Particle swarm optimization for multimodal functions: a clustering approach

The particle swarm optimization (PSO) algorithm is designed to find a single optimal solution and needs some modifications to be able to locate multiple optima on a multimodal function. In parallel with evolutionary computation algorithms, these modifications can be grouped in the framework of niching. In this work, we present a new approach to niching in PSO based on clustering particles to identify niches. The neighborhood structure, on which particles rely for communication, is exploited together with the niche information to locate multiple optima in parallel. Our approach was implemented in thek-means-based PSO (kPSO), which employs the standardk-means clustering algorithm, improved with a mechanism to adaptively identify the number of clusters.kPSO proved to be a competitive solution when compared with other existing algorithms, since it showed better performance on a benchmark set of multimodal functions

Multi-population methods with adaptive mutation for multi-modal optimization problems

open access journalThis paper presents an efficient scheme to locate multiple peaks on multi-modal optimization problems by using genetic algorithms (GAs). The premature convergence problem shows due to the loss of diversity, the multi-population technique can be applied to maintain the diversity in the population and the convergence capacity of GAs. The proposed scheme is the combination of multi-population with adaptive mutation operator, which determines two different mutation probabilities for different sites of the solutions. The probabilities are updated by the fitness and distribution of solutions in the search space during the evolution process. The experimental results demonstrate the performance of the proposed algorithm based on a set of benchmark problems in comparison with relevant algorithms

Evolving Through the Looking Glass: Learning Improved Search Spaces with Variational Autoencoders

Nature has spent billions of years perfecting our genetic representations, making them evolvable and expressive. Generative machine learning offers a shortcut: learn an evolvable latent space with implicit biases towards better solutions. We present SOLVE: Search space Optimization with Latent Variable Evolution, which creates a dataset of solutions that satisfy extra problem criteria or heuristics, generates a new latent search space, and uses a genetic algorithm to search within this new space to find solutions that meet the overall objective. We investigate SOLVE on five sets of criteria designed to detrimentally affect the search space and explain how this approach can be easily extended as the problems become more complex. We show that, compared to an identical GA using a standard representation, SOLVE with its learned latent representation can meet extra criteria and find solutions with distance to optimal up to two orders of magnitude closer. We demonstrate that SOLVE achieves its results by creating better search spaces that focus on desirable regions, reduce discontinuities, and enable improved search by the genetic algorithm. Fig. 1.Search space Optimization with Latent Variable Evolution (SOLVE). An optimizer produces a dataset of random solutions satisfying an extra criterion (e.g., constraint or secondary objective). A variational autoencoder learns this dataset and produces a learned latent representation biased towards the desired region of the search space. This learned representation is then used by a genetic algorithm to find solutions that meet the objective and extra criterion together

RPSGAe - Reduced Pareto Set Genetic Algorithm : application to polymer extrusion

Publicado na serie "Lecture notes in economics and mathematical systems" ; 535In this paper a Multiobjective Optimization Genetic Algorithm, denoted as Reduced Pareto Set Genetic Algorithm with Elitism (RPSGAe), is presented and its performance is assessed. The algorithm is compared with other Evolutionary Multi-Objective Algorithms - EMOAs (SPEA2, PAES and NSGA-II) using problems from the literature and statistical comparison techniques. The results obtained showed that the RPSGAe algorithm has good overall performance. Finally, the RPSGAe algorithm was applied to the optimization of the polymer extrusion process. The aim is to implement an automatic optimization scheme capable of defining the values of important process parameters, such as operating conditions and screw geometry, yielding the best performance in terms of prescribed attributes. The results obtained for specific case studies have physical meaning and correspond to a successful process optimization

A software framework based on a conceptual unified model for evolutionary multiobjective optimization: ParadisEO-MOEO

International audienceThis paper presents a general-purpose software framework dedicated to the design and the implementation of evolutionary multiobjective optimization techniques: ParadisEO-MOEO. A concise overview of evolutionary algorithms for multiobjective optimization is given. A substantial number of methods has been proposed so far, and an attempt of conceptually unifying existing approaches is presented here. Based on a fine-grained decomposition and following the main issues of fitness assignment, diversity preservation and elitism, a conceptual model is proposed and is validated by regarding a number of state-of-the-art algorithms as simple variants of the same structure. This model is then incorporated into the ParadisEO-MOEO software framework. This framework has proven its validity and high flexibility by enabling the resolution of many academic, real-world and hard multiobjective optimization problems

An Entropy-Based Approach for Preserving Diversity in Evolutionary Topical Search

Topic-based information retrieval is the process of matching a topic of interest against the resources that are indexed. An approach for retrieving topicrelevant resources is to generate queries that are able to reflect the topic of interest. Multi-objective Evolutionary Algorithms have demonstrated great potential to deal with the problem of topical query generation. In an evolutionary approach to topic-based information retrieval the topic of interest is used to generate an initial population of queries, which is evolved towards successively better candidate queries. A common problem with such an approach is poor recall due to loss of genetic diversity. This work proposes a novel strategy inspired on the information theoretic notion of entropy to favor population diversity with the aim of attaining good global recall. Preliminary experiments conducted on a large dataset of labeled documents show the effectiveness of the proposed strategy.Sociedad Argentina de Informática e Investigación Operativa (SADIO

Multi-Modal Optimization with k-Cluster Big Bang-Big Crunch Algorithm

Multi-modal optimization is often encountered in engineering problems, especially when different and alternative solutions are sought. Evolutionary algorithms can efficiently tackle multi-modal optimization thanks to their features such as the concept of population, exploration/exploitation, and being suitable for parallel computation. This paper introduces a multi-modal optimization version of the Big Bang-Big Crunch algorithm based on clustering, namely, k-BBBC. This algorithm guarantees a complete convergence of the entire population, retrieving on average the 99\% of local optima for a specific problem. Additionally, we introduce two post-processing methods to (i) identify the local optima in a set of retrieved solutions (i.e., a population), and (ii) quantify the number of correctly retrieved optima against the expected ones (i.e., success rate). Our results show that k-BBBC performs well even with problems having a large number of optima (tested on 379 optima) and high dimensionality (tested on 32 decision variables). When compared to other multi-modal optimization methods, it outperforms them in terms of accuracy (in both search and objective space) and success rate (number of correctly retrieved optima) -- especially when elitism is applied. Lastly, we validated our proposed post-processing methods by comparing their success rate to the actual one. Results suggest that these methods can be used to evaluate the performance of a multi-modal optimization algorithm by correctly identifying optima and providing an indication of success -- without the need to know where the optima are located in the search space.Comment: 17 pages, 7 figure

Seeking multiple solutions:an updated survey on niching methods and their applications

Multi-Modal Optimization (MMO) aiming to locate multiple optimal (or near-optimal) solutions in a single simulation run has practical relevance to problem solving across many fields. Population-based meta-heuristics have been shown particularly effective in solving MMO problems, if equipped with specificallydesigned diversity-preserving mechanisms, commonly known as niching methods. This paper provides an updated survey on niching methods. The paper first revisits the fundamental concepts about niching and its most representative schemes, then reviews the most recent development of niching methods, including novel and hybrid methods, performance measures, and benchmarks for their assessment. Furthermore, the paper surveys previous attempts at leveraging the capabilities of niching to facilitate various optimization tasks (e.g., multi-objective and dynamic optimization) and machine learning tasks (e.g., clustering, feature selection, and learning ensembles). A list of successful applications of niching methods to real-world problems is presented to demonstrate the capabilities of niching methods in providing solutions that are difficult for other optimization methods to offer. The significant practical value of niching methods is clearly exemplified through these applications. Finally, the paper poses challenges and research questions on niching that are yet to be appropriately addressed. Providing answers to these questions is crucial before we can bring more fruitful benefits of niching to real-world problem solving

A multi-angle hierarchical differential evolution approach for multimodal optimization problems

Multimodal optimization problem (MMOP) is one of the most common problems in engineering practices that requires multiple optimal solutions to be located simultaneously. An efficient algorithm for solving MMOPs should balance the diversity and convergence of the population, so that the global optimal solutions can be located as many as possible. However, most of existing algorithms are easy to be trapped into local peaks and cannot provide high-quality solutions. To better deal with MMOPs, considerations on the solution quality angle and the evolution stage angle are both taken into account in this paper and a multi-angle hierarchical differential evolution (MaHDE) algorithm is proposed. Firstly, a fitness hierarchical mutation (FHM) strategy is designed to balance the exploration and exploitation ability of different individuals. In the FHM strategy, the individuals are divided into two levels (i.e., low/high-level) according to their solution quality in the current niche. Then, the low/high-level individuals are applied to different guiding strategies. Secondly, a directed global search (DGS) strategy is introduced for the low-level individuals in the late evolution stage, which can improve the population diversity and provide these low-level individuals with the opportunity to re-search the global peaks. Thirdly, an elite local search (ELS) strategy is designed for the high-level individuals in the late evolution stage to refine their solution accuracy. Extensive experiments are developed to verify the performance of MaHDE on the widely used MMOPs test functions i.e., CEC’2013. Experimental results show that MaHDE generally outperforms the compared state-of-the-art multimodal algorithms

Runtime Analysis of Probabilistic Crowding and Restricted Tournament Selection for Bimodal Optimisation

Many real optimisation problems lead to multimodal domains and so require the identifi- cation of multiple optima. Niching methods have been developed to maintain the population diversity, to investigate many peaks in parallel and to reduce the effect of genetic drift. Using rigorous runtime analysis, we analyse for the first time two well known niching methods: probabilistic crowding and restricted tournament selection (RTS). We incorporate both methods into a (µ+1) EA on the bimodal function Twomax where the goal is to find two optima at opposite ends of the search space. In probabilistic crowding, the offspring compete with their parents and the survivor is chosen proportionally to its fitness. On Twomax probabilistic crowding fails to find any reasonable solution quality even in exponential time. In RTS the offspring compete against the closest individual amongst w (window size) individuals. We prove that RTS fails if w is too small, leading to exponential times with high probability. However, if w is chosen large enough, it finds both optima for Twomax in time O(µn log n) with high probability. Our theoretical results are accompanied by experimental studies that match the theoretical results and also shed light on parameters not covered by the theoretical results