Many-objective optimization algorithm based on adaptive reference vector

2021 ◽  
Vol 40 (1) ◽  
pp. 449-461
Author(s):  
Ziyu Hu ◽  
Xuemin Ma ◽  
Hao Sun ◽  
Jingming Yang ◽  
Zhiwei Zhao
Keyword(s):  
Selection Pressure ◽  
Test Problem ◽  
Pareto Front ◽  
Local Area ◽  
Reference Vector ◽  
Selection Mechanism ◽  
Multi Objective Optimization ◽  
Minimum Standard ◽  
Pareto Dominance ◽  
State Of Art

When dealing with multi-objective optimization, the proportion of non-dominated solutions increase rapidly with the increase of optimization objective. Pareto-dominance-based algorithms suffer the low selection pressure towards the true Pareto front. Decomposition-based algorithms may fail to solve the problems with highly irregular Pareto front. Based on the analysis of the two selection mechanism, a dynamic reference-vector-based many-objective evolutionary algorithm(RMaEA) is proposed. Adaptive-adjusted reference vector is used to improve the distribution of the algorithm in global area, and the improved non-dominated relationship is used to improve the convergence in a certain local area. Compared with four state-of-art algorithms on DTLZ benchmark with 5-, 10- and 15-objective, the proposed algorithm obtains 13 minimum mean IGD values and 8 minimum standard deviations among 15 test problem.

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.

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.

Pareto Set as a Model for Dispatching Resources in Emergency Centres (Preprint)

2018 ◽  
Author(s):  
Ricardo Guedes ◽  
Vasco Furtado ◽  
Tarcísio Pequeno ◽  
Joel Rodrigues
Keyword(s):  
Operational Research ◽  
Real Data ◽  
Pareto Set ◽  
Multi Objective Optimization ◽  
Pareto Dominance ◽  
Four Dimensions ◽  
Multi Objective ◽  
The Best Approximation ◽  
One Year ◽  
The Cost

UNSTRUCTURED The article investigates policies for helping emergency-centre authorities for dispatching resources aimed at reducing goals such as response time, the number of unattended calls, the attending of priority calls, and the cost of displacement of vehicles. Pareto Set is shown to be the appropriated way to support the representation of policies of dispatch since it naturally fits the challenges of multi-objective optimization. By means of the concept of Pareto dominance a set with objectives may be ordered in a way that guides the dispatch of resources. Instead of manually trying to identify the best dispatching strategy, a multi-objective evolutionary algorithm coupled with an Emergency Call Simulator uncovers automatically the best approximation of the optimal Pareto Set that would be the responsible for indicating the importance of each objective and consequently the order of attendance of the calls. The scenario of validation is a big metropolis in Brazil using one-year of real data from 911 calls. Comparisons with traditional policies proposed in the literature are done as well as other innovative policies inspired from different domains as computer science and operational research. The results show that strategy of ranking the calls from a Pareto Set discovered by the evolutionary method is a good option because it has the second best (lowest) waiting time, serves almost 100% of priority calls, is the second most economical, and is the second in attendance of calls. That is to say, it is a strategy in which the four dimensions are considered without major impairment to any of them.

Applications of Multiple Objective Genetic Algorithms in the Optimization Design of Tracked Self-Moving Power’s Layout

2013 ◽  
Vol 307 ◽  
pp. 161-165
Author(s):  
Hai Jin ◽  
Jin Fa Xie
Keyword(s):  
Optimization Design ◽  
Pareto Front ◽  
Layout Optimization ◽  
Multiple Objective ◽  
Multi Objective Optimization ◽  
Layout Problem ◽  
Basic Principles ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Set Up

A multi-objective genetic algorithm is applied into the layout optimization of tracked self-moving power. The layout optimization mathematical model was set up. Then introduced the basic principles of NSGA-Ⅱ, which is a Pareto multi-objective optimization algorithm. Finally, NSGA-Ⅱwas presented to solve the layout problem. The algorithm was proved to be effective by some practical examples. The results showed that the algorithm can spread toward the whole Pareto front, and provide many reasonable solutions once for all.

scholarly journals Multi-Objective Optimization Design of an Electrohydrostatic Actuator Based on a Particle Swarm Optimization Algorithm and an Analytic Hierarchy Process

Energies ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 2426 ◽  
Author(s):  
Bo Yu ◽  
Shuai Wu ◽  
Zongxia Jiao ◽  
Yaoxing Shang
Keyword(s):  
Particle Swarm Optimization ◽  
Power Consumption ◽  
Analytic Hierarchy Process ◽  
Optimization Design ◽  
Pareto Front ◽  
Multi Objective Optimization ◽  
Analytic Hierarchy ◽  
Swarm Optimization ◽  
Multi Objective ◽  
Hierarchy Process

During the last few years, the concept of more-electric aircraft has been pushed ahead by industry and academics. For a more-electric actuation system, the electrohydrostatic actuator (EHA) has shown its potential for better reliability, low maintenance cost and reducing aircraft weight. Designing an EHA for aviation applications is a hard task, which should balance several inconsistent objectives simultaneously, such as weight, stiffness and power consumption. This work presents a method to obtain the optimal EHA, which combines multi-objective optimization with a synthetic decision method, that is, a multi-objective optimization design method, that can combine designers’ preferences and experiences. The evaluation model of an EHA in terms of weight, stiffness and power consumption is studied in the first section. Then, a multi-objective particle swarm optimization (MOPSO) algorithm is introduced to obtain the Pareto front, and an analytic hierarchy process (AHP) is applied to help find the optimal design in the Pareto front. A demo of an EHA design illustrates the feasibility of the proposed method.

scholarly journals A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2837
Author(s):  
Saykat Dutta ◽  
Sri Srinivasa Raju M ◽  
Rammohan Mallipeddi ◽  
Kedar Nath Das ◽  
Dong-Gyu Lee
Keyword(s):  
Pareto Front ◽  
State Of The Art ◽  
Weight Vector ◽  
Dominance Relation ◽  
Additional Parameter ◽  
Pareto Dominance ◽  
Environmental Selection ◽  
Dominance Relationships ◽  
Test Suites ◽  
Selection Of

In multi/many-objective evolutionary algorithms (MOEAs), to alleviate the degraded convergence pressure of Pareto dominance with the increase in the number of objectives, numerous modified dominance relationships were proposed. Recently, the strengthened dominance relation (SDR) has been proposed, where the dominance area of a solution is determined by convergence degree and niche size (θ¯). Later, in controlled SDR (CSDR), θ¯ and an additional parameter (k) associated with the convergence degree are dynamically adjusted depending on the iteration count. Depending on the problem characteristics and the distribution of the current population, different situations require different values of k, rendering the linear reduction of k based on the generation count ineffective. This is because a particular value of k is expected to bias the dominance relationship towards a particular region on the Pareto front (PF). In addition, due to the same reason, using SDR or CSDR in the environmental selection cannot preserve the diversity of solutions required to cover the entire PF. Therefore, we propose an MOEA, referred to as NSGA-III*, where (1) a modified SDR (MSDR)-based mating selection with an adaptive ensemble of parameter k would prioritize parents from specific sections of the PF depending on k, and (2) the traditional weight vector and non-dominated sorting-based environmental selection of NSGA-III would protect the solutions corresponding to the entire PF. The performance of NSGA-III* is favourably compared with state-of-the-art MOEAs on DTLZ and WFG test suites with up to 10 objectives.

scholarly journals Integration of Operability Framework and Pareto Optimal Front to Calculate Optimal Condition of Ethane Cracking Process

2020 ◽  
pp. 105-113
Author(s):  
M. Farsi
Keyword(s):  
Pareto Front ◽  
Optimal Solution ◽  
Optimization Procedure ◽  
Operating Conditions ◽  
Base Case ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Pareto Optimal Front ◽  
Multi Objective ◽  
Cracking Process

The main aim of this research is to present an optimization procedure based on the integration of operability framework and multi-objective optimization concepts to find the single optimal solution of processes. In this regard, the Desired Pareto Index is defined as the ratio of desired Pareto front to the Pareto optimal front as a quantitative criterion to analyze the performance of chemical processes. The Desired Pareto Front is defined as a part of the Pareto front that all outputs are improved compared to the conventional operating condition. To prove the efficiency of proposed optimization method, the operating conditions of ethane cracking process is optimized as a base case. The ethylene and methane production rates are selected as the objectives in the formulated multi-objective optimization problem. Based on the simulation results, applying the obtained operating conditions by the proposed optimization procedure on the ethane cracking process improve ethylene production by about 3% compared to the conventional condition.  

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.

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