Use of genetic algorithms and gradient based optimization techniques for calcium phosphate precipitation

Phase equilibrium computations constitute an important problem for designing and optimizing crystallization processes. The Gibbs free energy is generally used as an objective function to find phase amount and composition at equilibrium. In such problems, the Gibbs free energy may be a quite complex function, with several local minima. This paper presents a contribution to handle this kind of problems by implementation of an optimization technique based on the successive use of a genetic algorithm (GA) and of a classical sequential quadratic programming (SQP) method: the GA is used to perform a preliminary search in the solution space for locating the neighborhood of the solution. Then, the SQP method is employed to refine the best solution provided by the GA. The basic operations involved in the design of the GA developed in this study (encoding with binary representation of real values, evaluation function, adaptive plan) are presented. Several test problems are first presented to demonstrate the validity of the approach. Then, calcium phosphate precipitation which is of major interest for P-recovery from wastewater, has been chosen as an illustration of the implemented algorithm

Incremental multiple objective genetic algorithms

This paper presents a new genetic algorithm approach to multi-objective optimization problemsIncremental Multiple Objective Genetic Algorithms (IMOGA). Different from conventional MOGA methods, it takes each objective into consideration incrementally. The whole evolution is divided into as many phases as the number of objectives, and one more objective is considered in each phase. Each phase is composed of two stages: first, an independent population is evolved to optimize one specific objective; second, the better-performing individuals from the evolved single-objective population and the multi-objective population evolved in the last phase are joined together by the operation of integration. The resulting population then becomes an initial multi-objective population, to which a multi-objective evolution based on the incremented objective set is applied. The experiment results show that, in most problems, the performance of IMOGA is better than that of three other MOGAs, NSGA-II, SPEA and PAES. IMOGA can find more solutions during the same time span, and the quality of solutions is better