On Finding the Maxima of a Set of Vectors
Journal of the ACM (JACM)
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
On the Performance Assessment and Comparison of Stochastic Multiobjective Optimizers
PPSN IV Proceedings of the 4th International Conference on Parallel Problem Solving from Nature
On the Normal Boundary Intersection Method for Generation of Efficient Front
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
In Search of Proper Pareto-optimal Solutions Using Multi-objective Evolutionary Algorithms
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part IV: ICCS 2007
An efficient non-dominated sorting method for evolutionary algorithms
Evolutionary Computation
Multiobjective Optimization: Interactive and Evolutionary Approaches
Multiobjective Optimization: Interactive and Evolutionary Approaches
Benefits of a population: five mechanisms that advantage population-based algorithms
IEEE Transactions on Evolutionary Computation
A framework for incorporating trade-off information using multi-objective evolutionary algorithms
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part II
A review of multiobjective test problems and a scalable test problem toolkit
IEEE Transactions on Evolutionary Computation
A Levenberg-Marquardt algorithm for unconstrained multicriteria optimization
Operations Research Letters
An evolutionary optimization approach for bulk material blending systems
PPSN'12 Proceedings of the 12th international conference on Parallel Problem Solving from Nature - Volume Part I
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A multi-objective optimization problem is characterized by multiple and conflicting objective functions. The conflicting nature of the objectives gives rise to the notion of trade-offs. A trade-off represents the ratio of change in the objective function values, when one of the objective function values increases and the value of some other objective function decreases. Various notions of trade-offs have been present in the classical multiple criteria decision making community and many scalarization approaches have been proposed in the literature to find a solution satisfying some given trade-off requirements. Almost all of these approaches are point-by-point algorithms. On the other hand, multi-objective evolutionary algorithms work with a population and, if properly designed, are able to find the complete preferred subset of the Pareto-optimal set satisfying an a priori given bound on trade-offs. In this paper, we analyze and put together various notions of trade-offs that we find in the classical literature, classifying them into two groups. We then go on to propose multi-objective evolutionary algorithms to find solutions belonging to the two classified groups. This is done by modifying a state-of-the-art evolutionary algorithm NSGA-II. An extensive computational study substantiates the claims of the paper.