Improving Results of Differential Evolution Algorithm

Optimisation problems are of prime importance in scientific and engineering communities. Many day-to-day tasks in these fields can be classified as optimisation problems. Due to their enormous solution spaces, optimisation problems frequently lie in class NP. In such cases, engineers and researchers have to rely on algorithms and techniques that can find sub-optimal solutions to these problems. One of the most dependable algorithms for numerical optimisation problems is Differential Evolution (DE). Since its introduction in the mid 1990’s, DE has been on the fore front when it comes to applicability of optimisation algorithms to variety of real-parameter optimisation problems. This popularity of DE has driven intensive research to further improve its capability to find optimal solutions. In this thesis we present a variant of DE to produce improved solutions with greater reliability. In doing so, we introduce a novel strategy to incorporate ancestral vectors into the optimisation process. We show that a controlled introduction of ancestral vectors into the optimisation process has a generally positive influence on convergence rate of the algorithm. Evaluation of the proposed algorithm forms a major part of this work, as an empirical evidence serves to demonstrate the performance of stochastic algorithms. The resulting implementation of the algorithm is made available as an open source software along with its reference manual

A Novel Memetic Framework for Enhancing Differential Evolution Algorithms via Combination With Alopex Local Search

Differential evolution (DE) represents a class of population-based optimization techniques that uses differences of vectors to search for optimal solutions in the search space. However, promising solutions/regions are not adequately exploited by a traditional DE algorithm. Memetic computing has been popular in recent years to enhance the exploitation of global algorithms via incorporation of local search. This paper proposes a new memetic framework to enhance DE algorithms using Alopex Local Search (MFDEALS). The novelty of the proposed MFDEALS framework lies in that the behavior of exploitation (by Alopex local search) can be controlled based on the DE global exploration status (population diversity and search stage). Additionally, an adaptive parameter inside the Alopex local search enables smooth transition of its behavior from exploratory to exploitative during the search process. A study of the important components of MFDEALS shows that there is a synergy between them. MFDEALS has been integrated with both the canonical DE method and the adaptive DE algorithm L-SHADE, leading to the MDEALS and ML-SHADEALS algorithms, respectively. Both algorithms were tested on the benchmark functions from the IEEE CEC’2014 Conference. The experiment results show that Memetic Differential Evolution with Alopex Local Search (MDEALS) not only improves the original DE algorithm but also outperforms other memetic DE algorithms by obtaining better quality solutions. Further, the comparison between ML-SHADEALS and L-SHADE demonstrates that applying the MFDEALS framework with Alopex local search can significantly enhance the performance of L-SHADEThis research was supported by grants from both Swedish Research Council (project number 2016-05431) and Spanish Ministry of Science TIN2016- 8113-R

Large-Scale Evolutionary Optimization Using Multi-Layer Strategy Differential Evolution

Differential evolution (DE) has been extensively used in optimization studies since its development in 1995 because of its reputation as an effective global optimizer. DE is a population-based meta-heuristic technique that develops numerical vectors to solve optimization problems. DE strategies have a significant impact on DE performance and play a vital role in achieving stochastic global optimization. However, DE is highly dependent on the control parameters involved. In practice, the fine-tuning of these parameters is not always easy. Here, we discuss the improvements and developments that have been made to DE algorithms. The Multi-Layer Strategies Differential Evolution (MLSDE) algorithm, which finds optimal solutions for large scale problems. To solve large scale problems were grouped different strategies together and applied them to date set. Furthermore, these strategies were applied to selected vectors to strengthen the exploration ability of the algorithm. Extensive computational analysis was also carried out to evaluate the performance of the proposed algorithm on a set of well-known CEC 2015 benchmark functions. This benchmark was utilized for the assessment and performance evaluation of the proposed algorithm

Digital Filter Design Using Improved Artificial Bee Colony Algorithms

Digital filters are often used in digital signal processing applications. The design objective of a digital filter is to find the optimal set of filter coefficients, which satisfies the desired specifications of magnitude and group delay responses. Evolutionary algorithms are population-based meta-heuristic algorithms inspired by the biological behaviors of species. Compared to gradient-based optimization algorithms such as steepest descent and Newton’s like methods, these bio-inspired algorithms have the advantages of not getting stuck at local optima and being independent of the starting point in the solution space. The limitations of evolutionary algorithms include the presence of control parameters, problem specific tuning procedure, premature convergence and slower convergence rate. The artificial bee colony (ABC) algorithm is a swarm-based search meta-heuristic algorithm inspired by the foraging behaviors of honey bee colonies, with the benefit of a relatively fewer control parameters. In its original form, the ABC algorithm has certain limitations such as low convergence rate, and insufficient balance between exploration and exploitation in the search equations. In this dissertation, an ABC-AMR algorithm is proposed by incorporating an adaptive modification rate (AMR) into the original ABC algorithm to increase convergence rate by adjusting the balance between exploration and exploitation in the search equations through an adaptive determination of the number of parameters to be updated in every iteration. A constrained ABC-AMR algorithm is also developed for solving constrained optimization problems.There are many real-world problems requiring simultaneous optimizations of more than one conflicting objectives. Multiobjective (MO) optimization produces a set of feasible solutions called the Pareto front instead of a single optimum solution. For multiobjective optimization, if a decision maker’s preferences can be incorporated during the optimization process, the search process can be confined to the region of interest instead of searching the entire region. In this dissertation, two algorithms are developed for such incorporation. The first one is a reference-point-based MOABC algorithm in which a decision maker’s preferences are included in the optimization process as the reference point. The second one is a physical-programming-based MOABC algorithm in which physical programming is used for setting the region of interest of a decision maker. In this dissertation, the four developed algorithms are applied to solve digital filter design problems. The ABC-AMR algorithm is used to design Types 3 and 4 linear phase FIR differentiators, and the results are compared to those obtained by the original ABC algorithm, three improved ABC algorithms, and the Parks-McClellan algorithm. The constrained ABC-AMR algorithm is applied to the design of sparse Type 1 linear phase FIR filters of filter orders 60, 70 and 80, and the results are compared to three state-of-the-art design methods. The reference-point-based multiobjective ABC algorithm is used to design of asymmetric lowpass, highpass, bandpass and bandstop FIR filters, and the results are compared to those obtained by the preference-based multiobjective differential evolution algorithm. The physical-programming-based multiobjective ABC algorithm is used to design IIR lowpass, highpass and bandpass filters, and the results are compared to three state-of-the-art design methods. Based on the obtained design results, the four design algorithms are shown to be competitive as compared to the state-of-the-art design methods

A comprehensive review of swarm optimization algorithms

Many swarm optimization algorithms have been introduced since the early 60’s, Evolutionary Programming to the most recent, Grey Wolf Optimization. All of these algorithms have demonstrated their potential to solve many optimization problems. This paper provides an in-depth survey of well-known optimization algorithms. Selected algorithms are briefly explained, and compared with each other comprehensively through experiments conducted using thirty well-known benchmark functions. Their advantages and disadvantages are also discussed. A number of statistical tests are then carried out to determine the significant performances. The results indicate the overall advantage of Differential Evolution (DE) and is closely followed by Particle Swarm Optimization (PSO), compared with other considered approaches

CHEMOTAXIS DIFFERENTIAL EVOLUTION OPTIMIZATION TECHNIQUES FOR GLOBAL OPTIMIZATION

Nature inspired and bio-inspired algorithms have been recently used for solving low and high dimensional search and optimization problems. In this context, Bacterial Foraging Optimization Algorithm (BFOA) and Differential Evolution (DE) have been widely employed as global optimization techniques inspired from social foraging behavior of Escheria coli bacteria and evolutionary ideas such as mutation, crossover, and selection, respectively. BFOA employs chemotaxis (tumble and run steps of a bacterium in its lifetime) activity for local search whereas the global search is performed by elimination-dispersal operator. Elimination-dispersal operator kills or disperses some bacteria and replaces others randomly in the search space. This operator mimics bacterium’s death or dispersal in case of high temperature or sudden water flow in the environment. DE employs the mutation and crossover operators to make a local and a global search that explore the search space. Exploration and exploitation balance of DE is performed by two different parameters: mutation scaling factor and crossover rate. These two parameters along with the number of population have an enormous impact on optimization performance. In this thesis, two novel hybrid techniques called Chemotaxis Differential Evolution Optimization Algorithm (CDEOA) for low dimensions and micro CDEOA (μCDEOA) for high dimensional problems are proposed. In these techniques, we incorporate the principles of DE into BFOA with two conditions. What makes our techniques different from its counterparts is that it is based on two optimization strategies: exploration of a bacterium in case of its failure to explore its vicinity for food source and exploitation of a bacterium in case of its achievement to exploit more food source. By means of these evolutionary ideas, we manage to establish an efficient balance between exploration of new areas in the search space and exploitation of search space gradients. Statistics of the computer simulations indicate that μCDEOA outperforms, or is comparable to, its competitors in terms of its convergence rates and quality of final solution for complex high dimensional problems