α-Pareto optimal solutions for fuzzy multiple objective optimization problems using MATLAB

2018 ◽  
Vol 73 (2) ◽  
pp. 53-59
Author(s):  
Tarek Abou-El-Enien
Keyword(s):  
Optimization Problems ◽  
Multiple Objective ◽  
Multiple Objective Optimization ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions

scholarly journals A Quantum Adiabatic Algorithm for Multiobjective Combinatorial Optimization

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 32 ◽  
Author(s):  
Benjamín Barán ◽  
Marcos Villagra
Keyword(s):  
Combinatorial Optimization ◽  
Multiobjective Optimization ◽  
Theorem Proving ◽  
Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Quantum Annealing ◽  
Multiobjective Optimization Problems ◽  
First Time

In this work we show how to use a quantum adiabatic algorithm to solve multiobjective optimization problems. For the first time, we demonstrate a theorem proving that the quantum adiabatic algorithm can find Pareto-optimal solutions in finite-time, provided some restrictions to the problem are met. A numerical example illustrates an application of the theorem to a well-known problem in multiobjective optimization. This result opens the door to solve multiobjective optimization problems using current technology based on quantum annealing.

Presorting as a method of acceleration of algorithms in multi-objective optimization problems

2016 ◽  
Vol 0 (0) ◽  
pp. 5-11
Author(s):  
Andrzej Ameljańczyk
Keyword(s):  
Distance Function ◽  
Pareto Front ◽  
Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Minkowski Distance ◽  
Finite Set ◽  
Feasible Solutions

The paper presents a method of algorithms acceleration for determining Pareto-optimal solutions (Pareto Front) multi-criteria optimization tasks, consisting of pre-ordering (presorting) set of feasible solutions. It is proposed to use the generalized Minkowski distance function as a presorting tool that allows build a very simple and fast algorithm Pareto Front for the task with a finite set of feasible solutions.

Evaluating the ε-Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions

2005 ◽  
Vol 13 (4) ◽  
pp. 501-525 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Manikanth Mohan ◽  
Shikhar Mishra
Keyword(s):  
Steady State ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Computational Time ◽  
Test Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Nsga Ii ◽  
Multi Objective

Since the suggestion of a computing procedure of multiple Pareto-optimal solutions in multi-objective optimization problems in the early Nineties, researchers have been on the look out for a procedure which is computationally fast and simultaneously capable of finding a well-converged and well-distributed set of solutions. Most multi-objective evolutionary algorithms (MOEAs) developed in the past decade are either good for achieving a well-distributed solutions at the expense of a large computational effort or computationally fast at the expense of achieving a not-so-good distribution of solutions. For example, although the Strength Pareto Evolutionary Algorithm or SPEA (Zitzler and Thiele, 1999) produces a much better distribution compared to the elitist non-dominated sorting GA or NSGA-II (Deb et al., 2002a), the computational time needed to run SPEA is much greater. In this paper, we evaluate a recently-proposed steady-state MOEA (Deb et al., 2003) which was developed based on the ε-dominance concept introduced earlier (Laumanns et al., 2002) and using efficient parent and archive update strategies for achieving a well-distributed and well-converged set of solutions quickly. Based on an extensive comparative study with four other state-of-the-art MOEAs on a number of two, three, and four objective test problems, it is observed that the steady-state MOEA is a good compromise in terms of convergence near to the Pareto-optimal front, diversity of solutions, and computational time. Moreover, the ε-MOEA is a step closer towards making MOEAs pragmatic, particularly allowing a decision-maker to control the achievable accuracy in the obtained Pareto-optimal solutions.

scholarly journals Sensitivity analysis for parametric vector optimization problems using differential equations approach

2001 ◽  
Vol 25 (9) ◽  
pp. 621-628
Author(s):  
Fatma M. Ali
Keyword(s):  
Differential Equations ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Vector Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Parametric Vector Optimization ◽  
Local Solutions

A new method for obtaining sensitivity information for parametric vector optimization problems(VOP)vis presented, where the parameters in the objective functions and anywhere in the constraints. This method depends on using differential equations technique for solving multiobjective nonlinear programing problems which is very effective in finding many local Pareto optimal solutions. The behavior of the local solutions for slight perturbation of the parameters in the neighborhood of their chosen initial values is presented by using the technique of trajectory continuation. Finally some examples are given to show the efficiency of the proposed method.

A Newton method for capturing Pareto optimal solutions of fuzzy multiobjective optimization problems

2019 ◽  
Vol 53 (3) ◽  
pp. 867-886
Author(s):  
Mehrdad Ghaznavi ◽  
Narges Hoseinpoor ◽  
Fatemeh Soleimani
Keyword(s):  
Multiobjective Optimization ◽  
Newton Method ◽  
Optimization Problems ◽  
Order Relation ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multiobjective Optimization Problems ◽  
Generalized Hukuhara Differentiability

In this study, a Newton method is developed to obtain (weak) Pareto optimal solutions of an unconstrained multiobjective optimization problem (MOP) with fuzzy objective functions. For this purpose, the generalized Hukuhara differentiability of fuzzy vector functions and fuzzy max-order relation on the set of fuzzy vectors are employed. It is assumed that the objective functions of the fuzzy MOP are twice continuously generalized Hukuhara differentiable. Under this assumption, the relationship between weakly Pareto optimal solutions of a fuzzy MOP and critical points of the related crisp problem is discussed. Numerical examples are provided to demonstrate the efficiency of the proposed methodology. Finally, the convergence analysis of the method under investigation is discussed.

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