Deterministic Genetic Algorithm

Many optimization problems in real life do not satisfy convexity conditions and usually have large combinatorial explosions with discontinuous space. Due to above difficulties, Genetic Algorithm (GA) has been receiving increased attentions. The successful applications can be found in disciplines such as biology, medicine, and different branches of engineering. The basic idea of GA is to start from a population instead of single point in the potential solution space of a specific problem and allow the population to evolve from generation to generation by generic operators such as selection, crossover, and mutation until the stopping criteria are satisfied. The improvement in GA is achieved by applying a new sampling technique, Hammersley Sequence Sampling (HSS), to both initial population generation and genetic operations. Clustered initial populations and biased genetic operations are avoided from the better uniformity over a multivariate parameter space of HSS. The new algorithm is names as Efficient Genetic Algorithm (EGA).

Stochastic Genetic Algorithm

The uncertainties come from the incomplete model information has to be incorporated into optimization for more accurate results. In this case, the objective function is represented in terms of probabilistic representation. The sampling/scenario optimization technique can be used for this type problem. More samples can bring closer approximation. However, it also increases the computation burden. To balance accuracy and efficiency, objective function is augmented with an error bandwidth term which represents the error in calculation contingent on the no. of samples. A framework is shown in the following Figure. The newly developed stochastic genetic algorithm is named as Hammersley Stochastic Genetic Algorithm (HSGA).

Multi-objective Genetic Algorithm(MOEGA)

The Multi-objective Genetic Algorithm developed here is based on weighting method. The better multi-dimensional uniformity property of Hammersley sequence sampling is used to generate weights in order to increase the efficiency of the search by avoiding clustered search bias towards one region. The uniformity property would spread out search directions towards Pareto frontier evenly as showed in the following figure. This algorithm provides better solution accuracy and is found to be computationally more efficient than other variants of multi-objective genetic algorithms.