Evolutionary Algorithms for Static and Dynamic Multiobjective Optimization

Many real-world optimization problems consist of a number of conflicting objectives that have to be optimized simultaneously. Due to the presence of multiple conflicting ob- jectives, there is no single solution that can optimize all the objectives. Therefore, the resulting multiobjective optimization problems (MOPs) resort to a set of trade-off op- timal solutions, called the Pareto set in the decision space and the Pareto front in the objective space. Traditional optimization methods can at best find one solution in a sin- gle run, thereby making them inefficient to solve MOPs. In contrast, evolutionary algo- rithms (EAs) are able to approximate multiple optimal solutions in a single run. This strength makes EAs good candidates for solving MOPs. Over the past several decades, there have been increasing research interests in developing EAs or improving their perfor- mance, resulting in a large number of contributions towards the applicability of EAs for MOPs. However, the performance of EAs depends largely on the properties of the MOPs in question, e.g., static/dynamic optimization environments, simple/complex Pareto front characteristics, and low/high dimensionality. Different problem properties may pose dis- tinct optimization difficulties to EAs. For example, dynamic (time-varying) MOPs are generally more challenging than static ones to EAs. Therefore, it is not trivial to further study EAs in order to make them widely applicable to MOPs with various optimization scenarios or problem properties. This thesis is devoted to exploring EAs’ ability to solve a variety of MOPs with dif- ferent problem characteristics, attempting to widen EAs’ applicability and enhance their general performance. To start with, decomposition-based EAs are enhanced by incorpo- rating two-phase search and niche-guided solution selection strategies so as to make them suitable for solving MOPs with complex Pareto fronts. Second, new scalarizing functions are proposed and their impacts on evolutionary multiobjective optimization are exten- sively studied. On the basis of the new scalarizing functions, an efficient decomposition- based EA is introduced to deal with a class of hard MOPs. Third, a diversity-first- and-convergence-second sorting method is suggested to handle possible drawbacks of convergence-first based sorting methods. The new sorting method is then combined with strength based fitness assignment, with the aid of reference directions, to optimize MOPs with an increase of objective dimensionality. After that, we study the field of dynamic multiobjective optimization where objective functions and constraints can change over time. A new set of test problems consisting of a wide range of dynamic characteristics is introduced at an attempt to standardize test environments in dynamic multiobjective optimization, thereby aiding fair algorithm comparison and deep performance analysis. Finally, a dynamic EA is developed to tackle dynamic MOPs by exploiting the advan- tages of both generational and steady-state algorithms. All the proposed approaches have been extensively examined against existing state-of-the-art methods, showing fairly good performance in a variety of test scenarios. The research work presented in the thesis is the output of initiative and novel attempts to tackle some challenging issues in evolutionary multiobjective optimization. This re- search has not only extended the applicability of some of the existing approaches, such as decomposition-based or Pareto-based algorithms, for complex or hard MOPs, but also contributed to moving forward research in the field of dynamic multiobjective optimiza- tion with novel ideas including new test suites and novel algorithm design

An adaptive multi-population differential artificial bee colony algorithm for many-objective service composition in cloud manufacturing

Several conflicting criteria must be optimized simultaneously during the service composition and optimal selection (SCOS) in cloud manufacturing, among which tradeoff optimization regarding the quality of the composite services is a key issue in successful implementation of manufacturing tasks. This study improves the artificial bee colony (ABC) algorithm by introducing a synergetic mechanism for food source perturbation, a new diversity maintenance strategy, and a novel computing resources allocation scheme to handle complicated many-objective SCOS problems. Specifically, differential evolution (DE) operators with distinct search behaviors are integrated into the ABC updating equation to enhance the level of information exchange between the foraging bees, and the control parameters for reproduction operators are adapted independently. Meanwhile, a scalarization based approach with active diversity promotion is used to enhance the selection pressure. In this proposal, multiple size adjustable subpopulations evolve with distinct reproduction operators according to the utility of the generating offspring so that more computational resources will be allocated to the better performing reproduction operators. Experiments for addressing benchmark test instances and SCOS problems indicate that the proposed algorithm has a competitive performance and scalability behavior compared with contesting algorithms

Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problems

Overlapping solutions occur when more than one solution in the space of decisions maps to the same solution in the space of objectives. This situation threatens the exploration capacity of Multi- Objective Evolutionary Algorithms (MOEAs), preventing them from having a good diversity in their population. The influence of overlapping solutions is intensified on multi-objective combinatorial problems with a low number of objectives. This paper presents a hybrid MOEA for handling overlapping solutions that combines the classic NSGA-II with a strategy based on Objective Space Division (OSD). Basically, in each generation of the algorithm, the objective space is divided into several regions using the nadir solution calculated from the current generation solutions. Furthermore, the solutions in each region are classified into non-dominated fronts using different optimization strategies in each of them. This significantly enhances the achieved diversity of the approximate front of non-dominated solutions. The proposed algorithm (called NSGA-II/OSD) is tested on a classic Operations Research problem: The Multi-Objective Knapsack Problem (0-1 MOKP) with two objectives. Classic NSGA-II, MOEA/D and Global WASF-GA are used to compare the performance of NSGA-II/OSD. In the case of MOEA/D two different versions are implemented, each of them with a different strategy for specifying the reference point. These MOEA/D reference point strategies are thoroughly studied and new insights are provided. This paper analyses in depth the impact of overlapping solutions on MOEAs, studying the number of overlapping solutions, the number of solution repairs, the hypervolume metric, the attainment surfaces and the approximation to the real Pareto front, for different sizes of 0-1 MOKPs with two objectives. The proposed method offers very good performance when compared to the classic NSGA-II, MOEA/D and Global WASF-GA algorithms, all of them well-known in the literature.Fil: González, Begoña. Universidad de Las Palmas de Gran Canaria; EspañaFil: Rossit, Daniel Alejandro. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Méndez, Máximo. Universidad de Las Palmas de Gran Canaria; EspañaFil: Frutos, Mariano. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentin

A Scalability Study and New Algorithms for Large-Scale Many-Objective Optimization

Many real-world optimization problems contain multiple (often conflicting) goals to be optimized concurrently, commonly referred to as multi-objective problems (MOPs). Over the past few decades, a plethora of multi-objective algorithms have been proposed, often tested on MOPs possessing two or three objectives. Unfortunately, when tasked with solving MOPs with four or more objectives, referred to as many-objective problems (MaOPs), a large majority of optimizers experience significant performance degradation. The downfall of these optimizers is that simultaneously maintaining a well-spread set of solutions along with appropriate selection pressure to converge becomes difficult as the number of objectives increase. This difficulty is further compounded for large-scale MaOPs, i.e., MaOPs possessing large amounts of decision variables. In this thesis, we explore the challenges of many-objective optimization and propose three new promising algorithms designed to efficiently solve MaOPs. Experimental results demonstrate the proposed optimizers to perform very well, often outperforming state-of-the-art many-objective algorithms

Evolutionary many-objective optimisation: pushing the boundaries

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonMany-objective optimisation poses great challenges to evolutionary algorithms. To start with, the ineffectiveness of the Pareto dominance relation, which is the most important criterion in multi-objective optimisation, results in the underperformance of traditional Pareto-based algorithms. Also, the aggravation of the conflict between proximity and diversity, along with increasing time or space requirement as well as parameter sensitivity, has become key barriers to the design of effective many-objective optimisation algorithms. Furthermore, the infeasibility of solutions' direct observation can lead to serious difficulties in algorithms' performance investigation and comparison. In this thesis, we address these challenges, aiming to make evolutionary algorithms as effective in many-objective optimisation as in two- or three-objective optimisation. First, we significantly enhance Pareto-based algorithms to make them suitable for many-objective optimisation by placing individuals with poor proximity into crowded regions so that these individuals can have a better chance to be eliminated. Second, we propose a grid-based evolutionary algorithm which explores the potential of the grid to deal with many-objective optimisation problems. Third, we present a bi-goal evolution framework that converts many objectives of a given problem into two objectives regarding proximity and diversity, thus creating an optimisation problem in which the objectives are the goals of the search process itself. Fourth, we propose a comprehensive performance indicator to compare evolutionary algorithms in optimisation problems with various Pareto front shapes and any objective dimensionality. Finally, we construct a test problem to aid the visual investigation of evolutionary search, with its Pareto optimal solutions in a two-dimensional decision space having similar distribution to their images in a higher-dimensional objective space. The work reported in this thesis is the outcome of innovative attempts at addressing some of the most challenging problems in evolutionary many-objective optimisation. This research has not only made some of the existing approaches, such as Pareto-based or grid-based algorithms that were traditionally regarded as unsuitable, now effective for many-objective optimisation, but also pushed other important boundaries with novel ideas including bi-goal evolution, a comprehensive performance indicator and a test problem for visual investigation. All the proposed algorithms have been systematically evaluated against existing state of the arts, and some of these algorithms have already been taken up by researchers and practitioners in the field.Department of Computer Science, Brunel University Londo

Effective and Efficient Evolutionary Many-Objective Optimization

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonMany-objective optimization is core to both artificial intelligence and data analytics as real-world problems commonly involve multiple objectives which are required to be optimized simultaneously. A large number of evolutionary algorithms have been developed to search for a set of Pareto optimal solutions for many-objective optimization problems. It is very rare that a many-objective evolutionary algorithm performs well in terms of both effectiveness and efficiency, two key evaluation criteria. Some algorithms may struggle to guide the solutions towards the Pareto front, e.g., Pareto-based algorithms, while other algorithms may have difficulty in diversifying the solutions evenly over the front on certain problems, e.g., decomposition-based algorithms. Furthermore, some effective algorithms may become very computationally expensive as the number of objectives increases, e.g., indicator-based algorithms. The aim of this thesis is to investigate how to make evolutionary algorithms perform well in terms of effectiveness and efficiency in many-objective optimization. After conducting a review of key concepts and the state of the art in the evolutionary many-objective optimization, this thesis shows how to improve the effectiveness of conventional Pareto-based algorithms on a challenging real-world problem in software engineering. This thesis then explores how to further enhance the effectiveness of leading many-objective evolutionary algorithms in general by extending the capability of a very popular and widely cited bi-goal evolution method. Last but not least, this thesis investigates how to strike a balance between effectiveness and efficiency of evolutionary algorithms when solving many-objective optimization problems. The work reported is based on either real-world or recognized synthetic datasets, and the proposed algorithms are compared and evaluated against leading algorithms in the field. The work does not only demonstrate ways of improving the effectiveness and efficiency of many-objective optimization algorithms but also led to promising areas for future research

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

Multiobjective genetic algorithm approaches to project scheduling under risk

In this thesis, project scheduling under risk is chosen as the topic of research. Project scheduling under risk is defined as a biobjective decision problem and is formulated as a 0-1 integer mathematical programming model. In this biobjective formulation, one of the objectives is taken as the expected makespan minimization and the other is taken as the expected cost minimization. As the solution approach to this biobjective formulation genetic algorithm (GA) is chosen. After carefully investigating the multiobjective GA literature, two strategies based on the vector evaluated GA are developed and a new GA is proposed. For these three GAs first the parameters are investigated through statistical experimentation and then the values are decided upon. The chosen parameters are used for the computational study part of this thesis. In this thesis three improvement heuristics are developed also to further improve the GA solutions. The aim of these improvement heuristics is to decrease the expected cost of the project while keeping the expected duration of the project fixed. These improvement heuristics are implemented at the end of the proposed GA and used to improve the results of the proposed GA. Finally the GAs and improvement heuristics are tested on three different sets of problems. The results are evaluated by pairwise comparisons of algorithms and of heuristics. Also an approximation of the true Pareto front is generated using the commercial mathematical modelling program, GAMS. The results are compared to that approximation and they seem comparable to that solution. The results of the improvement heuristics are also compared against each other and the performance of the heuristics is reported in detail