'Centre for Evaluation in Education and Science (CEON/CEES)'
Doi
Abstract
Introduction/purpose: In this paper, a new solution for solving a multiobjective integer programming problem with probabilistic multi – objective
optimization is formulated. Furthermore, discretization by means of the
good lattice point and sequential optimization are employed for a
successive simplifying treatment and deep optimization.
Methods: In probabilistic multi – objective optimization, a new concept of
preferable probability has been introduced to describe the preference
degree of each performance utility of a candidate; each performance utility
of a candidate contributes a partial preferable probability and the product of
all partial preferable probabilities deduces the total preferable probability of
a candidate; the total preferable probability thus transfers a multi-objective
problem into a single-objective one. Discretization by means of the good
lattice point is employed to conduct discrete sampling for a continuous
objective function and sequential optimization is used to perform deep
optimization. At first, the requirements of integers in the treatment could be
given up so as to simply conduct above procedures. Finally, the optimal
solutions of the input variables must be rounded to the nearest integers.
Results: This new scheme is used to deal with two production problems,
i.e., maximizing profit while minimizing pollution and determining a
purchasing plan for spending as little money as possible while getting as
large amount of raw materials as possible. Promising results are obtained
for the above two problems from the viewpoint of the probability theory for
simultaneous optimization of multiple objectives. Conclusion: This method properly considers simultaneous optimization of
multiple objectives in multi-objective integer programming, which naturally
reflects the essence of multi-objective programming, and opens a new way
of solving multi-objective problems
