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.

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.

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.

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.

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.

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.

scholarly journals A Smart-Distributed Pareto Front Using the ev-MOGA Evolutionary Algorithm

2014 ◽  
Vol 23 (02) ◽  
pp. 1450002 ◽  
Author(s):  
J. M. Herrero ◽  
G. Reynoso-Meza ◽  
M. Martínez ◽  
X. Blasco ◽  
J. Sanchis
Keyword(s):  
Pareto Front ◽  
Optimization Methods ◽  
Optimization Method ◽  
Initial Condition ◽  
Multi Objective Optimization ◽  
Computational Burden ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Normalized Normal Constraint ◽  
Normal Constraint

Obtaining multi-objective optimization solutions with a small number of points smartly distributed along the Pareto front is a challenge. Optimization methods, such as the normalized normal constraint (NNC), propose the use of a filter to achieve a smart Pareto front distribution. The NCC optimization method presents several disadvantages related with the procedure itself, initial condition dependency, and computational burden. In this article, the epsilon-variable multi-objective genetic algorithm (ev-MOGA) is presented. This algorithm characterizes the Pareto front in a smart way and removes the disadvantages of the NNC method. Finally, examples of a three-bar truss design and controller tuning optimizations are presented for comparison purposes.

scholarly journals On the Hardness of Offline Multi-objective Optimization

2007 ◽  
Vol 15 (4) ◽  
pp. 475-491 ◽  
Author(s):  
Olivier Teytaud
Keyword(s):  
Evolutionary Algorithms ◽  
Convergence Rate ◽  
Random Search ◽  
Computational Cost ◽  
Multiobjective Evolutionary Algorithms ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Insight Into ◽  
Better Than

It has been empirically established that multiobjective evolutionary algorithms do not scale well with the number of conflicting objectives. This paper shows that the convergence rate of all comparison-based multi-objective algorithms, for the Hausdorff distance, is not much better than the convergence rate of the random search under certain conditions. The number of objectives must be very moderate and the framework should hold the following assumptions: the objectives are conflicting and the computational cost is lower bounded by the number of comparisons is a good model. Our conclusions are: (i) the number of conflicting objectives is relevant (ii) the criteria based on comparisons with random-search for multi-objective optimization is also relevant (iii) having more than 3-objectives optimization is very hard. Furthermore, we provide some insight into cross-over operators.

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.

Multi-Objective Evolutionary Algorithms

2016 ◽  
pp. 301-345
Author(s):  
A. K. Nandi ◽  
K. Deb
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Algorithms ◽  
Optimization Problem ◽  
Performance Metrics ◽  
Research Work ◽  
Primary Objective ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Mould Material ◽  
Multi Objective

The primary objective in designing appropriate particle reinforced polyurethane composite which will be used as a mould material in soft tooling process is to minimize the cycle time of soft tooling process by providing faster cooling rate during solidification of wax/plastic component. This chapter exemplifies an effective approach to design particle reinforced mould materials by solving the inherent multi-objective optimization problem associated with soft tooling process using evolutionary algorithms. In this chapter, first a brief introduction of multi-objective optimization problem with the key issues is presented. Then, after a short overview on the working procedure of genetic algorithm, a well- established multi-objective evolutionary algorithm, namely NSGA-II along with various performance metrics are described. The inherent multi-objective problem in soft tooling process is demonstrated and subsequently solved using an elitist non-dominated sorting genetic algorithm, NSGA-II. Multi-objective optimization results obtained using NSGA-II are analyzed statistically and validated with real industrial application. Finally the fundamental results of this approach are summarized and various perspectives to the industries along with scopes for future research work are pointed out.

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