Abstract
We introduce and analyze a novel scalarization technique and an associated algorithm for generating an approximation of the Pareto front (i.e., the efficient set) of nonlinear multiobjective optimization problems. Our approach is applicable to nonconvex problems, in particular to those with disconnected Pareto fronts and disconnected domains (i.e., disconnected feasible sets). We establish the theoretical properties of our new scalarization technique and present an algorithm for its implementation. By means of test problems, we illustrate the strengths and advantages of our approach over existing scalarization techniques such as those derived from the Pascoletti–Serafini method, as well as the popular weighted-sum method.
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Acknowledgements
M.M. Rizvi acknowledges support by a UniSA President’s Scholarship and the School of Mathematics and Statistics at the University of South Australia. The authors would like to thank the Editors and the two reviewers for their constructive comments, which improved the paper.
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Burachik, R.S., Kaya, C.Y. & Rizvi, M.M. A New Scalarization Technique to Approximate Pareto Fronts of Problems with Disconnected Feasible Sets. J Optim Theory Appl 162, 428–446 (2014). https://doi.org/10.1007/s10957-013-0346-0
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DOI: https://doi.org/10.1007/s10957-013-0346-0