An adaptation reference-point-based multiobjective evolutionary algorithm

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.It is well known that maintaining a good balance between convergence and diversity is crucial to the performance of multiobjective optimization algorithms (MOEAs). However, the Pareto front (PF) of multiobjective optimization problems (MOPs) affects the performance of MOEAs, especially reference point-based ones. This paper proposes a reference-point-based adaptive method to study the PF of MOPs according to the candidate solutions of the population. In addition, the proportion and angle function presented selects elites during environmental selection. Compared with five state-of-the-art MOEAs, the proposed algorithm shows highly competitive effectiveness on MOPs with six complex characteristics

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

Improved sampling of the pareto-front in multiobjective genetic optimizations by steady-state evolution: a Pareto converging genetic algorithm

Previous work on multiobjective genetic algorithms has been focused on preventing genetic drift and the issue of convergence has been given little attention. In this paper, we present a simple steady-state strategy, Pareto Converging Genetic Algorithm (PCGA), which naturally samples the solution space and ensures population advancement towards the Pareto-front. PCGA eliminates the need for sharing/niching and thus minimizes heuristically chosen parameters and procedures. A systematic approach based on histograms of rank is introduced for assessing convergence to the Pareto-front, which, by definition, is unknown in most real search problems. We argue that there is always a certain inheritance of genetic material belonging to a population, and there is unlikely to be any significant gain beyond some point; a stopping criterion where terminating the computation is suggested. For further encouraging diversity and competition, a nonmigrating island model may optionally be used; this approach is particularly suited to many difficult (real-world) problems, which have a tendency to get stuck at (unknown) local minima. Results on three benchmark problems are presented and compared with those of earlier approaches. PCGA is found to produce diverse sampling of the Pareto-front without niching and with significantly less computational effort

Multi agent collaborative search based on Tchebycheff decomposition

This paper presents a novel formulation of Multi Agent Collaborative Search, for multi-objective optimization, based on Tchebycheff decomposition. A population of agents combines heuristics that aim at exploring the search space both globally (social moves) and in a neighborhood of each agent (individualistic moves). In this novel formulation the selection process is based on a combination of Tchebycheff scalarization and Pareto dominance. Furthermore, while in the previous implementation, social actions were applied to the whole population of agents and individualistic actions only to an elite sub-population, in this novel formulation this mechanism is inverted. The novel agent-based algorithm is tested at first on a standard benchmark of difficult problems and then on two specific problems in space trajectory design. Its performance is compared against a number of state-of-the-art multi objective optimization algorithms. The results demonstrate that this novel agent-based search has better performance with respect to its predecessor in a number of cases and converges better than the other state-of-the-art algorithms with a better spreading of the solutions

Evolutionary Decomposition of Complex Design Spaces

This dissertation investigates the support of conceptual engineering design through the decomposition of multi-dimensional search spaces into regions of high performance. Such decomposition helps the designer identify optimal design directions by the elimination of infeasible or undesirable regions within the search space. Moreover, high levels of interaction between the designer and the model increases overall domain knowledge and significantly reduces uncertainty relating to the design task at hand. The aim of the research is to develop the archetypal Cluster Oriented Genetic Algorithm (COGA) which achieves search space decomposition by using variable mutation (vmCOGA) to promote diverse search and an Adaptive Filter (AF) to extract solutions of high performance [Parmee 1996a, 1996b]. Since COGAs are primarily used to decompose design domains of unknown nature within a real-time environment, the elimination of apriori knowledge, speed and robustness are paramount. Furthermore COGA should promote the in-depth exploration of the entire search space, sampling all optima and the surrounding areas. Finally any proposed system should allow for trouble free integration within a Graphical User Interface environment. The replacement of the variable mutation strategy with a number of algorithms which increase search space sampling are investigated. Utility is then increased by incorporating a control mechanism that maintains optimal performance by adapting each algorithm throughout search by means of a feedback measure based upon population convergence. Robustness is greatly improved by modifying the Adaptive Filter through the introduction of a process that ensures more accurate modelling of the evolving population. The performance of each prospective algorithm is assessed upon a suite of two-dimensional test functions using a set of novel performance metrics. A six dimensional test function is also developed where the areas of high performance are explicitly known, thus allowing for evaluation under conditions of increased dimensionality. Further complexity is introduced by two real world models described by both continuous and discrete parameters. These relate to the design of conceptual airframes and cooling hole geometries within a gas turbine. Results are promising and indicate significant improvement over the vmCOGA in terms of all desired criteria. This further supports the utilisation of COGA as a decision support tool during the conceptual phase of design.British Aerospace plc, Warton and Rolls Royce plc, Filto

Evolutionary Computation 2020

Intelligent optimization is based on the mechanism of computational intelligence to refine a suitable feature model, design an effective optimization algorithm, and then to obtain an optimal or satisfactory solution to a complex problem. Intelligent algorithms are key tools to ensure global optimization quality, fast optimization efficiency and robust optimization performance. Intelligent optimization algorithms have been studied by many researchers, leading to improvements in the performance of algorithms such as the evolutionary algorithm, whale optimization algorithm, differential evolution algorithm, and particle swarm optimization. Studies in this arena have also resulted in breakthroughs in solving complex problems including the green shop scheduling problem, the severe nonlinear problem in one-dimensional geodesic electromagnetic inversion, error and bug finding problem in software, the 0-1 backpack problem, traveler problem, and logistics distribution center siting problem. The editors are confident that this book can open a new avenue for further improvement and discoveries in the area of intelligent algorithms. The book is a valuable resource for researchers interested in understanding the principles and design of intelligent algorithms

Geometric Particle Swarm Optimization for Multi-objective Optimization Using Decomposition

Multi-objective evolutionary algorithms (MOEAs) based on decomposition are aggregation-based algorithms which transform a multi-objective optimization problem (MOP) into several single-objective subproblems. Being effective, efficient, and easy to implement, Particle Swarm Optimization (PSO) has become one of the most popular single-objective optimizers for continuous problems, and recently it has been successfully extended to the multi-objective domain. However, no investigation on the application of PSO within a multi-objective decomposition framework exists in the context of combinatorial optimization. This is precisely the focus of the paper. More specifically, we study the incorporation of Geometric Particle Swarm Optimization (GPSO), a discrete generalization of PSO that has proven successful on a number of single-objective combinatorial problems, into a decomposition approach. We conduct experiments on manyobjective 1/0 knapsack problems i.e. problems with more than three objectives functions, substantially harder than multi-objective problems with fewer objectives. The results indicate that the proposed multi-objective GPSO based on decomposition is able to outperform two version of the wellknow MOEA based on decomposition (MOEA/D) and the most recent version of the non-dominated sorting genetic algorithm (NSGA-III), which are state-of-the-art multi-objective evolutionary approaches based on decomposition

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

Hybrid adaptive evolutionary algorithm based on decomposition

The performance of search operators varies across the different stages of the search/optimization process of evolutionary algorithms (EAs). In general, a single search operator may not do well in all these stages when dealing with different optimization and search problems. To mitigate this, adaptive search operator schemes have been introduced. The idea is that when a search operator hits a difficult patch (under-performs) in the search space, the EA scheme “reacts” to that by potentially calling upon a different search operator. Hence, several multiple-search operator schemes have been proposed and employed within EA. In this paper, a hybrid adaptive evolutionary algorithm based on decomposition (HAEA/D) that employs four different crossover operators is suggested. Its performance has been evaluated on the well-known IEEE CEC’09 test instances. HAEA/D has generated promising results which compare well against several well-known algorithms including MOEA/D, on a number of metrics such as the inverted generational distance (IGD), the hyper-volume, the Gamma and Delta functions. These results are included and discussed in this paper