Differential evolution with an evolution path: a DEEP evolutionary algorithm

Utilizing cumulative correlation information already existing in an evolutionary process, this paper proposes a predictive approach to the reproduction mechanism of new individuals for differential evolution (DE) algorithms. DE uses a distributed model (DM) to generate new individuals, which is relatively explorative, whilst evolution strategy (ES) uses a centralized model (CM) to generate offspring, which through adaptation retains a convergence momentum. This paper adopts a key feature in the CM of a covariance matrix adaptation ES, the cumulatively learned evolution path (EP), to formulate a new evolutionary algorithm (EA) framework, termed DEEP, standing for DE with an EP. Without mechanistically combining two CM and DM based algorithms together, the DEEP framework offers advantages of both a DM and a CM and hence substantially enhances performance. Under this architecture, a self-adaptation mechanism can be built inherently in a DEEP algorithm, easing the task of predetermining algorithm control parameters. Two DEEP variants are developed and illustrated in the paper. Experiments on the CEC'13 test suites and two practical problems demonstrate that the DEEP algorithms offer promising results, compared with the original DEs and other relevant state-of-the-art EAs

Multimodal estimation of distribution algorithms

Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima

Hybrid of memory andprediction strategies for dynamic multiobjective optimization

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Dynamic multiobjective optimization problems (DMOPs) are characterized by a time-variant Pareto optimal front (PF) and/or Pareto optimal set (PS). To handle DMOPs, an algorithm should be able to track the movement of the PF/PS over time efficiently. In this paper, a novel dynamic multiobjective evolutionary algorithm (DMOEA) is proposed for solving DMOPs, which includes a hybrid of memory and prediction strategies (HMPS) and the multiobjective evolutionary algorithm based on decomposition (MOEA/D). In particular, the resultant algorithm (MOEA/D-HMPS) detects environmental changes and identifies the similarity of a change to the historical changes, based on which two different response strategies are applied. If a detected change is dissimilar to any historical changes, a differential prediction based on the previous two consecutive population centers is utilized to relocate the population individuals in the new environment; otherwise, a memory-based technique devised to predict the new locations of the population members is applied. Both response mechanisms mix a portion of existing solutions with randomly generated solutions to alleviate the effect of prediction errors caused by sharp or irregular changes. MOEA/D-HMPS was tested on 14 benchmark problems and compared with state-of-the-art DMOEAs. The experimental results demonstrate the efficiency of MOEA/D-HMPS in solving various DMOPs

An overview of population-based algorithms for multi-objective optimisation

In this work we present an overview of the most prominent population-based algorithms and the methodologies used to extend them to multiple objective problems. Although not exact in the mathematical sense, it has long been recognised that population-based multi-objective optimisation techniques for real-world applications are immensely valuable and versatile. These techniques are usually employed when exact optimisation methods are not easily applicable or simply when, due to sheer complexity, such techniques could potentially be very costly. Another advantage is that since a population of decision vectors is considered in each generation these algorithms are implicitly parallelisable and can generate an approximation of the entire Pareto front at each iteration. A critique of their capabilities is also provided

Evolutionary multi-objective optimization using neural-based estimation of distribution algorithms

Ph.DDOCTOR OF PHILOSOPH

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

Multi-objective optimisation methods applied to aircraft techno-economic and environmental issues

Engineering methods that couple multi-objective optimisation (MOO) techniques with high fidelity computational tools are expected to minimise the environmental impact of aviation while increasing the growth, with the potential to reveal innovative solutions. In order to mitigate the compromise between computational efficiency and fidelity, these methods can be accelerated by harnessing the computational efficiency of Graphic Processor Units (GPUs). The aim of the research is to develop a family of engineering methods to support research in aviation with respect to the environmental and economic aspects. In order to reveal the non-dominated trade-o_, also known as Pareto Front(PF), among conflicting objectives, a MOO algorithm, called Multi-Objective Tabu Search 2 (MOTS2), is developed, benchmarked relative to state-of-the-art methods and accelerated by using GPUs. A prototype fluid solver based on GPU is also developed, so as to simulate the mixing capability of a microreactor that could potentially be used in fuel-saving technologies in aviation. By using the aforementioned methods, optimal aircraft trajectories in terms of flight time, fuel consumption and emissions are generated, and alternative designs of a microreactor are suggested, so as to assess the trade-offs between pressure losses and the micro-mixing capability. As a key contribution to knowledge, with reference to competitive optimisers and previous cases, the capabilities of the proposed methodology are illustrated in prototype applications of aircraft trajectory optimisation (ATO) and micromixing optimisation with 2 and 3 objectives, under operational and geometrical constraints, respectively. In the short-term, ATO ought to be applied to existing aircraft. In the long-term, improving the micro-mixing capability of a microreactor is expected to enable the use of hydrogen-based fuel. This methodology is also benchmarked and assessed relative to state-of-the-art techniques in ATO and micro-mixing optimisation with known and unknown trade-offs, whereas the former could only optimise 2 objectives and the latter could not exploit the computational efficiency of GPUs. The impact of deploying on GPUs a micro-mixing _ow solver, which accelerates the generation of trade-off against a reference study, and MOTS2, which illustrates the scalability potential, is assessed. With regard to standard analytical function test cases and verification cases in MOO, MOTS2 can handle the multi-modality of the trade-o_ of ZDT4, which is a MOO benchmark function with many local optima that presents a challenge for a state-of-the-art genetic algorithm for ATO, called NSGAMO, based on case studies in the public domain. However, MOTS2 demonstrated worse performance on ZDT3, which is a MOO benchmark function with a discontinuous trade-o_, for which NSGAMO successfully captured the target PF. Comparing their overall performance, if the shape of the PF is known, MOTS2 should be preferred in problems with multi-modal trade-offs, whereas NSGAMO should be employed in discontinuous PFs. The shape of the trade-o_ between the objectives in airfoil shape optimisation, ATO and micro-mixing optimisation was continuous. The weakness of MOTS2 to sufficiently capture the discontinuous PF of ZDT3 was not critical in the studied examples … [cont.]

Explicit Building Block Multiobjective Evolutionary Computation: Methods and Applications

This dissertation presents principles, techniques, and performance of evolutionary computation optimization methods. Concentration is on concepts, design formulation, and prescription for multiobjective problem solving and explicit building block (BB) multiobjective evolutionary algorithms (MOEAs). Current state-of-the-art explicit BB MOEAs are addressed in the innovative design, execution, and testing of a new multiobjective explicit BB MOEA. Evolutionary computation concepts examined are algorithm convergence, population diversity and sizing, genotype and phenotype partitioning, archiving, BB concepts, parallel evolutionary algorithm (EA) models, robustness, visualization of evolutionary process, and performance in terms of effectiveness and efficiency. The main result of this research is the development of a more robust algorithm where MOEA concepts are implicitly employed. Testing shows that the new MOEA can be more effective and efficient than previous state-of-the-art explicit BB MOEAs for selected test suite multiobjective optimization problems (MOPs) and U.S. Air Force applications. Other contributions include the extension of explicit BB definitions to clarify the meanings for good single and multiobjective BBs. A new visualization technique is developed for viewing genotype, phenotype, and the evolutionary process in finding Pareto front vectors while tracking the size of the BBs. The visualization technique is the result of a BB tracing mechanism integrated into the new MOEA that enables one to determine the required BB sizes and assign an approximation epistasis level for solving a particular problem. The culmination of this research is explicit BB state-of-the-art MOEA technology based on the MOEA design, BB classifier type assessment, solution evolution visualization, and insight into MOEA test metric validation and usage as applied to test suite, deception, bioinformatics, unmanned vehicle flight pattern, and digital symbol set design MOPs

A modular genetic programming system

Genetic Programming (GP) is an evolutionary algorithm for the automatic discovery of symbolic expressions, e.g. computer programs or mathematical formulae, that encode solutions to a user-defined task. Recent advances in GP systems and computer performance made it possible to successfully apply this algorithm to real-world applications. This work offers three main contributions to the state-of-the art in GP systems: (I) The documentation of RGP, a state-of-the art GP software implemented as an extension package to the popular R environment for statistical computation and graphics. GP and RPG are introduced both formally and with a series of tutorial examples. As R itself, RGP is available under an open source license. (II) A comprehensive empirical analysis of modern GP heuristics based on the methodology of Sequential Parameter Optimization. The effects and interactions of the most important GP algorithm parameters are analyzed and recommendations for good parameter settings are given. (III) Two extensive case studies based on real-world industrial applications. The first application involves process control models in steel production, while the second is about meta-model-based optimization of cyclone dust separators. A comparison with traditional and modern regression methods reveals that GP offers equal or superior performance in both applications, with the additional benefit of understandable and easy to deploy models. Main motivation of this work is the advancement of GP in real-world application areas. The focus lies on a subset of application areas that are known to be practical for GP, first of all symbolic regression and classification. It has been written with practitioners from academia and industry in mind