Difficulties in specifying reference points to calculate the inverted generational distance for many-objective optimization problems

Author(s):  
Hisao Ishibuchi ◽  
Hiroyuki Masuda ◽  
Yuki Tanigaki ◽  
Yusuke Nojima
Author(s):  
Lu Chen ◽  
Handing Wang ◽  
Wenping Ma

AbstractReal-world optimization applications in complex systems always contain multiple factors to be optimized, which can be formulated as multi-objective optimization problems. These problems have been solved by many evolutionary algorithms like MOEA/D, NSGA-III, and KnEA. However, when the numbers of decision variables and objectives increase, the computation costs of those mentioned algorithms will be unaffordable. To reduce such high computation cost on large-scale many-objective optimization problems, we proposed a two-stage framework. The first stage of the proposed algorithm combines with a multi-tasking optimization strategy and a bi-directional search strategy, where the original problem is reformulated as a multi-tasking optimization problem in the decision space to enhance the convergence. To improve the diversity, in the second stage, the proposed algorithm applies multi-tasking optimization to a number of sub-problems based on reference points in the objective space. In this paper, to show the effectiveness of the proposed algorithm, we test the algorithm on the DTLZ and LSMOP problems and compare it with existing algorithms, and it outperforms other compared algorithms in most cases and shows disadvantage on both convergence and diversity.


2021 ◽  
Author(s):  
◽  
Atiya Masood

<p>The Job Shop Scheduling (JSS) problem is considered to be a challenging one due to practical requirements such as multiple objectives and the complexity of production flows. JSS has received great attention because of its broad applicability in real-world situations. One of the prominent solutions approaches to handling JSS problems is to design effective dispatching rules. Dispatching rules are investigated broadly in both academic and industrial environments because they are easy to implement (by computers and shop floor operators) with a low computational cost. However, the manual development of dispatching rules is time-consuming and requires expert knowledge of the scheduling environment. The hyper-heuristic approach that uses genetic programming (GP) to solve JSS problems is known as GP-based hyper-heuristic (GP-HH). GP-HH is a very useful approach for discovering dispatching rules automatically.  Although it is technically simple to consider only a single objective optimization for JSS, it is now widely evidenced in the literature that JSS by nature presents several potentially conflicting objectives, including the maximal flowtime, mean flowtime, and mean tardiness. A few studies in the literature attempt to solve many-objective JSS with more than three objectives, but existing studies have some major limitations. First, many-objective JSS problems have been solved by multi-objective evolutionary algorithms (MOEAs). However, recent studies have suggested that the performance of conventional MOEAs is prone to the scalability challenge and degrades dramatically with many-objective optimization problems (MaOPs). Many-objective JSS using MOEAs inherit the same challenge as MaOPs. Thus, using MOEAs for many-objective JSS problems often fails to select quality dispatching rules. Second, although the reference points method is one of the most prominent and efficient methods for diversity maintenance in many-objective problems, it uses a uniform distribution of reference points which is only appropriate for a regular Pareto-front. However, JSS problems often have irregular Pareto-front and uniformly distributed reference points do not match well with the irregular Pareto-front. It results in many useless points during evolution. These useless points can significantly affect the performance of the reference points-based algorithms. They cannot help to enhance the solution diversity of evolved Pareto-front in many-objective JSS problems. Third, Pareto Local Search (PLS) is a prominent and effective local search method for handling multi-objective JSS optimization problems but the literature does not discover any existing studies which use PLS in GP-HH.  To address these limitations, this thesis's overall goal is to develop GP-HH approaches to evolving effective rules to handle many conflicting objectives simultaneously in JSS problems.  To achieve the first goal, this thesis proposes the first many-objective GP-HH method for JSS problems to find the Pareto-fronts of nondominated dispatching rules. Decision-makers can utilize this GP-HH method for selecting appropriate rules based on their preference over multiple conflicting objectives. This study combines GP with the fitness evaluation scheme of a many-objective reference points-based approach. The experimental results show that the proposed algorithm significantly outperforms MOEAs such as NSGA-II and SPEA2.  To achieve the second goal, this thesis proposes two adaptive reference point approaches (model-free and model-driven). In both approaches, the reference points are generated according to the distribution of the evolved dispatching rules. The model-free reference point adaptation approach is inspired by Particle Swarm Optimization (PSO). The model-driven approach constructs the density model and estimates the density of solutions from each defined sub-location in a whole objective space. Furthermore, the model-driven approach provides smoothness to the model by applying a Gaussian Process model and calculating the area under the mean function. The mean function area helps to find the required number of the reference points in each mean function. The experimental results demonstrate that both adaptive approaches are significantly better than several state-of-the-art MOEAs.  To achieve the third goal, the thesis proposes the first algorithm that combines GP as a global search with PLS as a local search in many-objective JSS. The proposed algorithm introduces an effective fitness-based selection strategy for selecting initial individuals for neighborhood exploration. It defines the GP's proper neighborhood structure and a new selection mechanism for selecting the effective dispatching rules during the local search. The experimental results on the JSS benchmark problem show that the newly proposed algorithm can significantly outperform its baseline algorithm (GP-NSGA-III).</p>


Author(s):  
Er-chao Li ◽  
Kang-wei Li

Aims: The main purpose of this paper is to solve the issues that the poor quality of offspring solutions generated by traditional evolutionary operators, and that the inability of the evolutionary algorithm based on decomposition to better solve the multi-objective optimization problems (MOPs) with complicated Pareto fronts (PFs). Background: For some complicated multi-objective optimization problems, the effect of the multi-objective evolutionary algorithm based on decomposition (MOEA/D) is poor. For specific complicated problems, there is less research on improving the algorithm's performance by setting and adjusting the direction vector in the decomposition-based evolutionary algorithm. And considering that in the existing algorithms, the optimal solutions are selected according to the selection strategy in the selection stage, without considering if it could produce the better solutions in the stage of individual generation to achieve the optimization effect faster. As a result of these, a multi-objective evolutionary algorithm that is based on two reference points decomposition and historical information prediction is proposed. Objective: In order to verify the feasibility of the proposed strategy, the F-series test function with complicated PFs is used as the test function to simulate the proposed strategy. Method: Firstly, the evolutionary operator based on Historical Information Prediction (EHIP) is used to generate better offspring solutions to improve the convergence of the algorithm; secondly, the decomposition strategy based on ideal point and nadir point is used to select solutions to solve the MOPs with complicated PFs, and the decomposition method with augmentation term is used to improve the population diversity when selecting solutions according to the nadir point. Finally, the proposed algorithm is compared to several popular algorithms by the F-series test function, and the comparison is made according to the corresponding performance metrics. Result: The performance of the algorithm is improved obviously compared with the popular algorithms after using the EHIP. When the decomposition method with augmentation term is added, the performance of the proposed algorithm is better than the algorithm with only the EHIP on the whole. However, the overall performance is better than the popular algorithms. Conclusion and Prospect: The experimental results show that the overall performance of the proposed algorithm is superior to the popular algorithms. The EHIP can produce better quality offspring solutions, and the decomposition strategy based on two reference points can well solve the MOPs with complicated PFs. This paper mainly demonstrates the theory without testing the practical problems. The following research mainly focuses on the application of the proposed algorithm to the practical problems such as robot path planning.


Author(s):  
Haijuan Zhang ◽  
Gai-Ge Wang

AbstractMulti-objective problems in real world are often contradictory and even change over time. As we know, how to find the changing Pareto front quickly and accurately is challenging during the process of solving dynamic multi-objective optimization problems (DMOPs). In addition, most solutions obey different distributions in decision space and the performance of NSGA-III when dealing with DMOPs should be further improved. In this paper, centroid distance is proposed and combined into NSGA-III with transfer learning together for DMOPs, called TC_NSGAIII. Centroid distance-based strategy is regarded as a prediction method to prevent some inappropriate individuals through measuring the distance of the population centroid and reference points. After the distance strategy, transfer learning is used for generating an initial population using the past experience. To verify the effectiveness of our proposed algorithm, NSGAIII, Tr_NSGAIII (NSGA-III combining with transfer learning only), Ce_NSGAIII (NSGA-III combining with centroid distance only), and TC_NSGAIII are compared. Seven state-of-the-art algorithms have been used for comparison on CEC 2015 benchmarks. Besides, transfer learning and centroid distance are regarded as a dynamic strategy, which is incorporated into three static algorithms, and the performance improvement is measured. What’s more, twelve benchmark functions from CEC 2015 and eight sets of parameters in each function are used in our experiments. The experimental results show that the performance of algorithms can be greatly improved through the proposed approach.


2021 ◽  
Vol 239 ◽  
pp. 112187
Author(s):  
Dênis E.C. Vargas ◽  
Afonso C.C. Lemonge ◽  
Helio J.C. Barbosa ◽  
Heder S. Bernardino

2020 ◽  
Vol 40 (3) ◽  
pp. 55-69
Author(s):  
Luis Felipe Ariza Vesga ◽  
Johan Sebastián Eslava Garzón ◽  
Rafael Puerta Ramirez

Multi-Objective and Many-objective Optimization problems have been extensively solved through evolutionary algorithms over a few decades. Despite the fact that NSGA-II and NSGA-III are frequently employed as a reference for a comparative evaluation of new evolutionary algorithms, the latter is proprietary. In this paper, we used the basic framework of the NSGA-II, which is very similar to the NSGA-III, with significant changes in its selection operator. We took the first front generated at the non-dominating sort procedure to obtain nonnegative and nonrepeated extreme points. This opensource version of the NSGA-III is called EF1-NSGA-III, and its implementation does not start from scratch; that would be reinventing the wheel. Instead, we took the NSGA-II code from the authors in the repository of the Kanpur Genetic Algorithms Laboratory to extend the EF1-NSGA-III. We then adjusted its selection operator from diversity, based on the crowding distance, to the one found on reference points and preserved its parameters. After that, we continued with the adaptive EF1-NSGA-III (A-EF1-NSGA-III), and the efficient adaptive EF1-NSGA-III (A2-EF1-NSGA-III), while also contributing to explain how to generate different types of reference points. The proposed algorithms resolve optimization problems with constraints of up to 10 objective functions. We tested them on a wide range of benchmark problems, and they showed notable improvements in terms of convergence and diversity by using the Inverted Generational Distance (IGD) and the HyperVolume (HV) performance metrics. The EF1-NSGA-III aims to resolve the power consumption for Centralized Radio Access Networks and the BiObjective Minimum DiameterCost Spanning Tree problems.


2018 ◽  
Vol 32 (34n36) ◽  
pp. 1840110 ◽  
Author(s):  
Chun Wang ◽  
Zhicheng Ji ◽  
Yan Wang

This paper considers many-objective flexible job shop scheduling problem (MaOFJSP) in which the number of optimization problems is larger than three. An integrated multi-objective optimization method is proposed which contains both optimization and decision making. The non-dominated sorting genetic algorithm III (NSGA-III) is utilized to find a trade-off solution set by simultaneously optimizing six objectives including makespan, workload balance, mean of earliness and tardiness, cost, quality, and energy consumption. Then, an integrated multi-attribute decision-making method is introduced to select one solution that fits into the decision maker’s preference. NSGA-III is compared with three multi-objective evolutionary algorithms (MOEAs)-based scheduling methods, and the simulation results show that NSGA-III performs better in generating the Pareto solutions. In addition, the impacts of using different reference points and decoding methods are investigated.


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