Theory of linear and integer programming
Theory of linear and integer programming
A multiobjective methodology for selecting subsystem automation options
Management Science
Integer and combinatorial optimization
Integer and combinatorial optimization
A primal dual integer programming algorithm
Discrete Applied Mathematics - ARIDAM IV and V
Interactive multiobjective optimization system WWW-NIMBUS on the internet
Computers and Operations Research - Special issue on artificial intelligence and decision support with multiple criteria
Two-phases Method and Branch and Bound Procedures to Solve the Bi–objective Knapsack Problem
Journal of Global Optimization
A New Subadditive Approach to Integer Programming
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
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The weighted sums approach for linear and convex multiple criteria optimization is well studied. The weights determine a linear function of the criteria approximating a decision makers overall utility. Any efficient solution may be found in this way. This is not the case for multiple criteria integer programming. However, in this case one may apply the more general e-constraint approach, resulting in particular single-criteria integer programming problems to generate efficient solutions. We show how this approach implies a more general, composite utility function of the criteria yielding a unified treatment of multiple criteria optimization with and without integrality constraints. Moreover, any efficient solution can be found using appropriate composite functions. The functions may be generated by the classical solution methods such as cutting plane and branch and bound algorithms.