Adaptive multimodal continuous ant colony optimization

Seeking multiple optima simultaneously, which multimodal optimization aims at, has attracted increasing attention but remains challenging. Taking advantage of ant colony optimization algorithms in preserving high diversity, this paper intends to extend ant colony optimization algorithms to deal with multimodal optimization. First, combined with current niching methods, an adaptive multimodal continuous ant colony optimization algorithm is introduced. In this algorithm, an adaptive parameter adjustment is developed, which takes the difference among niches into consideration. Second, to accelerate convergence, a differential evolution mutation operator is alternatively utilized to build base vectors for ants to construct new solutions. Then, to enhance the exploitation, a local search scheme based on Gaussian distribution is self-adaptively performed around the seeds of niches. Together, the proposed algorithm affords a good balance between exploration and exploitation. Extensive experiments on 20 widely used benchmark multimodal functions are conducted to investigate the influence of each algorithmic component and results are compared with several state-of-the-art multimodal algorithms and winners of competitions on multimodal optimization. These comparisons demonstrate the competitive efficiency and effectiveness of the proposed algorithm, especially in dealing with complex problems with high numbers of local optima

A general framework of multi-population methods with clustering in undetectable dynamic environments

Copyright @ 2011 IEEETo solve dynamic optimization problems, multiple population methods are used to enhance the population diversity for an algorithm with the aim of maintaining multiple populations in different sub-areas in the fitness landscape. Many experimental studies have shown that locating and tracking multiple relatively good optima rather than a single global optimum is an effective idea in dynamic environments. However, several challenges need to be addressed when multi-population methods are applied, e.g., how to create multiple populations, how to maintain them in different sub-areas, and how to deal with the situation where changes can not be detected or predicted. To address these issues, this paper investigates a hierarchical clustering method to locate and track multiple optima for dynamic optimization problems. To deal with undetectable dynamic environments, this paper applies the random immigrants method without change detection based on a mechanism that can automatically reduce redundant individuals in the search space throughout the run. These methods are implemented into several research areas, including particle swarm optimization, genetic algorithm, and differential evolution. An experimental study is conducted based on the moving peaks benchmark to test the performance with several other algorithms from the literature. The experimental results show the efficiency of the clustering method for locating and tracking multiple optima in comparison with other algorithms based on multi-population methods on the moving peaks benchmark

Bio-inspired computation: where we stand and what's next

In recent years, the research community has witnessed an explosion of literature dealing with the adaptation of behavioral patterns and social phenomena observed in nature towards efficiently solving complex computational tasks. This trend has been especially dramatic in what relates to optimization problems, mainly due to the unprecedented complexity of problem instances, arising from a diverse spectrum of domains such as transportation, logistics, energy, climate, social networks, health and industry 4.0, among many others. Notwithstanding this upsurge of activity, research in this vibrant topic should be steered towards certain areas that, despite their eventual value and impact on the field of bio-inspired computation, still remain insufficiently explored to date. The main purpose of this paper is to outline the state of the art and to identify open challenges concerning the most relevant areas within bio-inspired optimization. An analysis and discussion are also carried out over the general trajectory followed in recent years by the community working in this field, thereby highlighting the need for reaching a consensus and joining forces towards achieving valuable insights into the understanding of this family of optimization techniques

Uncertainty evaluation of reservoir simulation models using particle swarms and hierarchical clustering

History matching production data in finite difference reservoir simulation models has been and always will be a challenge for the industry. The principal hurdles that need to be overcome are finding a match in the first place and more importantly a set of matches that can capture the uncertainty range of the simulation model and to do this in as short a time as possible since the bottleneck in this process is the length of time taken to run the model. This study looks at the implementation of Particle Swarm Optimisation (PSO) in history matching finite difference simulation models. Particle Swarms are a class of evolutionary algorithms that have shown much promise over the last decade. This method draws parallels from the social interaction of swarms of bees, flocks of birds and shoals of fish. Essentially a swarm of agents are allowed to search the solution hyperspace keeping in memory each individual’s historical best position and iteratively improving the optimisation by the emergent interaction of the swarm. An intrinsic feature of PSO is its local search capability. A sequential niching variation of the PSO has been developed viz. Flexi-PSO that enhances the exploration and exploitation of the hyperspace and is capable of finding multiple minima. This new variation has been applied to history matching synthetic reservoir simulation models to find multiple distinct history 3 matches to try to capture the uncertainty range. Hierarchical clustering is then used to post-process the history match runs to reduce the size of the ensemble carried forward for prediction. The success of the uncertainty modelling exercise is then assessed by checking whether the production profile forecasts generated by the ensemble covers the truth case

Bio-inspired computation: where we stand and what's next

In recent years, the research community has witnessed an explosion of literature dealing with the adaptation of behavioral patterns and social phenomena observed in nature towards efficiently solving complex computational tasks. This trend has been especially dramatic in what relates to optimization problems, mainly due to the unprecedented complexity of problem instances, arising from a diverse spectrum of domains such as transportation, logistics, energy, climate, social networks, health and industry 4.0, among many others. Notwithstanding this upsurge of activity, research in this vibrant topic should be steered towards certain areas that, despite their eventual value and impact on the field of bio-inspired computation, still remain insufficiently explored to date. The main purpose of this paper is to outline the state of the art and to identify open challenges concerning the most relevant areas within bio-inspired optimization. An analysis and discussion are also carried out over the general trajectory followed in recent years by the community working in this field, thereby highlighting the need for reaching a consensus and joining forces towards achieving valuable insights into the understanding of this family of optimization techniques

Nature-inspired algorithms for solving some hard numerical problems

Optimisation is a branch of mathematics that was developed to find the optimal solutions, among all the possible ones, for a given problem. Applications of optimisation techniques are currently employed in engineering, computing, and industrial problems. Therefore, optimisation is a very active research area, leading to the publication of a large number of methods to solve specific problems to its optimality. This dissertation focuses on the adaptation of two nature inspired algorithms that, based on optimisation techniques, are able to compute approximations for zeros of polynomials and roots of non-linear equations and systems of non-linear equations. Although many iterative methods for finding all the roots of a given function already exist, they usually require: (a) repeated deflations, that can lead to very inaccurate results due to the problem of accumulating rounding errors, (b) good initial approximations to the roots for the algorithm converge, or (c) the computation of first or second order derivatives, which besides being computationally intensive, it is not always possible. The drawbacks previously mentioned served as motivation for the use of Particle Swarm Optimisation (PSO) and Artificial Neural Networks (ANNs) for root-finding, since they are known, respectively, for their ability to explore high-dimensional spaces (not requiring good initial approximations) and for their capability to model complex problems. Besides that, both methods do not need repeated deflations, nor derivative information. The algorithms were described throughout this document and tested using a test suite of hard numerical problems in science and engineering. Results, in turn, were compared with several results available on the literature and with the well-known Durand–Kerner method, depicting that both algorithms are effective to solve the numerical problems considered.A Optimização é um ramo da matemática desenvolvido para encontrar as soluções óptimas, de entre todas as possíveis, para um determinado problema. Actualmente, são várias as técnicas de optimização aplicadas a problemas de engenharia, de informática e da indústria. Dada a grande panóplia de aplicações, existem inúmeros trabalhos publicados que propõem métodos para resolver, de forma óptima, problemas específicos. Esta dissertação foca-se na adaptação de dois algoritmos inspirados na natureza que, tendo como base técnicas de optimização, são capazes de calcular aproximações para zeros de polinómios e raízes de equações não lineares e sistemas de equações não lineares. Embora já existam muitos métodos iterativos para encontrar todas as raízes ou zeros de uma função, eles usualmente exigem: (a) deflações repetidas, que podem levar a resultados muito inexactos, devido ao problema da acumulação de erros de arredondamento a cada iteração; (b) boas aproximações iniciais para as raízes para o algoritmo convergir, ou (c) o cálculo de derivadas de primeira ou de segunda ordem que, além de ser computacionalmente intensivo, para muitas funções é impossível de se calcular. Estas desvantagens motivaram o uso da Optimização por Enxame de Partículas (PSO) e de Redes Neurais Artificiais (RNAs) para o cálculo de raízes. Estas técnicas são conhecidas, respectivamente, pela sua capacidade de explorar espaços de dimensão superior (não exigindo boas aproximações iniciais) e pela sua capacidade de modelar problemas complexos. Além disto, tais técnicas não necessitam de deflações repetidas, nem do cálculo de derivadas. Ao longo deste documento, os algoritmos são descritos e testados, usando um conjunto de problemas numéricos com aplicações nas ciências e na engenharia. Os resultados foram comparados com outros disponíveis na literatura e com o método de Durand–Kerner, e sugerem que ambos os algoritmos são capazes de resolver os problemas numéricos considerados

Peeking beyond peaks:Challenges and research potentials of continuous multimodal multi-objective optimization

Multi-objective (MO) optimization, i.e., the simultaneous optimization of multiple conflicting objectives, is gaining more and more attention in various research areas, such as evolutionary computation, machine learning (e.g., (hyper-)parameter optimization), or logistics (e.g., vehicle routing). Many works in this domain mention the structural problem property of multimodality as a challenge from two classical perspectives: (1) finding all globally optimal solution sets, and (2) avoiding to get trapped in local optima. Interestingly, these streams seem to transfer many traditional concepts of single-objective (SO) optimization into claims, assumptions, or even terminology regarding the MO domain, but mostly neglect the understanding of the structural properties as well as the algorithmic search behavior on a problem's landscape. However, some recent works counteract this trend, by investigating the fundamentals and characteristics of MO problems using new visualization techniques and gaining surprising insights. Using these visual insights, this work proposes a step towards a unified terminology to capture multimodality and locality in a broader way than it is usually done. This enables us to investigate current research activities in multimodal continuous MO optimization and to highlight new implications and promising research directions for the design of benchmark suites, the discovery of MO landscape features, the development of new MO (or even SO) optimization algorithms, and performance indicators. For all these topics, we provide a review of ideas and methods but also an outlook on future challenges, research potential and perspectives that result from recent developments.</p

Multimodal Optimization by Covariance Matrix Self-Adaptation Evolution Strategy with Repelling Subpopulations

During the recent decades, many niching methods have been proposed and empirically verified on some available test problems. They often rely on some particular assumptions associated with the distribution, shape, and size of the basins, which can seldom be made in practical optimization problems. This study utilizes several existing concepts and techniques, such as taboo points, normalized Mahalanobis distance, and the Ursem's hill-valley function in order to develop a new tool for multimodal optimization, which does not make any of these assumptions. In the proposed method, several subpopulations explore the search space in parallel. Offspring of a subpopulation are forced to maintain a sufficient distance to the center of fitter subpopulations and the previously identified basins, which are marked as taboo points. The taboo points repel the subpopulation to prevent convergence to the same basin. A strategy to update the repelling power of the taboo points is proposed to address the challenge of basins of dissimilar size. The local shape of a basin is also approximated by the distribution of the subpopulation members converging to that basin. The proposed niching strategy is incorporated into the covariance matrix self-adaptation evolution strategy (CMSA-ES), a potent global optimization method. The resultant method, called the covariance matrix self-adaptation with repelling subpopulations (RS-CMSA), is assessed and compared to several state-of-the-art niching methods on a standard test suite for multimodal optimization. An organized procedure for parameter setting is followed which assumes a rough estimation of the desired/expected number of minima available. Performance sensitivity to the accuracy of this estimation is also studied by introducing the concept of robust mean peak ratio. Based on the numerical results using the available and the introduced performance measures, RS-CMSA emerges as the most successful method when robustness and efficiency are considered at the same time.FWN – Publicaties zonder aanstelling Universiteit Leide

Multi-population methods in unconstrained continuous dynamic environments: The challenges

Themulti-populationmethod has been widely used to solve unconstrained continuous dynamic optimization problems with the aim of maintaining multiple populations on different peaks to locate and track multiple changing peaks simultaneously. However, to make this approach efficient, several crucial challenging issues need to be addressed, e.g., how to determine the moment to react to changes, how to adapt the number of populations to changing environments, and how to determine the search area of each population. In addition, several other issues, e.g., communication between populations, overlapping search, the way to create multiple populations, detection of changes, and local search operators, should be also addressed. The lack of attention on these challenging issues within multi-population methods hinders the development of multi-population based algorithms in dynamic environments. In this paper, these challenging issues are comprehensively analyzed by a set of experimental studies from the algorithm design point of view. Experimental studies based on a set of popular algorithms show that the performance of algorithms is significantly affected by these challenging issues on the moving peaks benchmark. Keywords: Multi-population methods, dynamic optimization problems, evolutionary computatio