Adaptive Multi-objective Differential Evolution

Abstract

Multi-objective optimization exists everywhere in real-world applications such as engineering, financial, and scientific applications, because the outcome is directly linked to cost, profit and/or many other criteria that have heavy impacts on performance, safety, environment, etc. It is difficult to provide an ultimate comparison among different outcomes via only one dimension, as the involved multiple criteria/ objectives are generally competing and non-commensurable. For example, a financial manager needs to take both return and risk into consideration when making an investment decision; an air traffic controller needs to consider both the reduction of system-level airspace congestion and the satisfaction of different stakeholders’ preferences.

In this chapter, we investigate the application of parameter adaptive differential evolution to multi-objective optimization problems. To address the challenges in multi-objective optimization, we create an archive to store recently explored inferior solutions whose difference with the current population is utilized as direction information about the optimum, and consider a fairness measure in calculating crowding distances to prefer the solutions whose distances to the nearest neighbors are large and close to be uniform. As a result, the obtained solutions can spread well over the computed non-dominated front and the front can be moved fast toward the Paretooptimal front. The control parameters of the algorithm are adjusted in an adaptive manner, avoiding parameter tuning for problems of different characteristics.