Method of Feasible Directions with Hit-and-Run Sampling for Solving Linearly Constrained Multi-Objective Optimization Problems
Description
This Function solves linearly constrained multi-objective optimization problems of the form %%% Min F(x) =[f1(x),f2(x),...fp(x)] %%%%%%subject to A x \leq b, % %%Using Hit-and-Run sampling % Outcomes are illustrated with 2D/3D plots of Pareto fronts and efficient sets. %%% test Problems are numbered consecutively from 1 to 27, collected from the literature. % References: See individual problem comments for citations % Authors: Ramdani Zoubir*, Addoune Smail, Brahmi Boualem % Affiliation: Faculty of Mathematics and Computer Sciences, % University Mohamed El Bachir El Ibrahimi, Bordj Bou Arreridj, Algeria % Corresponding Author: Ramdani Zoubir (z.ramdani@univ-bba.dz) % Requirements: % - MPT3 Toolbox (https://www.mpt3.org/) % - MATLAB 2015 or later % % Inputs: % funcs_obj - Cell array of objective functions {f1, f2, ..., fm} % A - Constraint matrix (Ax <= b) % b - Right-hand side vector of constraints % UB - Upper bounds for variables % LB - Lower bounds for variables % prec - Convergence precision for objective improvement % prec2 - Tolerance for active constraints % max_iter - Maximum number of iterations % sigma - Armijo line search parameter % Type_obj - Optimization type ('min' or 'max') % N - Number of initial feasible solutions % % Outputs: % X_eff_IFD - Matrix of efficient solutions (rows are solutions) % Ynd_IFD - Matrix of non-dominated objective values % CPU_Time_IFD - Vector of CPU times per solution % NB_iter_IFD - Vector of iteration counts % XS0 - Matrix of initial feasible points from Hit-and-Run %
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Institutions
- University Mohamed El Bachir El Ibrahimi of Bordj Bou ArreridjBordj Bou Arréridj, Bordj Bou Arreridj