Model-based evolutionary algorithms for finding diverse high-quality solutions with an application in brachytherapy for prostate cancer

Evolutionary algorithms can be used to quickly obtain a high-quality solution to a real-world optimization problem. In practice, it can however be difficult to capture all desirable aspects of a solution into a quantitative objective function. To overcome this, we focus on the design, development, and application of model-based evolutionary algorithms for finding not one solution, but a set of diverse high-quality solutions, via multi-objective optimization and via multimodal optimization. By obtaining and comparing diverse high-quality solutions, the normally implicit trade-offs of a problem can be made explicit, which can help decision makers in selecting the most desirable solution for their problem.
We develop the simple yet effective hill-valley clustering method, which can be employed for efficient and effective multimodal optimization of single-objective and multi-objective problems. In addition, we advance the field of multi-objective optimization by demonstrating how efficient hypervolume-based multi-objective optimization with convergence to optimality can be accomplished. We show how this approach can be used to obtain smoothly navigable solution sets, aimed to make the selection of the most desirable solution more intuitive for the decision maker.
Finally, we consider a problem that arises in the treatment of prostate cancer with brachytherapy, which is a form of internal radiation therapy. We show that by approaching the problem as a bi-objective optimization problem, and solving it with an evolutionary algorithm, novel insight is gained in patient-specific trade-offs, and resulting treatment plans are almost always preferred over clinically-used treatment plans.