A study of interval metric and its application in multi-objective optimization with interval objectives

•Proposed new definition of interval order relations.•Proposed new definition of interval metric.•Theoretical development of multi-objective optimization in interval domain.•Developed Tournament Genetic Algorithm for solving multi-objective optimization problem in interval domain. The aim of this pa...

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Bibliographic Details
Published in:Computers & industrial engineering 2014-08, Vol.74, p.169-178
Main Authors: Bhunia, Asoke Kumar, Samanta, Subhra Sankha
Format: Article
Language:English
Subjects:
Boundaries
Computer simulation
Genetic algorithms
Interval objective
Interval order relations
Intervals
Mathematical models
Multiple objective programming
Mutation
Mutations
Optimization
Optimization algorithms
Pareto optimality
Pareto optimum
Sensitivity analysis
Studies
Tournament Genetic Algorithm
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Summary:•Proposed new definition of interval order relations.•Proposed new definition of interval metric.•Theoretical development of multi-objective optimization in interval domain.•Developed Tournament Genetic Algorithm for solving multi-objective optimization problem in interval domain. The aim of this paper is to discuss the optimality of interval multi-objective optimization problems with the help of different interval metric. For this purpose, we have proposed the new definitions of interval order relations by modifying the existing definitions and also modified different definitions of interval mathematics. Using the definitions of interval order relations and interval metric, the multi-objective optimization problem is converted into single objective optimization problem by different techniques. Then the corresponding problems have been solved by hybrid Tournament Genetic Algorithm with whole arithmetic crossover and double mutation (combination of non-uniform and boundary mutations). To illustrate the methodology, five numerical examples have been solved and the computational results have been compared. Finally, to test the efficiency of the proposed hybrid Tournament Genetic Algorithm, sensitivity analyses have been carried out graphically with respect to genetic algorithm parameters.
ISSN:0360-8352
1879-0550
DOI:10.1016/j.cie.2014.05.014