Generalized Extremal Optimization for Solving Complex Optimal Design Problems

Recently, Boettcher and Percus [1] proposed a new optimization method, called Extremal Optimization (EO), inspired by a simplified model of natural selection developed to show the emergence of Self-Organized Criticality (SOC) in ecosystems [2]. Although having been successfully applied to hard problems in combinatorial optimization, a drawback of the EO is that for each new optimization problem assessed, a new way to define the fitness of the design variables has to be created [2]. Moreover, to our knowledge it has been applied so far to combinatorial problems with no implementation to continuous functions. In order to make the EO easily applicable to a broad class of design optimization problems, Sousa and Ramos [3,4] have proposed a generalization of the EO that was named the Generalized Extremal Optimization (GEO) method. It is of easy implementation, does not make use of derivatives and can be applied to unconstrained or constrained problems, non-convex or disjoint design spaces, with any combination of continuous, discrete or integer variables. It is a global search meta-heuristic, as the Genetic Algorithm (GA) and the Simulated Annealing (SA), but with the a priori advantage of having only one free parameter to adjust. Having been already tested on a set of test functions, commonly used to assess the performance of stochastic algorithms, the GEO proved to be competitive to the GA and the SA, or variations of these algorithms [3,4]. The GEO method was devised to be applied to complex optimization problems, such as the optimal design of a heat pipe (HP). This problem has difficulties such as an objective function that presents design variables with strong non-linear interactions, subject to multiple constraints, being considered unsuitable to be solved by traditional gradient based optimization methods [5]. To illustrate the efficacy of the GEO on dealing with such kind of problems, we used it to optimize a HP for a space application with the goal of minimizing the HP's total mass, given a desirable heat transfer rate and boundary conditions on the condenser. The HP uses a mesh type wick and is made of Stainless Steel. A total of 18 constraints were taken into account, which included operational, dimensional and structural ones. Temperature dependent fluid properties were considered and the calculations were done for steady state conditions, with three fluids being considered as working fluids: ethanol, methanol and ammonia. Several runs were performed under different values of heat transfer