Mohamed Tifroute | Searcharxiv

arXiv2024

A Sequential Descent Method for Global Optimization

In this paper, a sequential search method for finding the global minimum of an objective function is presented, The descent gradient search is repeated until the global minimum is obtained. The global minimum is located by a process of finding progressively better local minima. We determine the set of points of intersection between the curve of the function and the horizontal plane which contains the local minima previously found. Then, a point in this set with the greatest descent slope is chosen to be a initial point for a new descent gradient search. The method has the descent property and the convergence is monotonic. To demonstrate the effectiveness of the proposed sequential descent method, several non-convex multidimensional optimization problems are solved. Numerical examples show that the global minimum can be sought by the proposed method of sequential descent.

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arXiv2020

Solving Nonsmooth Bi-Objective Environmental andEconomic Dispatch Problem using Smoothing Techniques

The Environmental and Economic Dispatch problem (EEDP)is a nonlinear Multi-objective Optimization Problem (MOP) which simultaneously satisfies multiple contradictory criteria, and it's a nonsmooth problem when valvepoint effects, multi-fuel effects and prohibited operating zones have been considered. It is an important optimization task in fossil fuel fired power plant operation for allocating generation among the committed units such that fuel cost and pollution (emission level) are optimized simultaneously while satisfying all operational constraints. In this paper, we use smoothing functions with the gradient consistency property to approximate the nonsmooth multi-objective Optimization problem. Our approach is based on the smoothing method. In fact, we explain the convergence analysis of smoothing method by using approximate Karush-Kuhn-Tucker condition, which is necessary for a point to be a local weak efficient solution and is also sufficient under convexity assumptions. Finally, we give an application of our approach for solving the bi-objective EEDP.

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