Global WASF-GA: An Evolutionary Algorithm in Multiobjective Optimization to Approximate the Whole Pareto Optimal Front

2017 ◽  
Vol 25 (2) ◽  
pp. 309-349 ◽  
Author(s):  
Rubén Saborido ◽  
Ana B. Ruiz ◽  
Mariano Luque
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Fitness Function ◽  
Weight Vector ◽  
Reference Points ◽  
Pareto Optimal ◽  
Computational Results ◽  
Nsga Ii ◽  
Nondominated Solutions ◽  
Pareto Optimal Front

In this article, we propose a new evolutionary algorithm for multiobjective optimization called Global WASF-GA ( global weighting achievement scalarizing function genetic algorithm), which falls within the aggregation-based evolutionary algorithms. The main purpose of Global WASF-GA is to approximate the whole Pareto optimal front. Its fitness function is defined by an achievement scalarizing function (ASF) based on the Tchebychev distance, in which two reference points are considered (both utopian and nadir objective vectors) and the weight vector used is taken from a set of weight vectors whose inverses are well-distributed. At each iteration, all individuals are classified into different fronts. Each front is formed by the solutions with the lowest values of the ASF for the different weight vectors in the set, using the utopian vector and the nadir vector as reference points simultaneously. Varying the weight vector in the ASF while considering the utopian and the nadir vectors at the same time enables the algorithm to obtain a final set of nondominated solutions that approximate the whole Pareto optimal front. We compared Global WASF-GA to MOEA/D (different versions) and NSGA-II in two-, three-, and five-objective problems. The computational results obtained permit us to conclude that Global WASF-GA gets better performance, regarding the hypervolume metric and the epsilon indicator, than the other two algorithms in many cases, especially in three- and five-objective problems.

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.

Multi-Objective Optimization Design of Complex Mechanical and Electrical Products Based on Improved Evolutionary Algorithm

2011 ◽  
Vol 311-313 ◽  
pp. 1384-1388 ◽  
Author(s):  
Wei Wei ◽  
Li Hong Qiao
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Design ◽  
Design Space ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Trade Off ◽  
Pareto Optimal Set ◽  
Optimal Set

The design of complex mechanical and electrical products has to achieve various objectives and satisfy various constraints. In many cases, there are trade-off relationships between these objectives, and thus it is difficult to optimize these objectives simultaneously. This invokes the need of the multiobjective optimization to achieve these objectives collectively. In this paper, multiple objectives for complex mechanical and electrical products are optimized, simultaneously using an improved multiobjective evolutionary algorithm: ISPEA2. The results showed that ISPEA2 could generate uniformly a pareto optimal set in the design space and has better robustness and convergence than SPEA2 and NSGA-II.

scholarly journals Comparison of Multiobjective Evolutionary Algorithms: Empirical Results

2000 ◽  
Vol 8 (2) ◽  
pp. 173-195 ◽  
Author(s):  
Eckart Zitzler ◽  
Kalyanmoy Deb ◽  
Lothar Thiele
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Experimental Results ◽  
Pareto Optimal ◽  
Multiobjective Evolutionary Algorithms ◽  
Test Functions ◽  
Test Function ◽  
Pareto Optimal Front ◽  
Systematic Comparison ◽  
Empirical Results

In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front (e.g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search.

APPLICATION OF NOVEL CLONAL ALGORITHM IN MULTIOBJECTIVE OPTIMIZATION

2010 ◽  
Vol 09 (02) ◽  
pp. 239-266 ◽  
Author(s):  
JIANYONG CHEN ◽  
QIUZHEN LIN ◽  
QINGBIN HU
Keyword(s):  
Multiobjective Optimization ◽  
Coarse Grained ◽  
Pareto Optimal ◽  
Pareto Optimal Front ◽  
Fine Grained ◽  
Initial Stage ◽  
Speed Up ◽  
Main Notion ◽  
Hybrid Mutation Operator ◽  
Cooling Schedule

In this paper, a novel clonal algorithm applied in multiobjecitve optimization (NCMO) is presented, which is designed from the improvement of search operators, i.e. dynamic mutation probability, dynamic simulated binary crossover (D-SBX) operator and hybrid mutation operator combining with Gaussian and polynomial mutations (GP-HM) operator. The main notion of these approaches is to perform more coarse-grained search at initial stage in order to speed up the convergence toward the Pareto-optimal front. Once the solutions are getting close to the Pareto-optimal front, more fine-grained search is performed in order to reduce the gaps between the solutions and the Pareto-optimal front. Based on this purpose, a cooling schedule is adopted in these approaches, reducing the parameters gradually to a minimal threshold, the aim of which is to keep a desirable balance between fine-grained search and coarse-grained search. By this means, the exploratory capabilities of NCMO are enhanced. When compared with various state-of-the-art multiobjective optimization algorithms developed recently, simulation results show that NCMO has remarkable performance.

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.

Multiobjective Optimization of a Microchannel Heat Sink Using Evolutionary Algorithm

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
Afzal Husain ◽  
Kwang-Yong Kim
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Performance Optimization ◽  
Heat Sink ◽  
Algorithm Design ◽  
Pareto Optimal ◽  
Microchannel Heat Sink ◽  
Objective Functions ◽  
Design Variables ◽  
Polynomial Response Surface

A multiobjective performance optimization of microchannel heat sink is carried out numerically applying surrogate analysis and evolutionary algorithm. Design variables related to microchannel width, depth, and fin width are selected, and two objective functions, thermal resistance and pumping power, are employed. With the help of finite volume solver, Navier–Stokes analyses are performed at the design sites obtained from full factorial design of sampling methods. Using the numerically evaluated objective function values, polynomial response surface is constructed for each objective functions, and multiobjective optimization is performed to obtain global Pareto optimal solutions. Analysis of optimum solutions is simplified by carrying out trade-off with design variables and objective functions. Objective functions exhibit changing sensitivity to design variables along the Pareto optimal front.

scholarly journals A Novel Multiobjective Evolutionary Algorithm Based on Regression Analysis

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Zhiming Song ◽  
Maocai Wang ◽  
Guangming Dai ◽  
Massimiliano Vasile
Keyword(s):  
Regression Analysis ◽  
Probability Distribution ◽  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problem ◽  
Dimensional Manifold ◽  
Decision Space ◽  
Nsga Ii ◽  
Multiobjective Evolutionary Algorithm ◽  
Piecewise Continuous

As is known, the Pareto set of a continuous multiobjective optimization problem with m objective functions is a piecewise continuous (m-1)-dimensional manifold in the decision space under some mild conditions. However, how to utilize the regularity to design multiobjective optimization algorithms has become the research focus. In this paper, based on this regularity, a model-based multiobjective evolutionary algorithm with regression analysis (MMEA-RA) is put forward to solve continuous multiobjective optimization problems with variable linkages. In the algorithm, the optimization problem is modelled as a promising area in the decision space by a probability distribution, and the centroid of the probability distribution is (m-1)-dimensional piecewise continuous manifold. The least squares method is used to construct such a model. A selection strategy based on the nondominated sorting is used to choose the individuals to the next generation. The new algorithm is tested and compared with NSGA-II and RM-MEDA. The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages. At the same time, MMEA-RA has higher efficiency than the other two algorithms. A few shortcomings of MMEA-RA have also been identified and discussed in this paper.

Manufacturer Order Fulfillment Based on Multi-Objective Optimization NSGA II Model

2013 ◽  
Vol 340 ◽  
pp. 136-140
Author(s):  
Liang You Shu ◽  
Ling Xiao Yang
Keyword(s):  
Optimization Model ◽  
Optimization Problems ◽  
Population Based ◽  
Pareto Optimal ◽  
Order Fulfillment ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Pareto Optimal Front ◽  
Multi Objective ◽  
Local Search Procedure

The aim of this paper is to study the production and delivery decision problem in the Manufacturer Order Fulfillment. Owing to the order fulfillment optimization condition of the manufacturer, the multi-objective optimization model of manufacturers' production and delivery has been founded. The solution of the multi-objective optimization model is also very difficult. Fast and Elitist Non-dominated Sorting Genetic Algorithm (NSGA II) have been applied successfully to various test and real-world optimization problems. These population based the algorithm provide a diverse set of non-dominated solutions. The obtained non-dominated set is close to the true Pareto-optimal front. But its convergence to the true Pareto-optimal front is not guaranteed. Hence SBX is used as a local search procedure. The proposed procedure is successfully applied to a special case. The results validate that the algorithm is effective to the multi-objective optimization model.

scholarly journals Optimization of Wind Turbine Airfoil Using Nondominated Sorting Genetic Algorithm and Pareto Optimal Front

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Ziaul Huque ◽  
Ghizlane Zemmouri ◽  
Donald Harby ◽  
Raghava Kommalapati
Keyword(s):  
Genetic Algorithm ◽  
Response Surface ◽  
Cfd Simulation ◽  
Lift Coefficient ◽  
Response Surfaces ◽  
Least Square ◽  
Pareto Optimal ◽  
Nsga Ii ◽  
Pareto Solution ◽  
Pareto Optimal Front

A Computational Fluid Dynamics (CFD) and response surface-based multiobjective design optimization were performed for six different 2D airfoil profiles, and the Pareto optimal front of each airfoil is presented. FLUENT, which is a commercial CFD simulation code, was used to determine the relevant aerodynamic loads. The Lift Coefficient (CL) and Drag Coefficient (CD) data at a range of 0°to 12°angles of attack (α) and at three different Reynolds numbers (Re=68,459, 479, 210, and 958, 422) for all the six airfoils were obtained. Realizablek-εturbulence model with a second-order upwind solution method was used in the simulations. The standard least square method was used to generate response surface by the statistical code JMP. Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) was used to determine the Pareto optimal set based on the response surfaces. Each Pareto optimal solution represents a different compromise between design objectives. This gives the designer a choice to select a design compromise that best suits the requirements from a set of optimal solutions. The Pareto solution set is presented in the form of a Pareto optimal front.

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