A pareto following variation operator for fast-converging multiobjective evolutionary algorithms

Abstract

One of the major difficulties when applying Multiobjective Evolutionary Algorithms (MOEA) to real world problems is the large number of objective function evaluations. Approximate (or surrogate) methods offer the possibility of reducing the number of evaluations, without reducing solution quality. Artificial Neural Network (ANN) based models are one approach that have been used to approximate the future front from the current available fronts with acceptable accuracy levels. However, the associated computational costs limit their effectiveness. In this work, we introduce a simple approach that has comparatively smaller computational cost and we have developed this model as a variation operator that can be used in any kind of multiobjective optimizer. When designing this model, we have considered the whole search procedure as a dynamic system that takes available objective values in current front as input and generates approximated design variables for the next front as output. Initial simulation experiments have produced encouraging results in comparison to NSGA-II. Our motivation was to increase the speed of the hosting optimizer. We have compared the performance of the algorithm with respect to the total number of function evaluation and Hypervolume metric. This variation operator has worst case complexity of O(nkN 3 ), where N is the population size, n and k is the number of design variables and objectives respectively.

Towards high speed multiobjective evolutionary optimizers

“…NSGA-II converges within 15000 function evaluations approximately, on the other hand, our model can reach the same Hypervolume within only 6000 function evaluations. The details of running time analysis can be found in [13].…”

“…Due to space constraints, we limit the discussion to a brief overview of the proposed model and preliminary simulation analysis. More detailed explanations and experimental results of our model can be found in [12] and [13]. …”

“…However, we have used the linear least square method in the time domain (front domain) to find the transfer function of the dynamic system. Although the page constraints do not allow us to elaborate description of this approach, the details can be found in [13]. However, Figure 5 may be helpful to understand the model.…”

Issues with performance measures for dynamic multi-objective optimisation

“…These algorithms can be categorised as evolutionary algorithms [1], [4], [5], [23], [28], [35], [33], particle swarm optimisation algorithms [8], [12], [19], [20], new CI algorithms proposed for dynamic multi-objective optimisation (DMOO) [6], [33] (for example membrane computing or P-systems [25]), approaches that transform a DMOOP into various single-objective optimisation problems (SOOPs) [22], [24], [32] and prediction-based algorithms [10], [18], [22], [30].…”

Multi-objective memetic algorithm: comparing artificial neural networks and pattern search filter method approaches

“…Finding good approximate methods is even harder for multi‐objective problems due to the number of objective functions and the possible interaction between them. Different approaches have been proposed in the literature (Gaspar‐Cunha and Vieira, 2003, 2005; Gaspar‐Cunha et al, 2004; Jin et al, 2002; Nain and Deb, 2002; Poloni et al, 2000; Talukder et al, 2008).…”