Combining model-based and genetics-based offspring generation for multi-objective optimization using a convergence criterion

Abstract — In our previous work [1], it has been shown that the performance of evolutionary multi-objective algorithms can be greatly enhanced if the regularity in the distribution of Pareto-optimal solutions is taken advantage using a probabilistic model. This paper suggests a new hybrid multi-objective evolutionary algorithm by introducing a convergence based criterion to determine when the model-based method and when the genetics-based method should be used to generate offspring in each generation. The basic idea is that the genetics-based method, i.e., crossover and mutation, should be used when the population is far away from the Pareto front and no obvious regularity in population distribution can be observed. When the population moves towards the Pareto front, the distribution of the individuals will show increasing regularity and in this case, the model-based method should be used to generate offspring. The proposed hybrid method is verified on widely used test problems and our simulation results show that the method is effective in achieving Pareto-optimal solutions compared to two state-of-the-art evolutionary multi-objective algorithms: NSGA-II and SPEA2, and our pervious method in [1]. I

МОДИФИКАЦИЯ МЕТАЭВРИСТИЧЕСКОГО МЕТОДА ФЕЙЕРВЕРКОВ ДЛЯ ЗАДАЧ МНОГОКРИТЕРИАЛЬНОЙ ОПТИМИЗАЦИИ НА ОСНОВЕ НЕДОМИНИРУЕМОЙ СОРТИРОВКИ

The article suggests a modification for numerical fireworks method of the single-objective optimization for solving the problem of multiobjective optimization. The method is metaheuristic. It does not guarantee finding the exact solution, but can give a good approximate result. Multiobjective optimization problem is considered with numerical criteria of equal importance. A possible solution to the problem is a vector of real numbers. Each component of the vector of a possible solution belongs to a certain segment. The optimal solution of the problem is considered a Pareto optimal solution. Because the set of Pareto optimal solutions can be infinite; we consider a method for finding an approximation consisting of a finite number of Pareto optimal solutions. The modification is based on the procedure of non-dominated sorting. It is the main procedure for solutions search. Non-dominated sorting is the ranking of decisions based on the values of the numerical vector obtained using the criteria. Solutions are divided into disjoint subsets. The first subset is the Pareto optimal solutions, the second subset is the Pareto optimal solutions if the first subset is not taken into account, and the last subset is the Pareto optimal solutions if the rest subsets are not taken into account. After such a partition, the decision is made to create new solutions. The method was tested on well-known bi-objective optimization problems: ZDT2, LZ01. Structure of the location of Pareto optimal solutions differs for the problems. LZ01 have complex structure of Pareto optimal solutions. In conclusion, the question of future research and the issue of modifying the method for problems with general constraints are discussed.В работе предлагается модификация численного метода фейерверков однокритериальной оптимизации для решения задач многокритериальной оптимизации. Метод относится к метаэвристическим алгоритмам, он не гарантирует нахождения точного решения, но может найти достаточно хорошее приближенное решение. Рассматриваются многокритериальные задачи оптимизации с числовыми критериями, имеющими одинаковую важность. Допустимое решение задачи представляется вектором из действительных чисел, значение каждой компоненты которого принадлежит определенному отрезку. Под оптимальным решением понимается решение, оптимальное по Парето. Так как точных решений, оптимальных по Парето, может быть бесконечно много, рассматривается способ нахождения приближения, состоящего из конечного числа решений, оптимальных по Парето. Модификация основана на процедуре недоминируемой сортировки, которая является основной процедурой для управления процессом поиска приближенного решения. Недоминируемая сортировка – это ранжирование решений на основе значений компонент числового вектора, полученных с помощью вычисления критериев. Каждая компонента соответствует определенному критерию, а множество решений разбивается на непересекающиеся подмножества. Первое подмножество – это решения, оптимальные по Парето, второе подмножество – это решения, оптимальные по Парето, если не учитывать первое подмножество, последнее подмножество – это решения, оптимальные по Парето, если не учитывать все предыдущие подмножества. После такого разбиения принимается решение о генерировании новых допустимых решений. Работа метода протестирована на общеизвестных задачах многокритериальной оптимизации с двумя критериями: ZDT2, LZ01. Задачи отличаются структурой расположения решений, оптимальных по Парето. Так LZ01 имеет достаточно сложную структуру решений, оптимальных по Парето. В заключении обсуждаются вопросы о дальнейшем направлении исследований и о возможности модификации метода для задач многокритериальной оптимизации с произвольными, а не параллелепипедными ограничениями

Freedom of Movement for Workers from Central and Eastern Europe: Experiences in Ireland and Sweden

In 2004 the European Union (EU) gained ten new Member States. However in many of the old Member States there were increasing concerns about the implications of this particular enlargement. Not only did it represent a large increase in the Union's population; in eight of the ten countries the wage levels were substantially below the wage levels in the old Member States. As several governments feared mass immigration, "welfare tourism" and negative effects on their labour markets, transitional rules were included in the Accession Treaty with regard to the freedom of movement for workers from the Central and East European Member (CEE) States.Two years after this momentous step in the European integration process, SIEPS decided to examine the effects from the 2004 enlargement in the countries that opened their labour market to workers from the CEE Member States. The study attempts to provide as thorough as possible a picture of the post-enlargement experiences in Ireland and Sweden

Meta-heuristic algorithms in car engine design: a literature survey

Meta-heuristic algorithms are often inspired by natural phenomena, including the evolution of species in Darwinian natural selection theory, ant behaviors in biology, flock behaviors of some birds, and annealing in metallurgy. Due to their great potential in solving difficult optimization problems, meta-heuristic algorithms have found their way into automobile engine design. There are different optimization problems arising in different areas of car engine management including calibration, control system, fault diagnosis, and modeling. In this paper we review the state-of-the-art applications of different meta-heuristic algorithms in engine management systems. The review covers a wide range of research, including the application of meta-heuristic algorithms in engine calibration, optimizing engine control systems, engine fault diagnosis, and optimizing different parts of engines and modeling. The meta-heuristic algorithms reviewed in this paper include evolutionary algorithms, evolution strategy, evolutionary programming, genetic programming, differential evolution, estimation of distribution algorithm, ant colony optimization, particle swarm optimization, memetic algorithms, and artificial immune system

On the Robustness of Median Sampling in Noisy Evolutionary Optimization

In real-world optimization tasks, the objective (i.e., fitness) function evaluation is often disturbed by noise due to a wide range of uncertainties. Evolutionary algorithms (EAs) have been widely applied to tackle noisy optimization, where reducing the negative effect of noise is a crucial issue. One popular strategy to cope with noise is sampling, which evaluates the fitness multiple times and uses the sample average to approximate the true fitness. In this paper, we introduce median sampling as a noise handling strategy into EAs, which uses the median of the multiple evaluations to approximate the true fitness instead of the mean. We theoretically show that median sampling can reduce the expected running time of EAs from exponential to polynomial by considering the (1+1)-EA on OneMax under the commonly used one-bit noise. We also compare mean sampling with median sampling by considering two specific noise models, suggesting that when the 2-quantile of the noisy fitness increases with the true fitness, median sampling can be a better choice. The results provide us with some guidance to employ median sampling efficiently in practice.Comment: 19 pages. arXiv admin note: text overlap with arXiv:1810.05045, arXiv:1711.0095

Synthesis of time-to-amplitude converter by mean coevolution with adaptive parameters

Copyright © 2011 the authors and Scientific Research Publishing Inc. This work is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/)The challenging task to synthesize automatically a time-to-amplitude converter, which unites by its functionality several digital circuits, has been successfully solved with the help of a novel methodology. The proposed approach is based on a paradigm according to which the substructures are regarded as additional mutation types and when ranged with other mutations form a new adaptive individual-level mutation technique. This mutation approach led to the discovery of an original coevolution strategy that is characterized by very low selection rates. Parallel island-model evolution has been running in a hybrid competitive-cooperative interaction throughout two incremental stages. The adaptive population size is applied for synchronization of the parallel evolutions

Identity Management in Information Age Government: Exploring Concepts, Definitions, Approaches and Solutions

Our research question is the following: What could be a useful working definition of Identity Management in government at present? a) What are conceptualisations, definitions and approaches of IDM in government according to academic literature? b) Which e-authentication solutions have been developed in other jurisdictions