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Nash equilibrium for a multiobjective control problem related to wastewater management

Néstor García-Chan, Rafael Muñoz-Sola, Miguel Ernesto Vázquez-Méndez (2009)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is concerned with mathematical modelling in the management of a wastewater treatment system. The problem is formulated as looking for a Nash equilibrium of a multiobjective pointwise control problem of a parabolic equation. Existence of solution is proved and a first order optimality system is obtained. Moreover, a numerical method to solve this system is detailed and numerical results are shown in a realistic situation posed in the estuary of Vigo (Spain).


Nature–inspired metaheuristic algorithms to find near–OGR sequences for WDM channel allocation and their performance comparison

Shonak Bansal, Neena Gupta, Arun Kumar Singh (2017)

Open Mathematics

Nowadays, nature–inspired metaheuristic algorithms are most powerful optimizing algorithms for solving the NP–complete problems. This paper proposes three approaches to find near–optimal Golomb ruler sequences based on nature–inspired algorithms in a reasonable time. The optimal Golomb ruler (OGR) sequences found their application in channel–allocation method that allows suppression of the crosstalk due to four–wave mixing in optical wavelength division multiplexing systems. The simulation results...

Neural networks learning as a multiobjective optimal control problem.

Maciej Krawczak (1997)

Mathware and Soft Computing

The supervised learning process of multilayer feedforward neural networks can be considered as a class of multi-objective, multi-stage optimal control problem. An iterative parametric minimax method is proposed in which the original optimization problem is embedded into a weighted minimax formulation. The resulting auxiliary parametric optimization problems at the lower level have simple structures that are readily tackled by efficient solution methods, such as the dynamic programming or the error...

Niching mechanisms in evolutionary computations

Zdzisław Kowalczuk, Tomasz Białaszewski (2006)

International Journal of Applied Mathematics and Computer Science

Different types of niching can be used in genetic algorithms (GAs) or evolutionary computations (ECs) to sustain the diversity of the sought optimal solutions and to increase the effectiveness of evolutionary multi-objective optimization solvers. In this paper four schemes of niching are proposed, which are also considered in two versions with respect to the method of invoking: a continuous realization and a periodic one. The characteristics of these mechanisms are discussed, while as their performance...

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