On the use of two reference points in decomposition based multiobjective evolutionary algorithms

Decomposition based multiobjective evolutionary algorithms approximate the Pareto front of a multiobjective optimization problem by optimizing a set of subproblems in a collaborative manner. Often, each subproblem is associated with a direction vector and a reference point. The settings of these parameters have a very critical impact on convergence and diversity of the algorithm. Some work has been done to study how to set and adjust direction vectors to enhance algorithm performance for particular problems. In contrast, little effort has been made to study how to use reference points for controlling diversity in decomposition based algorithms. In this paper, we first study the impact of the reference point setting on selection in decomposition based algorithms. To balance the diversity and convergence, a new variant of the multiobjective evolutionary algorithm based on decomposition with both the ideal point and the nadir point is then proposed. This new variant also employs an improved global replacement strategy for performance enhancement. Comparison of our proposed algorithm with some other state-of-the-art algorithms is conducted on a set of multiobjective test problems. Experimental results show that our proposed algorithm is promising

On Algorithmic Descriptions and Software Implementations for Multi-objective Optimisation: A Comparative Study

Multi-objective optimisation is a prominent subfield of optimisa-tion with high relevance in real-world problems, such as engineering design. Over the past two decades a multitude of heuristic algorithms for multi-objective optimisation have been introduced and some of them have become extremely popular. Some of the most promising and versatile algorithms are have been implemented in software platforms. This article experimentally investigates the process of interpreting and implementing algorithms by examining multiple popular implementations of three well-known algorithms for multi-objective optimisation. We observed that official and broadly employed software platforms interpreted and thus implemented the same heuristic search algorithm differently. These different interpretations affect the algorithmic structure as well as the software implementation. Numerical results show that these differences cause statistically significant differences in performance

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