Abstract
In the field of vector (or multi objective) optimization there has been a relatively little interest in solving combinatorial or discrete problems. During the 70’s just a few papers have been published on multi objective (m.o.) integer linear programming. However no special emphasis was put on the important aspect of computational complexity. This can be certainly ascribed to the fact that the theory of NP—completeness was developing at a fast pace in those same years.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bitran, G.R., Theory and algorithms for linear multiple objective programs with zero-one variables, Math. Progr. 17 (1979) 362–390.
Camerini, P.M., and Vercellis, C., The matroidal knapsack: a class of (often) well-solvable problems, Operations Research Letters 3 (1984) 157–162.
Chalmet, L.G., Lemonidis, L., and Elzinga, D.J., An algorithm for the bicriterion integer programming problem, European J. of Operations Resear (1986) 292–300.
Dyer, M.E., and Walker, J., A note on bicriterion programming, Math. Progr. 27 (1983) 355–361.
Garey, M.R., and Johnson, D.S., Computers and intractability, Freeman, San Francisco, USA, 1979.
Hansen, P., Bicriterion path problems, in Multiple criteria decision making, Fandel, G., and Gal, T., editors, 109–127, Springer, Berlin, 1980.
Hartley, R., Survey of algorithms for vector optimisation problems, in Multi-objective decision making, French, S., et al., editors, Academic Pw York, 1983.
Henig, M.I., The shortest path problem with two objective functions, European J. of Operations Research 25 (1985) 281–291.
Ignizio, J.P., Multiobjective mathematical programming via the Multiplex model and algorithm, European J. of Operations Research 22 (1985) 338–346.
Kung, H.T., Luccio, F., and Preparata, F., On finding the maxima of a set of vectors, J. of ACM 22 (1975) 469–476.
Lawler, E., Combinatorial optimization: networks and matroids, Holt, Rinehart and Winston, New York, 1976.
Lawler, E., Lenstra, J.K., Rinnooy Kan, A.H.G. and Shmoys, D.B., The traveling salesman problem, Wiley, Chichester, UK, 1985.
Martins, E.Q.V., On a multicriteria shortest path problem, European J. of Operations Research 16 (1984) 236–245.
Martins, E.Q.V., On a special class of bicriterion path problems, European J. of Operations Research 17 (1984) 85–94.
Papadimitriou, C.H., and Steiglitz, K., Combinatorial optimization: algorithms and complexity, Prentice Hall, 1982.
Ramesh, R., Karwan, M.H., and Zionts, S., A class of practical interactive branch and bound algorithms for multicriteria integer programming, Working paper 638 (1985), School of Management, State University of New York at Buffalo.
Ruiz-Diaz, F., and French, S., Multi objective combinational scheduling, in Multi-objective decision making, French, S., et al., editors, Academic Press, New York, 1983.
Serafini, P., Dual relaxation and branch-and-bound techniques for multi objective optimization, in Interactive decision analie, Grauer, M., and Wierzbicki, A.P., editors, 84–90, Springer, Berlin, 1984.
Serafini, P., A unified approach for scalar and vector optimization, in Mathematics for multi objective optimization, Serafini, P., editor, Springer, Vienna, 1985.
Veinott, A.F., and Dantzig, G.B., Integral extreme points, SIAM Rev. 10 (1968) 371–372.
Villareal, B., and Karwan, M.H., Multicriteria integer programming: a (hybrid)dynamic programming recursive approach, Math. Progr. 21 (1981) 204–223.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Serafini, P. (1987). Some Considerations about Computational Complexity for Multi Objective Combinatorial Problems. In: Jahn, J., Krabs, W. (eds) Recent Advances and Historical Development of Vector Optimization. Lecture Notes in Economics and Mathematical Systems, vol 294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46618-2_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-46618-2_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18215-3
Online ISBN: 978-3-642-46618-2
eBook Packages: Springer Book Archive