Evolutionary Metaheuristics to Solve Multiobjective Assignment Problem in Telecommunication Network

2020 ◽  
Vol 11 (2) ◽  
pp. 56-76
Author(s):  
Benkanoun Yazid ◽  
Bouroubi Sadek ◽  
Chaabane Djamal
Keyword(s):  
Evolutionary Algorithm ◽  
Large Scale ◽  
Optimization Problems ◽  
Choquet Integral ◽  
Telecommunication Network ◽  
Exact Algorithms ◽  
Nsga Ii ◽  
Pareto Optimal Set ◽  
System A ◽  
Integral Measure

The authors propose a computing approach for solving a multiobjective problem in the telecommunication network field, suggested by an Algerian industrial company. The principal goal is in developing a palliative solution to overcome some generated problems existing in the current management system. A mathematical operational model has been established. The exact algorithms that solve multiobjective optimization problems are not appropriate for large scale problems. However, the application of metaheuristics approach leads perfectly to approximate the Pareto optimal set. In this paper, the authors apply a well-known multiobjective evolutionary algorithm, the Non-dominated Sorting Genetic Algorithm (NSGA-II), compare the obtained results with those generated by the Strength Pareto Evolutionary Algorithm-II (SPEA2) and propose a way to help the decision maker, who is often confronted with the choice of a final solution, to make his preferences afterward using a utility function based on a Choquet integral measure. Finally, numerical experiments are presented to validate the approach.

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.

Optimization Design of a Walkable Fixture Mechanism

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Xiao-Jin Wan ◽  
Hanjie Zhang
Keyword(s):  
Performance Optimization ◽  
Error Propagation ◽  
Optimization Design ◽  
Large Scale ◽  
Optimization Problems ◽  
Optimization Procedure ◽  
Singular Values ◽  
Legged Robot ◽  
Nsga Ii ◽  
Propagation Matrix

In this paper, a novel fixture mechanism with combining a mobility of the legged robot and advantages of parallel mechanism is designed to hold the different size and shape, large-scale workpiece. The proposed mobile fixture mechanism holds the workpiece as a parallel manipulator while it walks as a legged robot. This kind of robotized fixtures can possess high self-configurable ability to accommodate a wider variety of products. In order to obtain the best kinematic dexterity and accuracy characteristics, comprehensive performance optimization is performed by non-dominated-genetic algorithm (NSGA-II). In the optimization procedure, a conventional kinematic transformation matrix (Jacobian matrix) and error propagation matrix are obtained through derivation and differential motion operations. The singular values and condition number based on velocity Jacobians and error amplification factors based on error propagation matrix are derived; in addition, relative pose error range of end effector is also derived. On the basis of the above measure indices, three kinds of nonlinear optimization problems are defined to obtain the optimal architecture parameters for better kinematic accuracy and dexterity in workspace. Comparison analyses of the optimized results are performed.

Comprehensive Survey of the Hybrid Evolutionary Algorithms

2013 ◽  
Vol 4 (2) ◽  
pp. 1-19 ◽  
Author(s):  
Wali Khan Mashwani
Keyword(s):  
Evolutionary Algorithms ◽  
Pareto Front ◽  
Optimization Problems ◽  
Mathematical Formulation ◽  
Multiobjective Evolutionary Algorithms ◽  
Nsga Ii ◽  
Pareto Optimal Set ◽  
Multiobjective Optimization Problems ◽  
Comprehensive Survey ◽  
Optimal Set

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) and an improved non-dominating sorting multiobjective genetic algorithm (NSGA-II) is two well known multiobjective evolutionary algorithms (MOEAs) in the field of evolutionary computation. This paper mainly reviews their hybrid versions and some other algorithms which are developed for solving multiobjective optimization problems (MOPs. The mathematical formulation of a MOP and some basic definitions for tackling MOPs, including Pareto optimality, Pareto optimal set (PS), Pareto front (PF) are provided in Section 1. Section 2 presents a brief introduction to hybrid MOEAs. The authors present literature review in subsections. Subsection 2.1 provides memetic multiobjective evolutionary algorithms. Subsection 2.2 presents the hybrid versions of well-known Pareto dominance based MOEAs. Subsection 2.4 summarizes some enhanced Versions of MOEA/D paradigm. Subsection 2.5 reviews some multimethod search approaches dealing optimization problems.

A Novel Objective Grouping Evolutionary Algorithm for Many-Objective Optimization Problems

2019 ◽  
Vol 34 (06) ◽  
pp. 2059018
Author(s):  
Xiaofang Guo ◽  
Xiaoli Wang
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Computational Cost ◽  
Pareto Solutions ◽  
Nsga Ii ◽  
Space Partition ◽  
Dominance Structure ◽  
Objective Reduction ◽  
Original Objective ◽  
Nondominated Sorting

The thorniest difficulties for multi-objective evolutionary algorithms (MOEAs) handling many-objective optimization problems (MaOPs) are the inefficiency of selection operators and high computational cost. To alleviate such difficulties and simplify the MaOPs, objective reduction algorithms have been proposed to remove the redundant objectives during the search process. However, those algorithms can only be applicable to specific problems with redundant objectives. Worse still, the Pareto solutions obtained by reduced objective set may not be the Pareto solutions of the original MaOPs. In this paper, we present a novel objective grouping evolutionary algorithm (OGEA) for general MaOPs. First, by dividing original objective set into several overlapping lower-dimensional subsets in terms of interdependence correlation information, we aim to separate the MaOPs into a number of sub-problems so that each of them can be able to preserve as much dominance structure in the original objective set as possible. Subsequently, we employ the nondominated sorting genetic algorithm II (NSGA-II) to generate Pareto solutions. Besides, instead of nondominated sorting on the whole population, a novel dual selection mechanism is proposed to choose individuals either having high ranks in subspaces or locating sparse region in the objective space for better proximity and diversity. Finally, we compare the proposed strategy with the other two classical space partition methods on benchmark DTLZ5 (I, M), DTLZ2 and a practical engineering problem. Numerical results show the proposed objective grouping algorithm can preserve more dominance structure in original objective set and achieve better quality of Pareto solutions.

scholarly journals An Environmental Selection and Transfer Learning Based Dynamic Multiobjective Optimization Evolutionary Algorithm

2021 ◽  
Author(s):  
Qiang He ◽  
Zheng Xiang ◽  
Peng Ren
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Transfer Learning ◽  
Optimization Problems ◽  
Evolutionary Process ◽  
Pareto Optimal ◽  
Nsga Ii ◽  
Environmental Selection ◽  
Dynamic Multiobjective Optimization ◽  
Prediction Strategy

Abstract In recent years, the dynamic multiobjective optimization problems (DMOPs), whose major strategy is to track the varying PS (Pareto Optimal Solution, PS) and/or PF (Pareto Optimal Frontier), caused a great deal of attention worldwide. As a promising solution, reusing of “experiences” to establish a prediction model is proved to be very useful and widely used in practice. However, most existing methods overlook the importance of environmental selection in the evolutionary processes. In this paper, we propose a dynamic multiobjective optimal evolutionary algorithm which is based on environmental selection and transfer learning (DMOEA-ESTL). This approach makes full use of the environmental selection and transfer learning technique to generate individuals for a new environment by reusing experience to maintain the diversity of the population and speed up the evolutionary process. As experimental validation, we embed this new scheme in the NSGA-II (non-dominated sorting genetic algorithm). We test the proposed algorithm with the help of six benchmark functions as well as compare it with the other two prediction based strategies FPS (Forward-looking Prediction Strategy, FPS) and PPS (Population Prediction Strategy, PPS). The experimental results testify that the proposed strategy can deal with the DMOPs effectively.

Multimodal Optimization Using a Bi-Objective Evolutionary Algorithm

2012 ◽  
Vol 20 (1) ◽  
pp. 27-62 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Amit Saha
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Search Space ◽  
Test Problems ◽  
Multimodal Optimization ◽  
Optimal Solutions ◽  
Optimization Task ◽  
Pareto Optimal Set ◽  
Single Objective

In a multimodal optimization task, the main purpose is to find multiple optimal solutions (global and local), so that the user can have better knowledge about different optimal solutions in the search space and as and when needed, the current solution may be switched to another suitable optimum solution. To this end, evolutionary optimization algorithms (EA) stand as viable methodologies mainly due to their ability to find and capture multiple solutions within a population in a single simulation run. With the preselection method suggested in 1970, there has been a steady suggestion of new algorithms. Most of these methodologies employed a niching scheme in an existing single-objective evolutionary algorithm framework so that similar solutions in a population are deemphasized in order to focus and maintain multiple distant yet near-optimal solutions. In this paper, we use a completely different strategy in which the single-objective multimodal optimization problem is converted into a suitable bi-objective optimization problem so that all optimal solutions become members of the resulting weak Pareto-optimal set. With the modified definitions of domination and different formulations of an artificially created additional objective function, we present successful results on problems with as large as 500 optima. Most past multimodal EA studies considered problems having only a few variables. In this paper, we have solved up to 16-variable test problems having as many as 48 optimal solutions and for the first time suggested multimodal constrained test problems which are scalable in terms of number of optima, constraints, and variables. The concept of using bi-objective optimization for solving single-objective multimodal optimization problems seems novel and interesting, and more importantly opens up further avenues for research and application.

scholarly journals A Customized Differential Evolutionary Algorithm for Bounded Constrained Optimization Problems

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
Wali Khan Mashwani ◽  
Zia Ur Rehman ◽  
Maharani A. Bakar ◽  
Ismail Koçak ◽  
Muhammad Fayaz
Keyword(s):  
Evolutionary Algorithms ◽  
Constrained Optimization ◽  
Evolutionary Algorithm ◽  
Evolutionary Computation ◽  
Large Scale ◽  
Optimization Problems ◽  
Science And Engineering ◽  
De Algorithm ◽  
Differential Evolutionary Algorithm ◽  
Nature Inspired Algorithms

Bound-constrained optimization has wide applications in science and engineering. In the last two decades, various evolutionary algorithms (EAs) were developed under the umbrella of evolutionary computation for solving various bound-constrained benchmark functions and various real-world problems. In general, the developed evolutionary algorithms (EAs) belong to nature-inspired algorithms (NIAs) and swarm intelligence (SI) paradigms. Differential evolutionary algorithm is one of the most popular and well-known EAs and has secured top ranks in most of the EA competitions in the special session of the IEEE Congress on Evolutionary Computation. In this paper, a customized differential evolutionary algorithm is suggested and applied on twenty-nine large-scale bound-constrained benchmark functions. The suggested C-DE algorithm has obtained promising numerical results in its 51 independent runs of simulations. Most of the 2013 IEEE-CEC benchmark functions are tackled efficiently in terms of proximity and diversity.

Comprehensive Survey of the Hybrid Evolutionary Algorithms

2015 ◽  
pp. 322-343
Author(s):  
Wali Khan Mashwani
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Mathematical Formulation ◽  
Multiobjective Evolutionary Algorithms ◽  
Nsga Ii ◽  
Pareto Optimal Set ◽  
Multiobjective Optimization Problems ◽  
Comprehensive Survey ◽  
Hybrid Evolutionary Algorithms ◽  
Optimal Set

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) and an improved non-dominating sorting multiobjective genetic algorithm (NSGA-II) are two well known multiobjective evolutionary algorithms (MOEAs) in the field of evolutionary computation. This paper mainly reviews their hybrid versions and some other algorithms which are developed for solving multiobjective optimization problems (MOPs. The mathematical formulation of a MOP and some basic definitions for tackling MOPs, including Pareto optimality, Pareto optimal set (PS), Pareto front (PF) are provided in Section 1. Section 2 presents a brief introduction to hybrid MOEAs. The authors present literature review in subsections. Subsection 2.1 provides memetic multiobjective evolutionary algorithms. Subsection 2.2 presents the hybrid versions of well-known Pareto dominance based MOEAs. Subsection 2.4 summarizes some enhanced Versions of MOEA/D paradigm. Subsection 2.5 reviews some multimethod search approaches dealing optimization problems.

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