Lexicographic Multi-Objective Linear Programming (LMOLP) problems can be solved in two ways: preemptive and nonpreemptive. The preemptive approach requires the solution of a series of LP problems, with changing constraints (each time the next objective is added, a new constraint appears). The nonpreemptive approach is based on a scalarization of the multiple objectives into a single-objective linear function by a weighted combination of the given objectives. It requires the specification of a set of weights, which is not straightforward and can be time consuming. In this work we present both mathematical and software ingredients necessary to solve LMOLP problems using a recently introduced computational methodology (allowing one to work numerically with infinities and infinitesimals) based on the concept of grossone. The ultimate goal of such an attempt is an implementation of a simplex-like algorithm, able to solve the original LMOLP problem by solving only one single-objective problem and without the need to specify finite weights. The expected advantages are therefore obvious.
Towards lexicographic multi-objective linear programming using grossone methodology
Marco Cococcioni, Massimo Pappalardo, Yaroslav D. Sergeyev; Towards lexicographic multi-objective linear programming using grossone methodology. AIP Conf. Proc. 20 October 2016; 1776 (1): 090040. https://doi.org/10.1063/1.4965404
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