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Stutzle, T. and Hoos, H. (1997) Max-Min Ant System and Local Search for the Travelling Salesman Problem. In: IEEE International Conference on Evolutionary Computation, IEEE Press, Piscataway, 309-314.

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• TITLE: Bi-Objective Optimization: A Pareto Method with Analytical Solutions

  AUTHORS: David W. K. Yeung, Yingxuan Zhang

  KEYWORDS: Multi-Objective Optimization, Pareto Optimal Front, Analytical Solution, Lagrange Method, Karush-Kuhn-Tucker Conditions

  JOURNAL NAME: Applied Mathematics, Vol.14 No.1, January 20, 2023

  ABSTRACT: Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front is obtained in closed-form, enabling the derivation of various solutions in a convenient and efficient way. The advantage of analytical solution is the possibility of deriving accurate, exact and well-understood solutions, which is especially useful for policy analysis. An extension of the method to include multiple objectives is provided with the objectives being classified into two types. Such an extension expands the applicability of the developed techniques.