The (M-1)+1 Framework of Relaxed Pareto Dominance for Evolutionary Many-Objective Optimization

Author(s):  
Shuwei Zhu ◽  
Lihong Xu ◽  
Erik Goodman ◽  
Kalyanmoy Deb ◽  
Zhichao Lu
Keyword(s):  
2018 ◽  
Author(s):  
Ricardo Guedes ◽  
Vasco Furtado ◽  
Tarcísio Pequeno ◽  
Joel Rodrigues

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.


2017 ◽  
Vol 5 (2) ◽  
pp. 162-176
Author(s):  
Ismail Saglam

Baron and Myerson (BM; 1982, Econometrica, 50(4), 911–930) propose an incentive-compatible, individually rational and ex ante socially optimal direct-revelation mechanism to regulate a monopolistic firm with unknown costs. Their mechanism is not ex post Pareto dominated by any other feasible direct-revelation mechanism. However, there also exist an uncountable number of feasible direct-revelation mechanisms that are not ex post Pareto dominated by the BM mechanism. To investigate whether the BM mechanism remains in the set of ex post undominated mechanisms when the Pareto axiom is slightly weakened, we introduce the ∈-Pareto dominance. This concept requires the relevant dominance relationships to hold in the support of the regulator’s beliefs everywhere except for a set of points of measure ∈, which can be arbitrarily small. We show that a modification of the BM mechanism which always equates the price to the marginal cost can ∈-Pareto dominate the BM mechanism at uncountably many regulatory environments, while it is never ∈-Pareto dominated by the BM mechanism at any regulatory environment.


2021 ◽  
Author(s):  
Zhigang Lu ◽  
Shengjing Qi ◽  
Jiangfeng Zhang ◽  
Yao Cai ◽  
Xiaoqiang Guo ◽  
...  

2021 ◽  
Vol 40 (1) ◽  
pp. 449-461
Author(s):  
Ziyu Hu ◽  
Xuemin Ma ◽  
Hao Sun ◽  
Jingming Yang ◽  
Zhiwei Zhao

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.


Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2837
Author(s):  
Saykat Dutta ◽  
Sri Srinivasa Raju M ◽  
Rammohan Mallipeddi ◽  
Kedar Nath Das ◽  
Dong-Gyu Lee

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.


2022 ◽  
Vol 22 (1) ◽  
pp. 1-28
Author(s):  
R. Paul Wiegand ◽  
Anthony Bucci ◽  
Amruth N. Kumar ◽  
Jennifer Albert ◽  
Alessio Gaspar

In this article, we leverage ideas from the theory of coevolutionary computation to analyze interactions of students with problems. We introduce the idea of informatively easy or hard concepts. Our approach is different from more traditional analyses of problem difficulty such as item analysis in the sense that we consider Pareto dominance relationships within the multidimensional structure of student–problem performance data rather than average performance measures. This method allows us to uncover not just the problems on which students are struggling but also the variety of difficulties different students face. Our approach is to apply methods from the Dimension Extraction Coevolutionary Algorithm to analyze problem-solving logs of students generated when they use an online software tutoring suite for introductory computer programming called problets . The results of our analysis not only have implications for how to scale up and improve adaptive tutoring software but also have the promise of contributing to the identification of common misconceptions held by students and thus, eventually, to the construction of a concept inventory for introductory programming.


Ciencia Unemi ◽  
2017 ◽  
Vol 9 (21) ◽  
pp. 58
Author(s):  
Marcelo Haro Gavidia ◽  
Guisella Chabla Galarza ◽  
Miguel Montalvo Robalino ◽  
David Coello Chabla ◽  
Pavel Novoa-Hernández

Uno de los principales objetivos en la educación es lograr que los estudiantes desarrollen la capacidad de trabajo en equipo. Esta capacidad potencia la socialización entre los estudiantes y la resolución de problemas complejos. Comúnmente, la creación de estos equipos es realizada por el docente de la asignatura, quien debe tener en cuenta múltiples criterios como la presencia de un estudiante líder y equipos heterogéneos. Cuando la asignatura tiene poco estudiantes, esta tarea suele ser fácil. Sin embargo, cuando se debe tener en cuenta a numerosos estudiantes, la tarea se torna compleja y por lo general no existe garantía de que los equipos creados cumplan con los criterios deseados. En este sentido, con el objetivo de favorecer el desarrollo óptimo de esta tarea docente, la presente investigación propone una solución computacional que automatiza la creación de equipos de trabajo de estudiantes. Específicamente, la tarea de la creación de los equipos se modeló matemáticamente como un problema de optimización de tipo combinatorio y multi-objetivo, que fue resuelto a su vez por un algoritmo evolutivo basado en los conceptos de Dominancia de Pareto. Para validar las propuestas, se realizaron varios experimentos computacionales que involucran escenarios reales, relacionados con la Unidad de Aprendizaje Inglés en varias carreras de la Universidad Técnica Estatal de Quevedo. ABSTRACTOne of the main goals for Higher Education is to educate students to work in teams. Such a skill not only improves their social behavior in the community, but also the ability for solving complex problems. Usually, the process of making teams is carried out by professor of the subject, who has to take into account several criteria (e.g. the presence of leader, heterogeneity of the team according the level of knowledge, sex, among others). When the subject has just few students, this task becomes easy. However, in the case of classes with a large number of students, this task becomes complex and there is no warranty about the accomplishment of the considered criteria. In that sense, the present work proposes a computational solution that automatizes the task of student teams building. Specifically, it was approached as a multi-objective combinatorial optimization problem, which was solved using a Pareto Dominance-based algorithm. In order to validate the proposal we performed several computational experiments involving real case studies from the English subject of three careers at the Technical State University of Quevedo. Results show that the proposed approach is able to build balanced teams according to the considered criteria.


2017 ◽  
Vol 63 (4) ◽  
pp. 493-503 ◽  
Author(s):  
Muneendra Ojha ◽  
Krishna Pratap Singh ◽  
Pavan Chakraborty ◽  
Shekhar Verma ◽  
Purnendu Shekhar Pandey

Sign in / Sign up

Export Citation Format

Share Document