Principles of Genetic Algorithms

2020 ◽  
pp. 60-76
Keyword(s):  
Genetic Algorithms ◽  
Indian Ocean ◽  
Evolutionary Algorithms ◽  
Significant Role ◽  
Pareto Front ◽  
Pareto Optimization ◽  
Multi Objective Optimization ◽  
Precise Position ◽  
The Indian Ocean ◽  
Optimization Rule

This chapter aims to review the fundamentals of genetic algorithms. Consequently, the chapter correspondingly lectures on the dissimilarities between the alteration genetic and evolutionary algorithms. The decision mathematical rules based on the Pareto algorithm are similarly deliberated. The Pareto optimization rule can have a significant role in the examination of the precise position of MH370 vanishing. In this circumstance, the majority of multi-objective optimization algorithms exercise this principle to acquire the non-dominated set of solutions, as a result of the Pareto-front to investigate how MH370 ended up in the Indian Ocean.

scholarly journals The dilemma between eliminating dominance-resistant solutions and preserving boundary solutions of extremely convex Pareto fronts

2021 ◽  
Author(s):  
Zhenkun Wang ◽  
Qingyan Li ◽  
Qite Yang ◽  
Hisao Ishibuchi
Keyword(s):  
Evolutionary Algorithms ◽  
Coping Strategies ◽  
Test Problem ◽  
Pareto Front ◽  
Optimization Problems ◽  
Feasible Region ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Fronts ◽  
Boundary Solutions

AbstractIt has been acknowledged that dominance-resistant solutions (DRSs) extensively exist in the feasible region of multi-objective optimization problems. Recent studies show that DRSs can cause serious performance degradation of many multi-objective evolutionary algorithms (MOEAs). Thereafter, various strategies (e.g., the $$\epsilon $$ ϵ -dominance and the modified objective calculation) to eliminate DRSs have been proposed. However, these strategies may in turn cause algorithm inefficiency in other aspects. We argue that these coping strategies prevent the algorithm from obtaining some boundary solutions of an extremely convex Pareto front (ECPF). That is, there is a dilemma between eliminating DRSs and preserving boundary solutions of the ECPF. To illustrate such a dilemma, we propose a new multi-objective optimization test problem with the ECPF as well as DRSs. Using this test problem, we investigate the performance of six representative MOEAs in terms of boundary solutions preservation and DRS elimination. The results reveal that it is quite challenging to distinguish between DRSs and boundary solutions of the ECPF.

How Genetic Algorithms Handle Pareto-Optimality in Design and Manufacturing

2007 ◽  
pp. 465-482
Author(s):  
N. Chakraborti
Keyword(s):  
Genetic Algorithms ◽  
Evolutionary Algorithms ◽  
Pareto Optimality ◽  
Multi Objective Optimization ◽  
Recent Past ◽  
Multi Objective ◽  
Manufacturing Sectors ◽  
Design And Manufacturing ◽  
Basic Concepts

An informal analysis is provided for the basic concepts associated with multi-objective optimization and the notion of Pareto-optimality, particularly in the context of genetic algorithms. A number of evolutionary algorithms developed for this purpose are also briefly introduced, and finally, a number of paradigm examples are presented from the materials and manufacturing sectors, where multi-objective genetic algorithms have been successfully utilized in the recent past.

Multiobjective Algorithm-Based Pareto Optimization for Modelling Trajectory Movement of MH370 Debris

2020 ◽  
pp. 281-309
Keyword(s):  
Indian Ocean ◽  
Ocean Circulation ◽  
Optimal Algorithm ◽  
World Ocean ◽  
Pareto Optimization ◽  
Altimeter Data ◽  
Dynamic Movement ◽  
The Indian Ocean ◽  
Global World ◽  
Current Circulation

It is well-known that the altimeter satellite data can model the global world ocean circulation. In this view, the ocean dynamic circulation altimeter data is required to understand the drift movement of MH370 across the Indian ocean. The integration between the Volterra-Lax-Wendroff algorithm and Pareto optimal algorithm is used to investigate the dynamic movement of MH370 debris over annual current circulation across the Indian Ocean. This chapter shows that the maximum value of the hit-rate (HR) is 160%, which is occurring with an extreme rapidity of eddy current of 0.65 m/s. In conclusion, it is a great impossibility for the existence of the debris along Mozambique, Reunion Island, Madagascar coastal waters, and Mossel Bay, South Africa, as proven by the Pareto optimization.

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.

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.

scholarly journals Improved Lebesgue Indicator-Based Evolutionary Algorithm: Reducing Hypervolume Computations

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 19
Author(s):  
Saúl Zapotecas-Martínez ◽  
Abel García-Nájera ◽  
Adriana Menchaca-Méndez
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Lebesgue Measure ◽  
Pareto Front ◽  
Optimization Problems ◽  
State Of The Art ◽  
Computational Cost ◽  
Computational Time ◽  
Multi Objective Optimization ◽  
Multi Objective

One of the major limitations of evolutionary algorithms based on the Lebesgue measure for multi-objective optimization is the computational cost required to approximate the Pareto front of a problem. Nonetheless, the Pareto compliance property of the Lebesgue measure makes it one of the most investigated indicators in the designing of indicator-based evolutionary algorithms (IBEAs). The main deficiency of IBEAs that use the Lebesgue measure is their computational cost which increases with the number of objectives of the problem. On this matter, the investigation presented in this paper introduces an evolutionary algorithm based on the Lebesgue measure to deal with box-constrained continuous multi-objective optimization problems. The proposed algorithm implicitly uses the regularity property of continuous multi-objective optimization problems that has suggested effectiveness when solving continuous problems with rough Pareto sets. On the other hand, the survival selection mechanism considers the local property of the Lebesgue measure, thus reducing the computational time in our algorithmic approach. The emerging indicator-based evolutionary algorithm is examined and compared versus three state-of-the-art multi-objective evolutionary algorithms based on the Lebesgue measure. In addition, we validate its performance on a set of artificial test problems with various characteristics, including multimodality, separability, and various Pareto front forms, incorporating concavity, convexity, and discontinuity. For a more exhaustive study, the proposed algorithm is evaluated in three real-world applications having four, five, and seven objective functions whose properties are unknown. We show the high competitiveness of our proposed approach, which, in many cases, improved the state-of-the-art indicator-based evolutionary algorithms on the multi-objective problems adopted in our investigation.

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