Conclusions

MOEAs algorithms have been successfully implemented for various aspects in medicine. MOEAs are now used increasingly in radiotherapy treatment planning, especially in high dose brachytherapy. The possibility exists to use MOEAs for he more widely used low dose brachytherapy treatment. For external intensity beam radiotherapy the number of parameters is very large but MOEAs with a support from deterministic algorithms can provide faster a representative set of non-dominated solutions of a quality clinical acceptable. The study of the results of the application may help to understand optimal beam directions and numbers of fields for specific types of cancer.

In other fields such image reconstruction, decision making, computer aided diagnosis the use of MOEAs instead of single objective optimization algorithms provides a range of solutions out of which better solutions can be obtained than by a trial and error method necessary to find weights that provide a satisfactory solution.

In this way MOEA in medicine can be viewed as an optimization of the optimization where better results can be obtained. While the optimization aspects have been discussed in details the decision making process is not considered in most of the MOEAs presented.

For complex problems that involve many objectives the performance of MOEAs over conventional scalar objective optimizations are more pronounced. A very large number of optimization runs are necessary to obtain a representative set of solutions. The mapping from decision to objective space produces solutions by the conventional methods that are clustered and not necessarily uniform distributed over the entire Pareto front. The results are that some good solutions to be obtained by conventional methods could require a very fine tuning of the importance factors. MOEAs can produce furthermore solutions in regions not accessible by conventional weighted scalar optimizations.

MOEAs used in medicine include NPGA by Horn and Nafpliotis and NSGA by Srinivas et al. Later more efficient algorithms like SPEA or NSGA-II were used. Some problems are high dimensional and MOEAs alone fail to produce sufficient good solutions. Most of the genetic operators and selection methods produce solutions that are far for the global Pareto optimal front. Even with a large number of generations the population converges prematurely. Initialization of the population with solutions provided by other methods helps to improve significantly the performance of the MOEA algorithms. Knowledge inclusion is important that reduce the search space and improves the performance of MOEAs.

Hybrid algorithms in IMRT in cooperation with deterministic gradient based optimization algorithms allow MOEAs to produce fast high quality solutions even for problems with as many as 5000 and more parameters. This is only possible for this specific type of problem. Without the support from other algorithms produce only very poor quality solutions.

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