We consider a non-linear version of the Generalized Assignment Problem, a well-known strongly NP-hard combinatorial optimization problem. We assume that the variables are continuous and that objective function and constraints are defined by non-linear functions of the variables. A mathematical model is introduced and used to derive upper bounds on the optimal solution value. We present constructive heuristics, obtained from decomposition and non-linear programming tools, and a binary linear programming model that provides approximate solutions. By combining the various methods and a local search framework, we finally obtain a hybrid heuristic approach. Extensive computational experiments show that the proposed methods outperform the direct application of non-linear solvers and provide high quality solutions in a reasonable amount of time.

Lower and upper bounds for the non-linear generalized assignment problem

Martello S.
;
Monaci M.
2020

Abstract

We consider a non-linear version of the Generalized Assignment Problem, a well-known strongly NP-hard combinatorial optimization problem. We assume that the variables are continuous and that objective function and constraints are defined by non-linear functions of the variables. A mathematical model is introduced and used to derive upper bounds on the optimal solution value. We present constructive heuristics, obtained from decomposition and non-linear programming tools, and a binary linear programming model that provides approximate solutions. By combining the various methods and a local search framework, we finally obtain a hybrid heuristic approach. Extensive computational experiments show that the proposed methods outperform the direct application of non-linear solvers and provide high quality solutions in a reasonable amount of time.
D'Ambrosio C.; Martello S.; Monaci M.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/764101
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