Adaptive Formation of Pareto Front in Evolutionary Multi-objective Optimization

Optimization is an important concept in science and engineering. Traditionally, methods are developed for unconstrained and constrained single objective optimization tasks. However, with the increasing complexity of optimization problems in the modern technological real world problems, multi-objective optimization algorithms are needed and being developed. With the advent of evolutionary algorithms in the last decades, multi-objective evolutionary algorithms (MOEAs) are extensively being investigated for solving associated optimization problems, e.g. (Deb et al., 2000, Zitzler & Thiele, 1999, Yao et al., 1999, Eiben et al., 1999). An updated survey of Ga-based MOEAs is given by (Coello, 1999). Evolutionary algorithms are particularly suitable for this, since they evolve simultaneously a population of potential solutions. These solutions are investigated in non-dominated solution space so that the optimized solutions in a multi-objective functions space form a front which is known as Pareto surface or front. Obtaining this simultaneous solution front in a single run is an appealing property that it is the incentive for a fast growing interest on MOEAs in the last decade. Although Pareto front is an important concept, its formation is not straightforward since the strict search of non-dominated regions in the multi-objective solution space prematurely excludes some of the potential solutions that results in an aggregated solutions in this very space. This means Pareto surface is not fully developed and the diversity of the solutions on the Pareto front is not fully exercised. Conventionally, non-dominated solutions with many objectives are usually low in number making the selection pressure toward the Pareto front also low, with aggregated solutions in the Pareto dominance-based MOEA algorithms (Sato, 2007). The purpose of this research is to investigate this issue and provide effective solutions with fast convergence together with diversity of solutions is maintained on the Pareto front. This goal has already attracted attention in the literature (Laumanns et al., 2002). This work addresses this issue with a novel concept of adaptive formation of Pareto front. This is demonstrated with an application from the domain of architectural design. The method is based on relaxed dominance domains, which basically refer to a degree of relaxation of the dominance in the terminology of MOEAs. In this book-chapter contribution, the relaxed dominance concept is explicitly described and applied. The organisation of this chapter is as follows. Section two describes the relaxed dominance concept. Section three describes the adaptive formation of Pareto front in a design application. This is followed by the conclusions in section four. O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg