Three-Objective Programming with Continuous Variable Genetic Algorithm

Author(s)
Adugna Fita

Abstract

The subject area of multiobjective optimization deals with the investigation of optimization problems that possess more than one objective function. Usually, there does not exist a single solution that optimizes all functions simultaneously; quite the contrary, we have solution set that is called nondominated set and elements of this set are usually infinite. It is from this set decision made by taking elements of nondominated set as alternatives, which is given by analysts. Since it is important for the decision maker to obtain as much information as possible about this set, our research objective is to determine a well-defined and meaningful approximation of the solution set for linear and nonlinear three objective optimization problems. In this paper a continuous variable genetic algorithm is used to find approximate near optimal solution set. Objective functions are considered as fitness function without modification. Initial solution was generated within box constraint and solutions will be kept in feasible region during mutation and recombination.

The subject area of multiobjective optimization deals with the investigation of optimization problems that possess more than one objective function. Usually, there does not exist a single solution that optimizes all functions simultaneously; quite the contrary, we have solution set that is called nondominated set and elements of this set are usually infinite. It is from this set decision made by taking elements of nondominated set as alternatives, which is given by analysts. Since it is important for the decision maker to obtain as much information as possible about this set, our research objective is to determine a well-defined and meaningful approximation of the solution set for linear and nonlinear three objective optimization problems. In this paper a continuous variable genetic algorithm is used to find approximate near optimal solution set. Objective functions are considered as fitness function without modification. Initial solution was generated within box constraint and solutions will be kept in feasible region during mutation and recombination.

Keywords

Chromosome, Crossover, Heuristics, Mutation, Optimization, Population, Ranking, Genetic Algorithms, Multi-Objective, Pareto Optimal Solutions, Parent Selection

Chromosome, Crossover, Heuristics, Mutation, Optimization, Population, Ranking, Genetic Algorithms, Multi-Objective, Pareto Optimal Solutions, Parent Selection

Cite this paper

Fita, A. (2014) Three-Objective Programming with Continuous Variable Genetic Algorithm.*Applied Mathematics*, **5**, 3297-3310. doi: 10.4236/am.2014.521307.

Fita, A. (2014) Three-Objective Programming with Continuous Variable Genetic Algorithm.

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