Gene-pool Optimal Mixing Evolutionary Algorithms (GOMEAs) have been shown to achieve state-of-the-art results on various types of optimization problems with various types of problem variables. Recently, a GOMEA for permutation spaces was introduced by leveraging the random keys encoding, obtaining promising first results on permutation flow shop instances. A key cited strength of GOMEAs is linkage learning, i.e., the ability to determine and leverage, during optimization, key dependencies between problem variables. However, the added value of linkage learning was not tested in depth for permutation GOMEA. Here, we introduce a new version of permutation GOMEA, called qGOMEA, that works directly in permutation space, removing the redundancy of using random keys. We additionally consider various linkage information sources, including random noise, in both GOMEA variants, and compare performance with various classic genetic algorithms on a wider range of problems than considered before. We find that, although the benefits of linkage learning are clearly visible for various artificial benchmark problems, this is far less the case for various real-world inspired problems. Finally, we find that qGOMEA performs best, and is more applicable to a wider range of permutation problems.

Purpose: Bi-objective treatment planning for high-dose-rate prostate brachytherapy is a novel treatment planning method with two separate objectives that represent target coverage and organ-at-risk sparing. In this study, we investigated the feasibility and plan quality of this method by means of a retrospective observer study. Methods and Materials: Current planning sessions were recorded to configure a bi-objective optimization model and to assess its applicability to our clinical practice. Optimization software, GOMEA, was then used to automatically generate a large set of plans with different trade-offs in the two objectives for each of 18 patients treated with high-dose-rate prostate brachytherapy. From this set, five plans per patient were selected for comparison to the clinical plan in terms of satisfaction of planning criteria and in a retrospective observer study. Three brachytherapists were asked to evaluate the blinded plans and select the preferred one. Results: Recordings demonstrated applicability of the bi-objective optimization model to our clinical practice. For 14/18 patients, GOMEA plans satisfied all planning criteria, compared with 4/18 clinical plans. In the observer study, in 53/54 cases, a GOMEA plan was preferred over the clinical plan. When asked for consensus among observers, this ratio was 17/18 patients. Observers highly appreciated the insight gained from comparing multiple plans with different trade-offs simultaneously. Conclusions: The bi-objective optimization model adapted well to our clinical practice. GOMEA plans were considered equal or superior to the clinical plans. In addition, presenting multiple high-quality plans provided novel insight into patient-specific trade-offs.

The Multi-objective Gene-pool Optimal Mixing Evolutionary Algorithm (MO-GOMEA) has been shown to be a promising solver for multi-objective combinatorial optimization problems, obtaining an excellent scalability on both standard benchmarks and real-world applications. To attain optimal performance, MO-GOMEA requires its two parameters, namely the population size and the number of clusters, to be set properly with respect to the problem instance at hand, which is a non-trivial task for any EA practitioner. In this article, we present a new version of MO-GOMEA in combination with the so-called Interleaved Multi-start Scheme (IMS) for the multi-objective domain that eliminates the manual setting of these two parameters. The new MO-GOMEA is then evaluated on multiple benchmark problems in comparison with two well-known multi-objective evolutionary algorithms (MOEAs): Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D). Experiments suggest that MO-GOMEA with the IMS is an easy-to-use MOEA that retains the excellent performance of the original MO-GOMEA.