A New Approach on Many Objective Diversity Measurement

In multi-objective particle swarm optimization (MOPSO) methods, selecting the best {it local guide} (the global best particle) for each particle of the population from a set of Pareto-optimal solutions has a great impact on the convergence and diversity of solutions, especially when optimizing problems with high number of objectives. here, we introduce the Sigma method as a new method for finding best local guides for each particle of the population. The Sigma method is implemented and is compared with another method, which uses the strategy of an existing MOPSO method for finding the local guides. These methods are examined for different test functions and the results are compared with the results of a multi-objective evolutionary algorithm (MOEA)

Diversity assessment in many-objective optimization

Maintaining diversity is one important aim of multiobjective optimization. However, diversity for many-objective optimization problems is less straightforward to define than for multi-objective optimization problems. Inspired by measures for biodiversity, we propose a new diversity metric for manyobjective optimization, which is an accumulation of the dissimilarity in the population, where an Lp-norm-based (p < 1) distance is adopted to measure the dissimilarity of solutions. Empirical results demonstrate our proposed metric can more accurately assess the diversity of solutions in various situations. We compare the diversity of the solutions obtained by four popular many-objective evolutionary algorithms using the proposed diversity metric on a large number of benchmark problems with two to ten objectives. The behaviors of different diversity maintenance methodologies in those algorithms are discussed in depth based on the experimental results. Finally, we show that the proposed diversity measure can also be employed for enhancing diversity maintenance or reference set generation in many-objective optimization

A New Approach on Many Objective Diversity Measurement

In this paper, we introduce two measurements for computing the diversity and spread of non-dominated solutions in the objective space. These measurements compute the angular positions of solutions in the objective space and are able to find a percentage which indicates the distribution of solutions in the space. Also, because we are able to compute the positions of the solutions, the spread of solutions along the non-dominated front can also be measured. This is more important when we evaluate solutions of a problem with a large number of objectives, the objective space of which cannot be illustrated graphically. These measurements are being examined to measure distribution of several sets of non-dominated solutions in the objective space