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

Computer-Aided Conceptual Design Through TRIZ-based Manipulation of Topological Optimizations

Organised by: Cranfield UniversityIn a recent project the authors proposed the adoption of Optimization Systems [1] as a bridging element between Computer-Aided Innovation (CAI) and PLM to identify geometrical contradictions [2], a particular case of the TRIZ physical contradiction [3]. A further development of the research has revealed that the solutions obtained from several topological optimizations can be considered as elementary customized modeling features for a specific design task. The topology overcoming the arising geometrical contradiction can be obtained through a manipulation of the density distributions constituting the conflicting pair. Already two strategies of density combination have been identified as capable to solve geometrical contradictions.Mori Seiki – The Machine Tool Compan

Optimal advertising campaign generation for multiple brands using MOGA

The paper proposes a new modified multiobjective genetic algorithm (MOGA) for the problem of optimal television (TV) advertising campaign generation for multiple brands. This NP-hard combinatorial optimization problem with numerous constraints is one of the key issues for an advertising agency when producing the optimal TV mediaplan. The classical approach to the solution of this problem is the greedy heuristic, which relies on the strength of the preceding commercial breaks when selecting the next break to add to the campaign. While the greedy heuristic is capable of generating only a group of solutions that are closely related in the objective space, the proposed modified MOGA produces a Pareto-optimal set of chromosomes that: 1) outperform the greedy heuristic and 2) let the mediaplanner choose from a variety of uniformly distributed tradeoff solutions. To achieve these results, the special problem-specific solution encoding, genetic operators, and original local optimization routine were developed for the algorithm. These techniques allow the algorithm to manipulate with only feasible individuals, thus, significantly improving its performance that is complicated by the problem constraints. The efficiency of the developed optimization method is verified using the real data sets from the Canadian advertising industry

A Study of the Combination of Variation Operators in the NSGA-II Algorithm

Multi-objective evolutionary algorithms rely on the use of variation operators as their basic mechanism to carry out the evolutionary process. These operators are usually fixed and applied in the same way during algorithm execution, e.g., the mutation probability in genetic algorithms. This paper analyses whether a more dynamic approach combining different operators with variable application rate along the search process allows to improve the static classical behavior. This way, we explore the combined use of three different operators (simulated binary crossover, differential evolution’s operator, and polynomial mutation) in the NSGA-II algorithm. We have considered two strategies for selecting the operators: random and adaptive. The resulting variants have been tested on a set of 19 complex problems, and our results indicate that both schemes significantly improve the performance of the original NSGA-II algorithm, achieving the random and adaptive variants the best overall results in the bi- and three-objective considered problems, respectively.UNIVERSIDAD DE MÁLAGA. CAMPUS DE EXCELENCIA INTERNACIONAL ANDALUCÍA TEC

Bregman Proximal Gradient Algorithm with Extrapolation for a class of Nonconvex Nonsmooth Minimization Problems

In this paper, we consider an accelerated method for solving nonconvex and nonsmooth minimization problems. We propose a Bregman Proximal Gradient algorithm with extrapolation(BPGe). This algorithm extends and accelerates the Bregman Proximal Gradient algorithm (BPG), which circumvents the restrictive global Lipschitz gradient continuity assumption needed in Proximal Gradient algorithms (PG). The BPGe algorithm has higher generality than the recently introduced Proximal Gradient algorithm with extrapolation(PGe), and besides, due to the extrapolation step, BPGe converges faster than BPG algorithm. Analyzing the convergence, we prove that any limit point of the sequence generated by BPGe is a stationary point of the problem by choosing parameters properly. Besides, assuming Kurdyka-{\'L}ojasiewicz property, we prove the whole sequences generated by BPGe converges to a stationary point. Finally, to illustrate the potential of the new method BPGe, we apply it to two important practical problems that arise in many fundamental applications (and that not satisfy global Lipschitz gradient continuity assumption): Poisson linear inverse problems and quadratic inverse problems. In the tests the accelerated BPGe algorithm shows faster convergence results, giving an interesting new algorithm.Comment: Preprint submitted for publication, February 14, 201