### The Use of Fuzzy Interval Genetic Algorithm for Solving Multiobjective Nonlinear Mixed Integer Programming Model

Abstract

Multiple conflicting objectives characterize many management systems. In the typical problem of siting facilities, various linear types of large scale multiobjective mixed integer programming models (locational models) are frequently used in search of the satisfactory solution. However, due to the intrinsic complexity existing in the real world systems, nonlinear formulations are inevitably encountered in either the objective functions or the constraints in the modelling process. It is known that genetic algorithm technique is capable of solving complex multimodal decision spaces and is efficient in handling nonlinear types of problems. This paper presents a new approach by using the fuzzy interval genetic algorithm (FIGA) for solving the multiobjective nonlinear mixed integer programming model with uncertain information. When the decision variables are defined in a fuzzy environment and the parameters are described with grey expressions, the description of those uncertain information is then incorporated into the random search in the genetic algorithm such that approximate solutions to a nonlinear optimization problem can be produced.