Chaotic Quantum Double Delta Swarm Algorithm using Chebyshev Maps: Theoretical Foundations, Performance Analyses and Convergence Issues

Quantum Double Delta Swarm (QDDS) Algorithm is a new metaheuristic algorithm inspired by the convergence mechanism to the center of potential generated within a single well of a spatially co-located double-delta well setup. It mimics the wave nature of candidate positions in solution spaces and draws upon quantum mechanical interpretations much like other quantum-inspired computational intelligence paradigms. In this work, we introduce a Chebyshev map driven chaotic perturbation in the optimization phase of the algorithm to diversify weights placed on contemporary and historical, socially-optimal agents' solutions. We follow this up with a characterization of solution quality on a suite of 23 single-objective functions and carry out a comparative analysis with eight other related nature-inspired approaches. By comparing solution quality and successful runs over dynamic solution ranges, insights about the nature of convergence are obtained. A two-tailed t-test establishes the statistical significance of the solution data whereas Cohen's d and Hedge's g values provide a measure of effect sizes. We trace the trajectory of the fittest pseudo-agent over all function evaluations to comment on the dynamics of the system and prove that the proposed algorithm is theoretically globally convergent under the assumptions adopted for proofs of other closely-related random search algorithms.Comment: 27 pages, 4 figures, 19 table

Novelty grammar swarms

Tese de mestrado, Engenharia Informática (Sistemas de Informação), Universidade de Lisboa, Faculdade de Ciências, 2015Particle Swarm Optimization (PSO) é um dos métodos de optimização populacionais mais conhecido. Normalmente é aplicado na otimização funções de fitness, que indicam o quão perto o algoritmo está de atingir o objectivo da pesquisa, fazendo com que esta se foque em áreas de fitness mais elevado. Em problemas com muitos ótimos locais, regularmente a pesquisa fica presa em locais com fitness elevado mas que não são o verdadeiro objetivo. Com vista a solucionar este problema em certos domínios, nesta tese é introduzido o Novelty-driven Particle Swarm Optimization (NdPSO). Este algoritmo é inspirado na pesquisa pela novidade (novelty search), um método relativamente recente que guia a pesquisa de forma a encontrar instâncias significativamente diferentes das anteriores. Desta forma, o NdPSO ignora por completo o objetivo perseguindo apenas a novidade, isto torna-o menos susceptivel a ser enganado em problemas com muitos optimos locais. Uma vez que o novelty search mostrou potencial a resolver tarefas no âmbito da programação genética, em particular na evolução gramatical, neste projeto o NdPSO é usado como uma extensão do método de Grammatical Swarm que é uma combinação do PSO com a programação genética. A implementação do NdPSO é testada em três domínios diferentes, representativos daqueles para o qual este algoritmo poderá ser mais vantajoso que os algoritmos guiados pelo objectivo. Isto é, domínios enganadores nos quais seja relativamente intuitivo descrever um comportamento. Em cada um dos domínios testados, o NdPSO supera o aloritmo standard do PSO, uma das suas variantes mais conhecidas (Barebones PSO) e a pesquisa aleatória, mostrando ser uma ferramenta promissora para resolver problemas enganadores. Uma vez que esta é a primeira aplicação da pesquisa por novidade fora do paradigma evolucionário, neste projecto é também efectuado um estudo comparativo do novo algoritmo com a forma mais comum de usar a pesquisa pela novidade (na forma de algoritmo evolucionário).Particle Swarm Optimization (PSO) is a well-known population-based optimization algorithm. Most often it is applied to optimize fitness functions that specify the goal of reaching a desired objective or behavior. As a result, search focuses on higher-fitness areas. In problems with many local optima, search often becomes stuck, and thus can fail to find the intended objective. To remedy this problem in certain kinds of domains, this thesis introduces Novelty-driven Particle Swarm Optimization (NdPSO). Taking motivation from the novelty search algorithm in evolutionary computation, in this method search is driven only towards finding instances significantly different from those found before. In this way, NdPSO completely ignores the objective in its pursuit of novelty, making it less susceptible to deception and local optima. Because novelty search has previously shown potential for solving tasks in Genetic Programming, particularly, in Grammatical Evolution, this paper implements NdPSO as an extension of the Grammatical Swarm method which in effect is a combination of PSO and Genetic Programming.The resulting NdPSO implementation was tested in three different domains representative of those in which it might provide advantage over objective-driven PSO, in particular, those which are deceptive and in which a meaningful high-level description of novel behavior is easy to derive. In each of the tested domains NdPSO outperforms both objective-based PSO and random-search, demonstrating its promise as a tool for solving deceptive problems. Since this is the first application of the search for novelty outside the evolutionary paradigm an empirical comparative study of the new algorithm to a standard novelty search Evolutionary Algorithm is performed

On the adaptivity and complexity embedded into differential evolution

This research deals with the comparison of the two modern approaches for evolutionary algorithms, which are the adaptivity and complex chaotic dynamics. This paper aims on the investigations on the chaos-driven Differential Evolution (DE) concept. This paper is aimed at the embedding of discrete dissipative chaotic systems in the form of chaotic pseudo random number generators for the DE and comparing the influence to the performance with the state of the art adaptive representative jDE. This research is focused mainly on the possible disadvantages and advantages of both compared approaches. Repeated simulations for Lozi map driving chaotic systems were performed on the simple benchmark functions set, which are more close to the real optimization problems. Obtained results are compared with the canonical not-chaotic and not adaptive DE. Results show that with used simple test functions, the performance of ChaosDE is better in the most cases than jDE and Canonical DE, furthermore due to the unique sequencing in CPRNG given by the hidden chaotic dynamics, thus better and faster selection of unique individuals from population, ChaosDE is faster. © 2016 Author(s)

A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications

Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1995. It is now one of the most commonly used optimization techniques. This survey presented a comprehensive investigation of PSO. On one hand, we provided advances with PSO, including its modifications (including quantum-behaved PSO, bare-bones PSO, chaotic PSO, and fuzzy PSO), population topology (as fully connected, von Neumann, ring, star, random, etc.), hybridization (with genetic algorithm, simulated annealing, Tabu search, artificial immune system, ant colony algorithm, artificial bee colony, differential evolution, harmonic search, and biogeography-based optimization), extensions (to multiobjective, constrained, discrete, and binary optimization), theoretical analysis (parameter selection and tuning, and convergence analysis), and parallel implementation (in multicore, multiprocessor, GPU, and cloud computing forms). On the other hand, we offered a survey on applications of PSO to the following eight fields: electrical and electronic engineering, automation control systems, communication theory, operations research, mechanical engineering, fuel and energy, medicine, chemistry, and biology. It is hoped that this survey would be beneficial for the researchers studying PSO algorithms

Random Adjustment - Based Chaotic Metaheuristic Algorithms for Image Contrast Enhancement

Metaheuristic algorithm is a powerful optimization method, in which it can solve problemsby exploring the ordinarily large solution search space of these instances, that are believed tobe hard in general. However, the performances of these algorithms signicantly depend onthe setting of their parameter, while is not easy to set them accurately as well as completelyrelying on the problem\u27s characteristic. To ne-tune the parameters automatically, manymethods have been proposed to address this challenge, including fuzzy logic, chaos, randomadjustment and others. All of these methods for many years have been developed indepen-dently for automatic setting of metaheuristic parameters, and integration of two or more ofthese methods has not yet much conducted. Thus, a method that provides advantage fromcombining chaos and random adjustment is proposed. Some popular metaheuristic algo-rithms are used to test the performance of the proposed method, i.e. simulated annealing,particle swarm optimization, dierential evolution, and harmony search. As a case study ofthis research is contrast enhancement for images of Cameraman, Lena, Boat and Rice. Ingeneral, the simulation results show that the proposed methods are better than the originalmetaheuristic, chaotic metaheuristic, and metaheuristic by random adjustment

Study of Cooperative Control System for Multiple Mobile Robots Using Particle Swarm Optimization

The idea of using multiple mobile robots for tracking targets in an unknown environment can be realized with Particle Swarm Optimization proposed by Kennedy and Eberhart in 1995. The actual implementation of an efficient algorithm like Particle Swarm Optimization (PSO) is required when robots need to avoid the randomly placed obstacles in unknown environment and reach the target point. However, ordinary methods of obstacle avoidance have not proven good results in route planning. PSO is a self-adaptive population-based method in which behavior of the swarm is iteratively generated from the combination of social and cognitive behaviors and is an effective technique for collective robotic search problem. When PSO is used for exploration, this algorithm enables robots to travel on trajectories that lead to total swarm convergence on some target

PSO algorithm enhanced with Lozi Chaotic Map - Tuning experiment

In this paper it is investigated the effect of tuning of control parameters of the Lozi Chaotic Map employed as a chaotic pseudo-random number generator for the particle swarm optimization algorithm. Three different benchmark functions are selected from the IEEE CEC 2013 competition benchmark set. The Lozi map is extensively tuned and the performance of PSO is evaluated

Performance of Multi-chaotic PSO on a shifted benchmark functions set

In this paper the performance of Multi-chaotic PSO algorithm is investigated using two shifted benchmark functions. The purpose of shifted benchmark functions is to simulate the time-variant real-world problems. The results of chaotic PSO are compared with canonical version of the algorithm. It is concluded that using the multi-chaotic approach can lead to better results in optimization of shifted functions