scholarly journals Decomposition in decision and objective space for multi-modal multi-objective optimization

2021 ◽  
Vol 62 ◽  
pp. 100842
Author(s):  
Monalisa Pal ◽  
Sanghamitra Bandyopadhyay
Keyword(s):  
Multi Objective Optimization ◽  
Multi Objective ◽  
Objective Space

scholarly journals Search Acceleration of Evolutionary Multi-Objective Optimization Using an Estimated Convergence Point

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 129 ◽  
Author(s):  
Yan Pei ◽  
Jun Yu ◽  
Hideyuki Takagi
Keyword(s):  
Parameter Space ◽  
Statistical Tests ◽  
Distribution Characteristic ◽  
Multi Objective Optimization ◽  
Pareto Improvement ◽  
Pareto Solutions ◽  
Pareto Solution ◽  
Multi Objective ◽  
Objective Space ◽  
Convergence Point

We propose a method to accelerate evolutionary multi-objective optimization (EMO) search using an estimated convergence point. Pareto improvement from the last generation to the current generation supports information of promising Pareto solution areas in both an objective space and a parameter space. We use this information to construct a set of moving vectors and estimate a non-dominated Pareto point from these moving vectors. In this work, we attempt to use different methods for constructing moving vectors, and use the convergence point estimated by using the moving vectors to accelerate EMO search. From our evaluation results, we found that the landscape of Pareto improvement has a uni-modal distribution characteristic in an objective space, and has a multi-modal distribution characteristic in a parameter space. Our proposed method can enhance EMO search when the landscape of Pareto improvement has a uni-modal distribution characteristic in a parameter space, and by chance also does that when landscape of Pareto improvement has a multi-modal distribution characteristic in a parameter space. The proposed methods can not only obtain more Pareto solutions compared with the conventional non-dominant sorting genetic algorithm (NSGA)-II algorithm, but can also increase the diversity of Pareto solutions. This indicates that our proposed method can enhance the search capability of EMO in both Pareto dominance and solution diversity. We also found that the method of constructing moving vectors is a primary issue for the success of our proposed method. We analyze and discuss this method with several evaluation metrics and statistical tests. The proposed method has potential to enhance EMO embedding deterministic learning methods in stochastic optimization algorithms.

A Kind of Evolutionary Multi-Objective Optimization Algorithm Based on AIS

2013 ◽  
Vol 442 ◽  
pp. 419-423
Author(s):  
Ming Song Li
Keyword(s):  
Immune System ◽  
Optimization Algorithm ◽  
Clonal Selection ◽  
Research Area ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Objective Space ◽  
Speed Up ◽  
Important Research Area ◽  
Intelligent Information

Problem of multi-objective optimization based on Artificial Immune System (AIS) is an important research area of current evolutionary computing. Starting from the intelligent information processing mechanism of immune theory and the immune system itself, a kind of evolutionary multi-objective optimization algorithm based on AIS is proposed. Clonal selection, scattered crossover and hypermutation based on the learning mechanism are characteristics of the algorithm. Algorithm implements clonal selection according to the distribution of individuals in the objective space, which benefit obtaining Pareto optimal boundary distributed more widely and speed up the convergence. Compared with the existing algorithms, the algorithm has been greatly improved in convergence, diversity, and distribution of 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.

Application of Multi-Objective Optimization Algorithm Based on Physical Programming in Ship Conceptual Design

2014 ◽  
Vol 904 ◽  
pp. 408-413
Author(s):  
Zhai Liu Hao ◽  
Zu Yuan Liu ◽  
Bai Wei Feng
Keyword(s):  
Conceptual Design ◽  
Optimization Algorithm ◽  
Optimization Design ◽  
Uniform Design ◽  
Multi Objective Optimization ◽  
Pareto Solutions ◽  
Physical Programming ◽  
Multi Objective ◽  
Objective Space ◽  
Preference Structures

Ship optimization design is a typical multi-objective problem. The multi-objective optimization algorithm based on physical programming is able to obtain evenly distributed Pareto front. But the number of Pareto solutions and the search positions of pseudo-preference structures still exit some disadvantages that are improved in this paper. Firstly uniform design for mixture experiments is used to arbitrarily set the number of Pareto solutions and evenly distribute the search positions of pseudo-preference structures. Then the objective space is searched by shrinking of search domain and rotation of pseudo-preference structure technology. The optimization quality is able to be improved. Finally, the improved multi-objective optimization algorithm is applied to ship conceptual design optimization and compared with the multi-objective evolutionary algorithm to verify the effectiveness of the improved algorithm.

Operational Costs Optimization in Water Distribution Systems

2014 ◽  
Author(s):  
Dhafar Al-Ani ◽  
HamedHossien Afshari ◽  
Saeid Habibi
Keyword(s):  
Distribution Systems ◽  
Water Distribution ◽  
Optimization Problems ◽  
Water Distribution Systems ◽  
Cost Savings ◽  
Search Space ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Objective Space

Pump management and reservoir management have many similarities, and therefore, should ideally be analyzed in an integrated way to plan effectively the daily operation of water distribution systems. Historically, these two management activities have been evolved as separate tasks in energy-efficiency (i.e., energy optimization) studies and are often carried out in an isolated way. The latter being most often associated directly with the concepts of multimodal and multi-objective optimization problems, whereas the former is usually considered as a single optimization problem to be solved. When some single optimization problems appear at part of the solution tied to a local (i.e., regional) search-space (i.e., objective space), this artificial integration (i.e., multi-modal and multi-objective optimization) can always obtain optimal solutions. Similarly when system constraints and load conditions are considered, a set of feasible and innovative optimal solutions can be obtained in order to continue the enhancement of energy consumption that turns into a significant reduction in the overall operational cost (i.e., a potential of 6.24% cost savings) without affecting the level of services provided to the clients in a safe and protected manner.

scholarly journals Non-dominated sorting Harris’s hawk multi-objective optimizer based on reference point approach

2019 ◽  
Vol 15 (3) ◽  
pp. 1603 ◽  
Author(s):  
Shaymah Akram Yasear ◽  
Ku Ruhana Ku-Mahamud
Keyword(s):  
Reference Point ◽  
Pareto Front ◽  
Optimization Problems ◽  
Population Diversity ◽  
Experimental Results ◽  
Multi Objective Optimization ◽  
Next Generation ◽  
Multi Objective ◽  
Objective Space ◽  
Reference Point Approach

A non-dominated sorting Harris’s hawk multi-objective optimizer (NDSHHMO) algorithm is presented in this paper. The algorithm is able to improve the population diversity, convergence of non-dominated solutions toward the Pareto front, and prevent the population from trapping into local optimal. This was achieved by integrating fast non-dominated sorting with the original Harris’s hawk multi-objective optimizer (HHMO).  Non-dominated sorting divides the objective space into levels based on fitness values and then selects non-dominated solutions to produce the next generation of hawks. A set of well-known multi-objective optimization problems has been used to evaluate the performance of the proposed NDSHHMO algorithm. The results of the NDSHHMO algorithm were verified against the results of an HHMO algorithm. Experimental results demonstrate the efficiency of the proposed NDSHHMO algorithm in terms of enhancing the ability of convergence toward the Pareto front and significantly improve the search ability of the HHMO.

Multi-Objective Optimization Based on Brain Storm Optimization Algorithm

2013 ◽  
Vol 4 (3) ◽  
pp. 1-21 ◽  
Author(s):  
Yuhui Shi ◽  
Jingqian Xue ◽  
Yali Wu
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
Solution Space ◽  
Population Based ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Brain Storm Optimization ◽  
Objective Space ◽  
Different Characteristics ◽  
Single Objective

In recent years, many evolutionary algorithms and population-based algorithms have been developed for solving multi-objective optimization problems. In this paper, the authors propose a new multi-objective brain storm optimization algorithm in which the clustering strategy is applied in the objective space instead of in the solution space in the original brain storm optimization algorithm for solving single objective optimization problems. Two versions of multi-objective brain storm optimization algorithm with different characteristics of diverging operation were tested to validate the usefulness and effectiveness of the proposed algorithm. Experimental results show that the proposed multi-objective brain storm optimization algorithm is a very promising algorithm, at least for solving these tested multi-objective optimization problems.

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