APPLICATION OF A HYBRID VERSION OF NSGA-II FOR MULTIOBJECTIVE DOSE OPTIMIZATION IN BRACHYTHERAPY
M. Lahanas, N. Milickovic, M. Papagiannopoulou, K. Karouzakis, D. Baltas and N. Zamboglou
In high dose rate (HDR) brachytherapy which is a method of cancer treatment, up to 300 parameters must be optimized to satisfy often-competing objectives. We use multiobjective evolutionary algorithms (MOEA) for the dose optimization problem with objectives expressed in terms of dose-volume histogram (DVH) derived quantities. The objectives can to some extent be also described by variances of dose distributions where deterministic algorithms can be applied but they are trapped sometimes in local minima. DVHs based objectives are used directly in the decision-making process and are therefore preferred. In this case deterministic algorithms cannot be applied. NSGA-II although superior than other MOEAs tested requires a large number of generations to converge near to the global Pareto set. The two main goals of the optimization are: (a) convergence to the global Pareto set and (b) accumulation of many non-dominated solutions. A deterministic algorithm is used in NSGA-II to drive a few members of the population closer to the global Pareto front. These members act as seeds and attract quickly the population towards the global Pareto front, see Fig. 1. These supported solutions are generated using objectives in terms of variances combined together using uniformly distributed random weights. Additionally a hill-climbing operator based on simulated annealing (SA) is used periodically to improve the convergence of the population. The objective space is 3-6 dimensional. A very large population size would be necessary to cover the entire Pareto surface, therefore a secondary population is used to archive all non-dominated solutions found. As the number of objectives increases methods to avoid clustering such as used in SPEA require a considerable time. We use the PAES archiving method for the accumulation of non-dominated solution. MOEAs are mainly Pareto ranking or local search based. We combine the Pareto based NSGA-II algorithm with a local search based hill-climbing routine. MOEAs produce good solutions for low-dimensional problems but the quality of the solutions deteriorates as the number of objectives and parameters increases. An analysis of the probability distributions of random solutions in objective space shows that for a large number of decision variables the probability of obtaining at random a solution close to the global Pareto decreases significantly. The population converges to only a local Pareto set far from the global set, if it converges at all. We use supported solutions, an external population that accumulates non dominated solutions and the periodic application of a local search that improves the performance of NSGA-II. The hybrid algorithm provides a representation of the trade-off surface with more than 1000 solutions in a few minutes. A sequential SA algorithm requires more than 10 hours for the same statistics. The large set of solutions can be processed and allows clinicians to obtain a solution that satisfies at best their objectives. Additionally it provides by the analysis of the trade-offs an insight into the possibilities of which criteria and to what extend can be satisfied.