Multi-objective Uniform-diversity Genetic Algorithm (MUGA)

Abstract

Optimization in engineering design has always been of great importance and interest particularly in solving complex real-world design problems. Basically, the optimization process is defined as finding a set of values for a vector of design variables so that it leads to an optimum value of an objective or cost function. In such single-objective optimization problems, there may or may not exist some constraint functions on the design variables and they are respectively referred to as constrained or unconstrained optimization problems. There are many calculus-based methods including gradient approaches to search for mostly local optimum solutions and these are well documented in (Arora, 1989; Rao, 1996). However, some basic difficulties in the gradient methods such as their strong dependence on the initial guess can cause them to find a local optimum rather than a global one. This has led to other heuristic optimization methods, particularly Genetic Algorithms (GAs) being used extensively during the last decade. Such nature-inspired evolutionary algorithms (Goldberg, 1989; Back et al., 1997) differ from other traditional calculus based techniques. The main difference is that GAs work with a population of candidate solutions, not a single point in search space. This helps significantly to avoid being trapped in local optima (Renner & Ekart, 2003) as long as the diversity of the population is well preserved. In multi-objective optimization problems, there are several objective or cost functions (a vector of objectives) to be optimized (minimized or maximized) simultaneously. These objectives often conflict with each other so that as one objective function improves, another deteriorates. Therefore, there is no single optimal solution that is best with respect to all the objective functions. Instead, there is a set of optimal solutions, well known as Pareto optimal solutions (Srinivas & Deb, 1994; Fonseca & Fleming, 1993; Coello Coello & Christiansen, 2000; Coello Coello & Van Veldhuizen, 2002), which distinguishes significantly the inherent natures between single-objective and multi-objective optimization problems. V. Pareto (1848-1923) was the French-Italian economist who first developed the concept of multiobjective optimization in economics (Pareto, 1896). The concept of a Pareto front in the space of objective functions in multi-objective optimization problems (MOPs) stands for a set of solutions that are non-dominated to each other but are superior to the rest of solutions in the search space. Evidently, changing the vector of design variables in such a Pareto optimal O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m