several issues are considered and discussed with emphasis on a selected number of techniques: heuristics and polyhedral approaches, and problems: knapsack, quadratic 0-1 programming, machine scheduling, routing and network design. I. Introduction Combinatorial Optimisation (CO) studies prob- lems which are characterised by a finite number of feasible solutions. Although, in principle, the optimal solution to such a finite problem can be found by a simple enumeration, in practice this task is frequently impossible, especially for practi- cal problems of realistic size where the number of feasible solutions can be extremely high. CO re- searchers study the structural properties of the problems and use these properties to devise both * Corresponding author. exact and approximate general solution tech- niques. In general, CO problems are classified according to their computational complexity. This worst-case analysis does not always reflect the actual computational tractability. For this reason, it is the real difficulty of the problems that drives the development of solution approaches. This paper is a review of some of the problems and solution methods of CO as seen through the eyes of the next generation of researchers. Though partial, and in some cases possibly naive, this review intends to address the questions usually faced by young researchers when entering the field. Common questions are: What is the future of CO? Why should a young researcher enter the field of CO? How can we promote CO? How can 0377-2217/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0377-2217(95)00005-4