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

Adaptation and self-organization in evolutionary algorithms

The objective of Evolutionary Computation is to solve practical problems (e.g.optimization, data mining) by simulating the mechanisms of natural evolution. This thesis addresses several topics related to adaptation and self-organization in evolving systems with the overall aims of improving the performance of Evolutionary Algorithms (EA), understanding its relation to natural evolution, and incorporating new mechanisms for mimicking complex biological systems. Part I of this thesis presents a new mechanism for allowing an EA to adapt its behavior in response to changes in the environment. Using the new approach, adaptation of EA behavior (i.e. control of EA design parameters) is driven by an analysis of population dynamics, as opposed to the more traditional use of fitness measurements. Comparisons with a number of adaptive control methods from the literature indicate substantial improvements in algorithm performance for a range of artificial and engineering design problems. Part II of this thesis involves a more thorough analysis of EA behavior based on the methods derived in Part 1. In particular, several properties of EA population dynamics are measured and compared with observations of evolutionary dynamics in nature. The results demonstrate that some large scale spatial and temporal features of EA dynamics are remarkably similar to their natural counterpart. Compatibility of EA with the Theory of Self-Organized Criticality is also discussed. Part III proposes fundamentally new directions in EA research which are inspired by the conclusions drawn in Part II. These changes involve new mechanisms which allow self-organization of the EA to occur in ways which extend beyond its common convergence in parameter space. In particular, network models for EA populations are developed where the network structure is dynamically coupled to EA population dynamics. Results indicate strong improvements in algorithm performance compared to cellular Genetic Algorithms and non-distributed EA designs. Furthermore, topological analysis indicates that the population network can spontaneously evolve to display similar characteristics to the interaction networks of complex biological systems

A clustering particle swarm optimizer for locating and tracking multiple optima in dynamic environments

This article is posted here with permission from the IEEE - Copyright @ 2010 IEEEIn the real world, many optimization problems are dynamic. This requires an optimization algorithm to not only find the global optimal solution under a specific environment but also to track the trajectory of the changing optima over dynamic environments. To address this requirement, this paper investigates a clustering particle swarm optimizer (PSO) for dynamic optimization problems. This algorithm employs a hierarchical clustering method to locate and track multiple peaks. A fast local search method is also introduced to search optimal solutions in a promising subregion found by the clustering method. Experimental study is conducted based on the moving peaks benchmark to test the performance of the clustering PSO in comparison with several state-of-the-art algorithms from the literature. The experimental results show the efficiency of the clustering PSO for locating and tracking multiple optima in dynamic environments in comparison with other particle swarm optimization models based on the multiswarm method.This work was supported by the Engineering and Physical Sciences Research Council of U.K., under Grant EP/E060722/1

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

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

Multiobjective Design and Innovization of Robust Stormwater Management Plans

In the United States, states are federally mandated to develop watershed management plans to mitigate pollution from increased impervious surfaces due to land development such as buildings, roadways, and parking lots. These plans require a major investment in water retention infrastructure, known as structural Best Management Practices (BMPs). However, the discovery of BMP configurations that simultaneously minimize implementation cost and pollutant load is a complex problem. While not required by law, an additional challenge is to find plans that not only meet current pollutant load targets, but also take into consideration anticipated changes in future precipitation patterns due to climate change. In this dissertation, a multi-scale, multiobjective optimization method is presented to tackle these three objectives. The method is demonstrated on the Bartlett Brook mixed-used impaired watershed in South Burlington, VT. New contributions of this work include: (A) A method for encouraging uniformity of spacing along the non-dominated front in multiobjective evolutionary optimization. This method is implemented in multiobjective differential evolution, is validated on standard benchmark biobjective problems, and is shown to outperform existing methods. (B) A procedure to use GIS data to estimate maximum feasible BMP locations and sizes in subwatersheds. (C) A multi-scale decomposition of the watershed management problem that precalculates the optimal cost BMP configuration across the entire range of possible treatment levels within each subwatershed. This one-time pre-computation greatly reduces computation during the evolutionary optimization and enables formulation of the problem as real-valued biobjective global optimization, thus permitting use of multiobjective differential evolution. (D) Discovery of a computationally efficient surrogate for sediment load. This surrogate is validated on nine real watersheds with different characteristics and is used in the initial stages of the evolutionary optimization to further reduce the computational burden. (E) A lexicographic approach for incorporating the third objective of finding non-dominated solutions that are also robust to climate change. (F) New visualization methods for discovering design principles from dominated solutions. These visualization methods are first demonstrated on simple truss and beam design problems and then used to provide insights into the design of complex watershed management plans. It is shown how applying these visualization methods to sensitivity data can help one discover solutions that are robust to uncertain forcing conditions. In particular, the visualization method is applied to discover new design principles that may make watershed management plans more robust to climate change