Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Evolutionary Algorithms for Solving Multi-Objective Problems
Evolutionary Algorithms for Solving Multi-Objective Problems
Through the Labyrinth Evolution Finds a Way: A Silicon Ridge
ICES '96 Proceedings of the First International Conference on Evolvable Systems: From Biology to Hardware
Metaheuristics in combinatorial optimization: Overview and conceptual comparison
ACM Computing Surveys (CSUR)
Benefits and drawbacks for the use of epsilon-dominance in evolutionary multi-objective optimization
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Pareto-, aggregation-, and indicator-based methods in many-objective optimization
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
On the effect of populations in evolutionary multi-objective optimisation**
Evolutionary Computation
Combinatorial Optimization: Theory and Algorithms
Combinatorial Optimization: Theory and Algorithms
Effects of removing overlapping solutions on the performance of the NSGA-II algorithm
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
IEEE Transactions on Evolutionary Computation
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
IEEE Transactions on Evolutionary Computation
MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition
IEEE Transactions on Evolutionary Computation
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Objective functions in combinatorial optimization are discrete. The number of possible values of a discrete objective function is totally different from problem to problem. Optimization of a discrete objective function is often very difficult. In the case of multiobjective optimization, a different objective function has a different number of possible values. This means that each axis of the objective space has a different granularity. Some axes may have fine granularities while others are coarse. In this paper, we examine the effect of discrete objective functions with different granularities on the search behavior of EMO (evolutionary multiobjective optimization) algorithms through computational experiments. Experimental results show that a discrete objective function with a coarse granularity slows down the search of EMO algorithms along that objective. An interesting observation is that such a slow-down along one objective often leads to the speed-up of the search along other objectives. We also examine the effect of adding a small random noise to each discrete objective function in order to increase the number of possible objective values.