A scalar projection and angle based evolutionary algorithm for many-objective optimization problems

In decomposition-based multi-objective evolutionary algorithms, the setting of search directions (or weight vectors), and the choice of reference points (i.e., the ideal point or the nadir point) in scalarizing functions, are of great importance to the performance of the algorithms. This paper proposes a new decomposition-based many-objective optimizer by simultaneously using adaptive search directions and two reference points. For each parent, binary search directions are constructed by using its objective vector and the above two reference points. Each individual is simultaneously evaluated on two fitness functions—which are motivated by scalar projections—that are deduced to be the differences between two penalty-based boundary intersection (PBI) functions, and two inverted PBI functions, respectively. Solutions with the best value on each fitness function are emphasized. Moreover, an angle-based elimination procedure is adopted to select diversified solutions for the next generation. The use of adaptive search directions aims at effectively handling problems with irregular Pareto-optimal fronts, and the philosophy of using the ideal and nadir points simultaneously is to take advantages of the complementary effects of the two points when handling problems with either concave or convex fronts. The performance of the proposed approach is compared with seven state-of-the-art multi-/many-objective evolutionary algorithms on 32 test problems with up to 15 objectives. It is shown by the experimental results that the proposed algorithm is flexible when handling problems with different types of Pareto-optimal fronts, obtaining promising results regarding both the quality of the returned solution set and the efficiency of the new algorithm

A convergence and diversity guided leader selection strategy for many-objective particle swarm optimization

Recently, particle swarm optimizer (PSO) is extended to solve many-objective optimization problems (MaOPs) and becomes a hot research topic in the field of evolutionary computation. Particularly, the leader particle selection (LPS) and the search direction used in a velocity update strategy are two crucial factors in PSOs. However, the LPS strategies for most existing PSOs are not so efficient in high-dimensional objective space, mainly due to the lack of convergence pressure or loss of diversity. In order to address these two issues and improve the performance of PSO in high-dimensional objective space, this paper proposes a convergence and diversity guided leader selection strategy for PSO, denoted as CDLS, in which different leader particles are adaptively selected for each particle based on its corresponding situation of convergence and diversity. In this way, a good tradeoff between the convergence and diversity can be achieved by CDLS. To verify the effectiveness of CDLS, it is embedded into the PSO search process of three well-known PSOs. Furthermore, a new variant of PSO combining with the CDLS strategy, namely PSO/CDLS, is also presented. The experimental results validate the superiority of our proposed CDLS strategy and the effectiveness of PSO/CDLS, when solving numerous MaOPs with regular and irregular Pareto fronts (PFs)

Global Trajectory Optimisation : Can We Prune the Solution Space When Considering Deep Space Manoeuvres? [Final Report]

This document contains a report on the work done under the ESA/Ariadna study 06/4101 on the global optimization of space trajectories with multiple gravity assist (GA) and deep space manoeuvres (DSM). The study was performed by a joint team of scientists from the University of Reading and the University of Glasgow