Improved NSGAII with a New Distribution and its Application in Multi-Objective Reservoir Operation

2011 ◽  
Vol 90-93 ◽  
pp. 2734-2739
Author(s):  
Ruan Yun ◽  
Cui Song Yu
Keyword(s):  
Genetic Algorithms ◽  
Control Strategy ◽  
Reservoir Operation ◽  
Large Scale ◽  
Pareto Front ◽  
Optimization Problem ◽  
Shape Parameter ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
New Distribution

Non-dominated sorting genetic algorithms II (NSGAII) has been widely used for multi- objective optimizations. To overcome its premature shortcoming, an improved NSGAII with a new distribution was proposed in this paper. Comparative to NSGAII, improved NSGAII uses an elitist control strategy to protect its lateral diversity among current non-dominated fronts. To implement elitist control strategy, a new distribution (called dogmatic distribution) was proposed. For ordinary multi-objective optimization problem (MOP), an ordinary exploration ability of improved NSGAII should be maintained by using a larger shape parameter r; while for larger-scale complex MOP, a larger exploration ability of improved NSGAII should be maintained by using a less shape parameter r. The application of improved NSGAII in multi-objective operation of Wohu reservoir shows that improved NSGAII has advantages over NSGAII to get better Pareto front especially for large-scale complex multi-objective reservoir operation problems.

Toward the Use of Pareto Performance Solutions and Pareto Robustness Solutions for Multi-Objective Robust Optimization Problems

2012 ◽  
Author(s):  
Weijun Wang ◽  
Stéphane Caro ◽  
Fouad Bennis ◽  
Oscar Brito Augusto
Keyword(s):  
Robust Optimization ◽  
Pareto Front ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Multi Objective Optimization ◽  
Robust Solutions ◽  
Multi Objective ◽  
Robust Optimization Problem ◽  
Design Solutions ◽  
Further Development

For Multi-Objective Robust Optimization Problem (MOROP), it is important to obtain design solutions that are both optimal and robust. To find these solutions, usually, the designer need to set a threshold of the variation of Performance Functions (PFs) before optimization, or add the effects of uncertainties on the original PFs to generate a new Pareto robust front. In this paper, we divide a MOROP into two Multi-Objective Optimization Problems (MOOPs). One is the original MOOP, another one is that we take the Robustness Functions (RFs), robust counterparts of the original PFs, as optimization objectives. After solving these two MOOPs separately, two sets of solutions come out, namely the Pareto Performance Solutions (PP) and the Pareto Robustness Solutions (PR). Make a further development on these two sets, we can get two types of solutions, namely the Pareto Robustness Solutions among the Pareto Performance Solutions (PR(PP)), and the Pareto Performance Solutions among the Pareto Robustness Solutions (PP(PR)). Further more, the intersection of PR(PP) and PP(PR) can represent the intersection of PR and PP well. Then the designer can choose good solutions by comparing the results of PR(PP) and PP(PR). Thanks to this method, we can find out the optimal and robust solutions without setting the threshold of the variation of PFs nor losing the initial Pareto front. Finally, an illustrative example highlights the contributions of the paper.

scholarly journals Direct Tracking of the Pareto Front of a Multi-Objective Optimization Problem

2020 ◽  
Vol 8 (9) ◽  
pp. 699
Author(s):  
Daniele Peri
Keyword(s):  
Pareto Front ◽  
Optimization Problem ◽  
Ship Design ◽  
Multi Objective Optimization ◽  
Design Problems ◽  
Multi Objective ◽  
Regular Sampling ◽  
Normal Boundary ◽  
Direct Tracking ◽  
Local Sampling

In this paper, some methodologies aimed at the identification of the Pareto front of a multi-objective optimization problem are presented and applied. Three different approaches are presented: local sampling, Pareto front resampling and Normal Boundary Intersection (NBI). A first approximation of the Pareto front is obtained by a regular sampling of the design space, and then the Pareto front is improved and enriched using the other two above mentioned techniques. A detailed Pareto front is obtained for an optimization problem where algebraic objective functions are applied, also in comparison with standard techniques. Encouraging results are also obtained for two different ship design problems. The use of the algebraic functions allows for a comparison with the real Pareto front, correctly detected. The variety of the ship design problems allows for a generalization of the applicability of the methodology.

A Lion’s Pride Inspired Algorithm for VLSI Floorplanning

2019 ◽  
Vol 29 (01) ◽  
pp. 2050003
Author(s):  
Lalin L. Laudis ◽  
N. Ramadass
Keyword(s):  
Design Process ◽  
Integrated Circuit ◽  
Large Scale ◽  
Optimization Problem ◽  
Standard Test ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Scale Integration ◽  
Vlsi Floorplanning

The complexity of any integrated circuit pushes the researchers to optimize the various parameters in the design process. Usually, the Nondeterministic Polynomial problems in the design process of Very Large Scale Integration (VLSI) are considered as a Single Objective Optimization Problem (SOOP). However, due to the increasing demand for the multi-criterion optimization, researchers delve up on Multi-Objective Optimization methodologies to solve a problem with multiple objectives. Moreover, it is evident from the literature that biologically inspired algorithm works very well in optimizing a Multi-Objective Optimization Problem (MOOP). This paper proposes a new Lion’s pride inspired algorithm to solve any MOOP. The methodologies mimic the traits of a Lion which always strives to become the Pride Lion. The Algorithm was tested with VLSI floorplanning problem wherein the area and dead space are the objectives. The algorithm was also tested with several standard test problems. The tabulated results justify the ruggedness of the proposed algorithm in solving any MOOP.

Using a Family of Curves to Approximate the Pareto Front of a Multi-Objective Optimization Problem

2014 ◽  
pp. 682-691 ◽  
Author(s):  
Saúl Zapotecas Martínez ◽  
Víctor A. Sosa Hernández ◽  
Hernán Aguirre ◽  
Kiyoshi Tanaka ◽  
Carlos A. Coello Coello
Keyword(s):  
Pareto Front ◽  
Optimization Problem ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Family Of Curves

scholarly journals An Entropy-Based Multiobjective Evolutionary Algorithm with an Enhanced Elite Mechanism

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Yufang Qin ◽  
Junzhong Ji ◽  
Chunnian Liu
Keyword(s):  
Evolutionary Algorithm ◽  
Pareto Front ◽  
Optimization Problem ◽  
State Of The Art ◽  
Early Stage ◽  
Test Problems ◽  
Multiobjective Optimization Problem ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective

Multiobjective optimization problem (MOP) is an important and challenging topic in the fields of industrial design and scientific research. Multi-objective evolutionary algorithm (MOEA) has proved to be one of the most efficient algorithms solving the multi-objective optimization. In this paper, we propose an entropy-based multi-objective evolutionary algorithm with an enhanced elite mechanism (E-MOEA), which improves the convergence and diversity of solution set in MOPs effectively. In this algorithm, an enhanced elite mechanism is applied to guide the direction of the evolution of the population. Specifically, it accelerates the population to approach the true Pareto front at the early stage of the evolution process. A strategy based on entropy is used to maintain the diversity of population when the population is near to the Pareto front. The proposed algorithm is executed on widely used test problems, and the simulated results show that the algorithm has better or comparative performances in convergence and diversity of solutions compared with two state-of-the-art evolutionary algorithms: NSGA-II, SPEA2 and the MOSADE.

An Efficient Framework Using Normalized Dominance Operator for Multi-Objective Evolutionary Algorithms

2019 ◽  
Vol 10 (1) ◽  
pp. 15-37 ◽  
Author(s):  
Muneendra Ojha ◽  
Krishna Pratap Singh ◽  
Pavan Chakraborty ◽  
Shekhar Verma
Keyword(s):  
Evolutionary Algorithms ◽  
Pareto Front ◽  
Optimization Problem ◽  
Computational Cost ◽  
Optimization Methods ◽  
Objective Test ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Pareto Dominance ◽  
Multi Objective

Multi-objective optimization algorithms using evolutionary optimization methods have shown strength in solving various problems using several techniques for producing uniformly distributed set of solutions. In this article, a framework is presented to solve the multi-objective optimization problem which implements a novel normalized dominance operator (ND) with the Pareto dominance concept. The proposed method has a lesser computational cost as compared to crowding-distance-based algorithms and better convergence. A parallel external elitist archive is used which enhances spread of solutions across the Pareto front. The proposed algorithm is applied to a number of benchmark multi-objective test problems with up to 10 objectives and compared with widely accepted aggregation-based techniques. Experiments produce a consistently good performance when applied to different recombination operators. Results have further been compared with other established methods to prove effective convergence and scalability.

Improved Memetic NSGA-II Using a Deep Neighborhood Search

2021 ◽  
Vol 12 (4) ◽  
pp. 138-154
Author(s):  
Samir Mahdi ◽  
Brahim Nini
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Pareto Front ◽  
Neighborhood Search ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Pareto Optimal Front ◽  
Slow Convergence ◽  
Multi Objective

Elitist non-sorted genetic algorithms as part of Pareto-based multi-objective evolutionary algorithms seems to be one of the most efficient algorithms for multi-objective optimization. However, it has some shortcomings, such as low convergence accuracy, uneven Pareto front distribution, and slow convergence. A number of review papers using memetic technique to improve NSGA-II have been published. Hence, it is imperative to improve memetic NSGA-II by increasing its solving accuracy. In this paper, an improved memetic NSGA-II, called deep memetic non-sorted genetic algorithm (DM-NSGA-II), is proposed, aiming to obtain more non-dominated solutions uniformly distributed and better converged near the true Pareto-optimal front. The proposed algorithm combines the advantages of both exact and heuristic approaches. The effectiveness of DM-NSGA-II is validated using well-known instances taken from the standard literature on multi-objective knapsack problem. As will be shown, the performance of the proposed algorithm is demonstrated by comparing it with M-NSGA-II using hypervolume metric.

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