Exploiting linkage information in real-valued optimization with the real-valued gene-pool optimal mixing evolutionary algorithm

The recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) has been shown to be among the state-of-the-art for solving discrete optimization problems. Key to the success of GOMEA is its ability to efficiently exploit the linkage structure of a problem. Here, we introduce the Real-Valued GOMEA (RV-GOMEA), which incorporates several aspects of the real-valued EDA known as AMaLGaM into GOMEA in order to make GOMEA well-suited for real-valued optimization. The key strength of GOMEA to competently exploit linkage structure is effectively preserved in RV-GOMEA, enabling excellent performance on problems that exhibit a linkage structure that is to some degree decomposable. Moreover, the main variation operator of GOMEA enables substantial improvements in performance if the problem allows for partial evaluations, which may be very well possible in many real-world applications. Comparisons of performance with state-of-the-art algorithms such as CMA-ES and AMaLGaM on a set of well-known benchmark problems show that RV-GOMEA achieves comparable, excellent scalability in case of black-box optimization. Moreover, RV-GOMEA achieves unprecedented scalability on problems that allow for partial evaluations, reaching near-optimal solutions for problems with up to millions of real-valued variables within one hour on a normal desktop computer

The Multiple Insertion Pyramid: A Fast Parameter-Less Population Scheme

textabstractThe Parameter-less Population Pyramid (P3) uses a novel population scheme, called the population pyramid. This population scheme does not require a fixed population size, instead it keeps adding new solutions to an ever growing set of layered populations. P3 is very efficient in terms of number of fitness function evaluations but its runtime is significantly higher than that of the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) which uses the same method of exploration. This higher run-time is caused by the need to rebuild the linkage tree every time a single new solution is added to the population pyramid.We propose a new population scheme, called the multiple insertion pyramid that results in a faster variant of P3 by inserting multiple solutions at the same time and operating on populations instead of on single solutions

Fast and insightful bi-objective optimization for prostate cancer treatment planning with high-dose-rate brachytherapy

Purpose: Prostate high-dose-rate brachytherapy (HDR-BT) planning involves determining the movement that a high-strength radiation stepping source travels through the patient's body, such that the resulting radiation dose distribution sufficiently covers tumor volumes and safely spares nearby healthy organs from radiation risks. The Multi-Objective Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (MO-RV-GOMEA) has been shown to be able to effectively handle this inherent bi-objective nature of HDR-BT planning. However, in clinical practice there is a very restricted planning time budget (often less than 1 h) for HDR-BT planning, and a considerable amount of running time needs to be spent before MO-RV-GOMEA finds a good trade-off front of treatment plans (about20–30 min on a single CPU core) with sufficiently accurate dose calculations, limiting the applicability of the approach in the clinic. To address this limitation, we propose an efficiency enhancement technique for MO-RV-GOMEA solving the bi-objective prostate HDR-BT planning problem.Methods: Dose-Volume (DV) indices are often used to assess the quality of HDR-BT plans. The accuracy of these indices depends on the number of dose calculation points at which radiation doses are computed. These are randomly uniformly sampled inside target volumes and organs at risk. In available HDR-BT planning optimization algorithms, the number of dose calculation points is fixed. The more points are used, the better the accuracy of the obtained results will be, but also the longer the algorithms need to be run. In this work, we introduce a so-called multi-resolution scheme that gradually increases the number of dose calculation points during the optimization run such that the running time can be substantially reduced without compromising on the accuracy of the obtained results.Results and conclusion: Experiments on a data set of 18 patient cases show that with the multi-resolution scheme, MO-RV-GOMEA can achieve a sufficiently good trade-off front of treatment plans after five minutes of running time on a single CPU core (4–6 times faster than the old approach with a fixed number of dose calculation points). When the optimization with the multi-resolution scheme is run on a quad-core machine, five minutes are enough to obtain trade-off fronts that are nearly as good as those obtained by running optimization with the old approach in one hour (i.e., 12 times faster). This leaves ample time to perform the selection of the preferred treatment plan from the trade-off front for the specific patient at hand. Furthermore, comparisons with real clinical treatment plans, which were manually made by experienced BT planners within 30–60 min, confirm that the plans obtained by our approach are superior in terms of DV indices. These results indicate that our proposed approach has the potential to be employed in clinical practice.</p

Medium-Voltage Distribution Network Expansion Planning with Gene-pool Optimal Mixing Evolutionary Algorithms

Medium-voltage distribution network expansion planning involves finding the most economical adjustments of both the capacity and the topology of the network such that no operational constraints are violated and the expected loads, that the expansion is planned for, can be supplied. This paper tackles this important real-world problem using realistic yet computationally feasible models and, for the first time, using two instances of the recently proposed class of Gene-pool Optimal Mixing Evolutionary Algorithms (GOMEAs) that have previously been shown to be a highly efficient integration of local search and genetic recombination, but only on standard benchmark problems. One GOMEA instance that we use employs linkage learning and one instance assumes no dependencies among problem variables. We also conduct experiments with a widely used traditional Genetic Algorithm (GA). Our results show that the favorable performance of GOMEA instances over traditional GAs extends to the real-world problem at hand. Moreover, the use of linkage learning is shown to further increase the algorithm's effectiveness in converging toward optimal solutions

Unveiling evolutionary algorithm representation with DU maps

Evolutionary algorithms (EAs) have proven to be effective in tackling problems in many different domains. However, users are often required to spend a significant amount of effort in fine-tuning the EA parameters in order to make the algorithm work. In principle, visualization tools may be of great help in this laborious task, but current visualization tools are either EA-specific, and hence hardly available to all users, or too general to convey detailed information. In this work, we study the Diversity and Usage map (DU map), a compact visualization for analyzing a key component of every EA, the representation of solutions. In a single heat map, the DU map visualizes for entire runs how diverse the genotype is across the population and to which degree each gene in the genotype contributes to the solution. We demonstrate the generality of the DU map concept by applying it to six EAs that use different representations (bit and integer strings, trees, ensembles of trees, and neural networks). We present the results of an online user study about the usability of the DU map which confirm the suitability of the proposed tool and provide important insights on our design choices. By providing a visualization tool that can be easily tailored by specifying the diversity (D) and usage (U) functions, the DU map aims at being a powerful analysis tool for EAs practitioners, making EAs more transparent and hence lowering the barrier for their use

Robust evolutionary algorithms

Evolutionary Algorithms (EAs) have shown great potential to solve complex real world problems, but their dependence on problem specific configuration in order to obtain high quality performance prevents EAs from achieving widespread use. While it is widely accepted that statically configuring an EA is already a complex problem, dynamic configuration of an EA is a combinatorially harder problem. Evidence provided here supports the claim that EAs achieve the best results when using dynamic configurations. By designing methods that automatically configure parts of an EA or by changing how EAs work to avoid configurable aspects, EAs can be made more robust, allowing them better performance on a wider variety of problems with less requirements on the user. Two methods are presented in this thesis to increase the robustness of EAs. The first is a novel algorithm designed to automatically configure and dynamically update the recombination method which is used by the EA to exploit known information to create new solutions. The techniques used by this algorithm can likely be applied to other aspects of an EA in the future, leading to even more robust EAs. The second is an existing set of algorithms which only require a single configurable parameter. The analysis of the existing set led to the creation of a new variation, as well as a better understanding of how these algorithms work. Both methods are able to outperform more traditional EAs while also making both easier to apply to new problems. By building upon these methods, and perhaps combining them, EAs can become even more robust and become more widely used --Abstract, page iv