scholarly journals MOEA/D with Adaptive Weight Adjustment

2014 ◽  
Vol 22 (2) ◽  
pp. 231-264 ◽  
Author(s):  
Yutao Qi ◽  
Xiaoliang Ma ◽  
Fang Liu ◽  
Licheng Jiao ◽  
Jianyong Sun ◽  
...  
Keyword(s):  
Optimal Solution ◽  
Weight Vector ◽  
Test Problems ◽  
Great Success ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Decomposition Scheme ◽  
Adaptive Weight

Recently, MOEA/D (multi-objective evolutionary algorithm based on decomposition) has achieved great success in the field of evolutionary multi-objective optimization and has attracted a lot of attention. It decomposes a multi-objective optimization problem (MOP) into a set of scalar subproblems using uniformly distributed aggregation weight vectors and provides an excellent general algorithmic framework of evolutionary multi-objective optimization. Generally, the uniformity of weight vectors in MOEA/D can ensure the diversity of the Pareto optimal solutions, however, it cannot work as well when the target MOP has a complex Pareto front (PF; i.e., discontinuous PF or PF with sharp peak or low tail). To remedy this, we propose an improved MOEA/D with adaptive weight vector adjustment (MOEA/D-AWA). According to the analysis of the geometric relationship between the weight vectors and the optimal solutions under the Chebyshev decomposition scheme, a new weight vector initialization method and an adaptive weight vector adjustment strategy are introduced in MOEA/D-AWA. The weights are adjusted periodically so that the weights of subproblems can be redistributed adaptively to obtain better uniformity of solutions. Meanwhile, computing efforts devoted to subproblems with duplicate optimal solution can be saved. Moreover, an external elite population is introduced to help adding new subproblems into real sparse regions rather than pseudo sparse regions of the complex PF, that is, discontinuous regions of the PF. MOEA/D-AWA has been compared with four state of the art MOEAs, namely the original MOEA/D, Adaptive-MOEA/D, [Formula: see text]-MOEA/D, and NSGA-II on 10 widely used test problems, two newly constructed complex problems, and two many-objective problems. Experimental results indicate that MOEA/D-AWA outperforms the benchmark algorithms in terms of the IGD metric, particularly when the PF of the MOP is complex.

scholarly journals An Improved Parallelized Multi-Objective Optimization Method for Complex Geographical Spatial Sampling: AMOSA-II

2020 ◽  
Vol 9 (4) ◽  
pp. 236
Author(s):  
Xiaolan Li ◽  
Bingbo Gao ◽  
Zhongke Bai ◽  
Yuchun Pan ◽  
Yunbing Gao
Keyword(s):  
Markov Chains ◽  
Optimization Problems ◽  
Optimization Method ◽  
Spatial Sampling ◽  
Computational Time ◽  
Test Problems ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective

Complex geographical spatial sampling usually encounters various multi-objective optimization problems, for which effective multi-objective optimization algorithms are much needed to help advance the field. To improve the computational efficiency of the multi-objective optimization process, the archived multi-objective simulated annealing (AMOSA)-II method is proposed as an improved parallelized multi-objective optimization method for complex geographical spatial sampling. Based on the AMOSA method, multiple Markov chains are used to extend the traditional single Markov chain; multi-core parallelization technology is employed based on multi-Markov chains. The tabu-archive constraint is designed to avoid repeated searches for optimal solutions. Two cases were investigated: one with six typical traditional test problems, and the other for soil spatial sampling optimization applications. Six performance indices of the two cases were analyzed—computational time, convergence, purity, spacing, min-spacing and displacement. The results revealed that AMOSA-II performed better which was more effective in obtaining preferable optimal solutions compared with AMOSA and NSGA-II. AMOSA-II can be treated as a feasible means to apply in other complex geographical spatial sampling optimizations.

scholarly journals Multi-objective optimization design of spur gear based on NSGA-II and decision making

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401882493 ◽  
Author(s):  
Qizhi Yao
Keyword(s):  
Decision Maker ◽  
Optimization Design ◽  
Optimal Solution ◽  
Spur Gear ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Deviation Index ◽  
Decision Variables

Optimization design of spur gear is a complicated work because the performance characteristics depend on different types of decision variables and objectives. Traditional single-objective optimization design of the spur gear always results in poor outcomes relative to other objectives due to objectives’ competition with each other. Therefore, this study works on the spur gear design based on the multi-objective optimization model of elitist non-dominated sorting genetic algorithm (NSGA-II). In the model, gear module, teeth number, and transmission ratio are decision variables, while center distance, bearing capacity coefficient, and meshing efficiency are objectives. Final optimal solutions are picked out from Pareto frontier calculated from NSGA-II using the decision makers of Shannon Entropy, linear programming technique for multidimensional analysis of preference (LINMAP), and technique of order preference by similarity to an ideal solution (TOPSIS). Meanwhile, a deviation index is used to evaluate the reasonable status of the optimal solutions. From triple-objective and dual-objective optimization results, it is found that the optimal solution selected from LINMAP decision maker shows a relatively small deviation index. It indicates that LINMAP decision maker may yield better optimal solution. This study could provide some beneficial information for spur design.

scholarly journals Multi-objective optimization of solar thermal photovoltaic hybrid power generation system based on NSGA-II algorithm

2021 ◽  
Vol 336 ◽  
pp. 02022
Author(s):  
Liang Meng ◽  
Wen Zhou ◽  
Yang Li ◽  
Zhibin Liu ◽  
Yajing Liu
Keyword(s):  
Power Generation ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Solar Thermal ◽  
Multi Objective Optimization ◽  
Generation System ◽  
Nsga Ii ◽  
Multi Objective ◽  
Hybrid Power ◽  
Power Generation System

In this paper, NSGA-Ⅱ is used to realize the dual-objective optimization and three-objective optimization of the solar-thermal photovoltaic hybrid power generation system; Compared with the optimal solution set of three-objective optimization, optimization based on technical and economic evaluation indicators belongs to the category of multi-objective optimization. It can be considered that NSGA-Ⅱ is very suitable for multi-objective optimization of solar-thermal photovoltaic hybrid power generation system and other similar multi-objective optimization problems.

Hybrid QPSO-NNIA2 Algorithm for Multi-Objective Optimization Problem

2019 ◽  
Vol 33 (08) ◽  
pp. 1959025
Author(s):  
Lan Zhang
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problem ◽  
Nearest Neighbor ◽  
Superior Performance ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Evolution Algebra ◽  
Neighbor List

To improve the convergence and distribution of a multi-objective optimization algorithm, a hybrid multi-objective optimization algorithm, based on the quantum particle swarm optimization (QPSO) algorithm and adaptive ranks clone and neighbor list-based immune algorithm (NNIA2), is proposed. The contribution of this work is threefold. First, the vicinity distance was used instead of the crowding distance to update the archived optimal solutions in the QPSO algorithm. The archived optimal solutions are updated and maintained by using the dynamic vicinity distance based m-nearest neighbor list in the QPSO algorithm. Secondly, an adaptive dynamic threshold of unfitness function for constraint handling is introduced in the process. It is related to the evolution algebra and the feasible solution. Thirdly, a new metric called the distribution metric is proposed to depict the diversity and distribution of the Pareto optimal. In order to verify the validity and feasibility of the QPSO-NNIA2 algorithm, we compare it with the QPSO, NNIA2, NSGA-II, MOEA/D, and SPEA2 algorithms in solving unconstrained and constrained multi-objective problems. The simulation results show that the QPSO-NNIA2 algorithm achieves superior convergence and superior performance by three metrics compared to other algorithms.

Research on multi-objective optimization of switched flux motor based on improved NSGA-II algorithm

2019 ◽  
Vol 233 (6) ◽  
pp. 1268-1279 ◽  
Author(s):  
Liying Jin ◽  
Shengdun Zhao ◽  
Wei Du ◽  
Xuesong Yang ◽  
Wensheng Wang ◽  
...  
Keyword(s):  
Permanent Magnets ◽  
Optimal Solution ◽  
Torque Ripple ◽  
Maximum Output ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Tooth Width ◽  
The Individual ◽  
Rotor Tooth

In order to optimize the local search efficiency of multi-objective parameters of flux switching permanent motor based on traditional NSGA-II algorithm, an improved NSGA-II (iNSGA-II) algorithm is proposed, with an anti-redundant mutation operator and forward comparison operation designed for quick identification of non-dominated individuals. In the initial stage of the iNSGA-II algorithm, half of the individual populations were randomly generated, while the other half was generated according to feature distribution information. Taking the flux switching permanent motor stator/rotor gap, permanent magnets width, stator tooth width, rotor tooth width and other parameters as optimization variables, the flux switching permanent motor maximum output shaft torque and minimum torque ripple are taken as optimization objectives, thus a multi-objective optimization model is established. Real number coding was adopted for obtaining the Pareto optimal solution of flux switching permanent motor structure parameters. The results showed that the iNSGA-II algorithm is better than the traditional NSGA-II on convergence. A 1.8L TOYOTA PRIUS model was selected as the prototype vehicle. By using the optimized parameters, a joint optimization simulation model was established by calling ADVISOR’s back-office function. The simulation results showed that the entire vehicle’s 100-km acceleration time is under 8 s and the battery’s SOC value maintains at 0.5–0.7 in the entire cycle, implying that the iNSGA-II algorithm optimizes the flux switching permanent motor design and is suitable for the initial design and optimizing calculation of the flux switching permanent motor.

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.

On Benchmark Problems and Metrics for Decision Space Performance Analysis in Multi-Objective Optimization

2017 ◽  
Vol 16 (01) ◽  
pp. 1750006 ◽  
Author(s):  
Bin Zhang ◽  
Kamran Shafi ◽  
Hussein Abbass
Keyword(s):  
Performance Analysis ◽  
Fitness Landscape ◽  
Benchmark Problems ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Decision Space ◽  
Nsga Ii ◽  
Multi Objective ◽  
Objective Space ◽  
Problem Instances

A number of benchmark problems exist for evaluating multi-objective evolutionary algorithms (MOEAs) in the objective space. However, the decision space performance analysis is a recent and relatively less explored topic in evolutionary multi-objective optimization research. Among other implications, such analysis can lead to designing more realistic test problems, gaining better understanding about optimal and robust design areas, and design and evaluation of knowledge-based optimization algorithms. This paper complements the existing research in this area and proposes a new method to generate multi-objective optimization test problems with clustered Pareto sets in hyper-rectangular defined areas of decision space. The test problem is parametrized to control number of decision variables, number and position of optimal areas in the decision space and modality of fitness landscape. Three leading MOEAs, including NSGA-II, NSGA-III, and MOEA/D, are evaluated on a number of problem instances with varying characteristics. A new metric is proposed that measures the performance of algorithms in terms of their coverage of the optimal areas in the decision space. The empirical analysis presented in this research shows that the decision space performance may not necessarily be reflective of the objective space performance and that all algorithms are sensitive to population size parameter for the new test problems.

MULTI-OBJECTIVE OPTIMIZATION OF THERMO-ECOLOGICAL CRITERIA BASED PERFORMANCE PARAMETERS OF REHEAT AND REGENERATIVE BRAYSSON CYCLE

2021 ◽  
pp. 1-36
Author(s):  
R Chandramouli ◽  
G Ravi Kiran Sastry ◽  
S. K. Gugulothu ◽  
M S S Srinivasa Rao
Keyword(s):  
Power Density ◽  
Pressure Ratio ◽  
Optimal Solution ◽  
Coefficient Of Performance ◽  
Optimal Solutions ◽  
Performance Parameters ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Multi Stage ◽  
Ecological Criteria

Abstract The reheat and regenerative Braysson cycle being an alternative for combined cycle power plants needs to be optimized for its efficient utilization of energy resources. Therefore, to obtain the best possible overall pressure ratio, regenerator effectiveness and pressure ratio across multi-stage compression in order to simultaneously maximize exergy efficiency, non-dimensional power density and ecological coefficient of performance for three different maximum temperature situations, multi-objective optimization of the above cycle is carried out using Non-dominated sorting genetic algorithm-II (NSGA-II). The optimal solutions given by the Pareto frontier are further assessed through widely used decision makers namely LINMAP, TOPSIS and Bellman-Zadeh techniques. The optimal solutions attained by the decision making process are further evaluated for their deviation from the non-ideal and ideal solutions. The optimal solution obtained through TOPSIS possess the minimum deviation index. Finally the results are authenticated by performing an error analysis. Such optimal scenarios achieved for the three maximum temperatures are further analysed to achieve the final objective of the most optimal solution which happens to be at 1200K. The simultaneous optimization of performance parameters which reflect the thermo-ecological criteria to be satisfied by a power plant has resulted in values of 0.479, 0.327 & 0.922 for exergy efficiency, non-dimensional power density and ecological coefficient of performance respectively. These optimized performance parameters are obtained for an overall pressure ratio of 7.5, regenerator effectiveness of 0.947 and pressure ratio across multi-stage compression of 1.311.

Multi-Objective Optimization Algorithm Based on Gene Expression Programming and Virus Evolution

2011 ◽  
Vol 225-226 ◽  
pp. 372-376
Author(s):  
Wei Hong Wang ◽  
Yan Ye Du ◽  
Qu Li
Keyword(s):  
Gene Expression ◽  
Gene Expression Programming ◽  
Research Direction ◽  
Virus Evolution ◽  
Host Population ◽  
Test Problems ◽  
Local Optimum ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective

Evolutionary Multi-objective Optimization (EMO) is a hot research direction nowadays and one of the state-of-the-art evolutionary multi-objective optimization algorithms ——NSGA-II has gain wide attention and application in many fields. Gene Expression Programming (GEP) has a powerful search capability, but falls into local optimum easily. Based on the transformed GEP, NSGA-II and the virus evolution mechanism, a new multi-objective evolutionary algorithm GEP Virus NSGA-II is proposed. With the infection operation of virus population, the diversity of the host population is increased, and it’s much easier to jump out of the local optimum. And this algorithm has got good experimental results on 9 standard test problems.

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