The k-center problem is a fundamental problem we often face when considering complex service systems. Typical challenges include the placement of warehouses in logistics or positioning of servers for content delivery networks. We previously have proposed Dragoon as an effective algorithm to approach the k-center problem. This paper evaluates Dragoon with a focus on potential worst case behavior in comparison to other techniques. We use an evolutionary algorithm to generate instances of the k-center problem that are especially challenging for Dragoon. Ultimately, our experiments confirm the previous good results of Dragoon, however, we also can reliably find scenarios where it is clearly outperformed by other approaches.

Averting the effects of anthropogenic climate change requires a transition from fossil fuels to low-carbon technology. A way to achieve this is to decarbonize the electricity grid. However, further efforts must be made in other fields such as transport and heating for full decarbonization. This would reduce carbon emissions due to electricity generation, and also help to decarbonize other sources such as automotive and heating by enabling a low-carbon alternative. Carbon taxes have been shown to be an efficient way to aid in this transition. In this paper, we demonstrate how to to find optimal carbon tax policies through a genetic algorithm approach, using the electricity market agent-based model ElecSim. To achieve this, we use the NSGA-II genetic algorithm to minimize average electricity price and relative carbon intensity of the electricity mix. We demonstrate that it is possible to find a range of carbon taxes to suit differing objectives. Our results show that we are able to minimize electricity cost to below \textsterling10/MWh as well as carbon intensity to zero in every case. In terms of the optimal carbon tax strategy, we found that an increasing strategy between 2020 and 2035 was preferable. Each of the Pareto-front optimal tax strategies are at least above \textsterling81/tCO2 for every year. The mean carbon tax strategy was \textsterling240/tCO2.

Many risk-sensitive applications require Machine Learning (ML) models to be interpretable. Attempts to obtain interpretable models typically rely on tuning, by trial-and-error, hyper-parameters of model complexity that are only loosely related to interpretability. We show that it is instead possible to take a meta-learning approach: an ML model of non-trivial Proxies of Human Interpretability (PHIs) can be learned from human feedback, then this model can be incorporated within an ML training process to directly optimize for interpretability. We show this for evolutionary symbolic regression. We first design and distribute a survey finalized at finding a link between features of mathematical formulas and two established PHIs, simulatability and decomposability. Next, we use the resulting dataset to learn an ML model of interpretability. Lastly, we query this model to estimate the interpretability of evolving solutions within bi-objective genetic programming. We perform experiments on five synthetic and eight real-world symbolic regression problems, comparing to the traditional use of solution size minimization. The results show that the use of our model leads to formulas that are, for a same level of accuracy-interpretability trade-off, either significantly more or equally accurate. Moreover, the formulas are also arguably more interpretable. Given the very positive results, we believe that our approach represents an important stepping stone for the design of next-generation interpretable (evolutionary) ML algorithms.

Routing of multiple vehicles is an important and difficult problem with applications in the logistic domain [1], especially in the area of customer servicing [2]. In postal services, after-sales services, and in business to business delivery or pick up services one or more vehicles have to be efficiently routed towards customers. If customers can request services over time, the problem becomes dynamic: besides a set of fixed customers, new requests can appear at any point in time. Of course, it is desirable that as many customers as possible are serviced while the tour of any vehicle is kept short. However, it is usually infeasible (due to human resources, labor regulations, or other constraints) to service all customer requests. And clearly, the less customers are left unserviced, the longer the tours become. Thus, the problem is inherently multi-objective. Any efficient solution (smallest maximum tour across all vehicles) is a compromise between the desire to service as many customers as possible (e.g.

The Traveling-Salesperson-Problem (TSP) is arguably one of the best-known NP-hard combinatorial optimization problems. The two sophisticated heuristic solvers LKH and EAX and respective (restart) variants manage to calculate close-to optimal or even optimal solutions, also for large instances with several thousand nodes in reasonable time. In this work we extend existing benchmarking studies by addressing anytime behaviour of inexact TSP solvers based on empirical runtime distributions leading to an increased understanding of solver behaviour and the respective relation to problem hardness. It turns out that performance ranking of solvers is highly dependent on the focused approximation quality. Insights on intersection points of performances offer huge potential for the construction of hybridized solvers depending on instance features. Moreover, instance features tailored to anytime performance and corresponding performance indicators will highly improve automated algorithm selection models by including comprehensive information on solver quality.

Multi-Armed Bandit (MAB) techniques have been successfully applied to many classes of sequential decision problems in the past decades. However, non-stationary settings -- very common in real-world applications -- received little attention so far, and theoretical guarantees on the regret are known only for some frequentist algorithms. In this paper, we propose an algorithm, namely Sliding-Window Thompson Sampling (SW-TS), for nonstationary stochastic MAB settings. Our algorithm is based on Thompson Sampling and exploits a sliding-window approach to tackle, in a unified fashion, two different forms of non-stationarity studied separately so far: abruptly changing and smoothly changing. In the former, the reward distributions are constant during sequences of rounds, and their change may be arbitrary and happen at unknown rounds, while, in the latter, the reward distributions smoothly evolve over rounds according to unknown dynamics. Under mild assumptions, we provide regret upper bounds on the dynamic pseudo-regret of SW-TS for the abruptly changing environment, for the smoothly changing one, and for the setting in which both the non-stationarity forms are present. Furthermore, we empirically show that SW-TS dramatically outperforms state-of-the-art algorithms even when the forms of non-stationarity are taken separately, as previously studied in the literature.

Modeling and simulation is certainly a vast discipline with a broad and complex body of knowledge having, beyond the surface, a large technical and theoretical background (Minsky, 1965) (Banks et al., 2009) (Zeigler et al., 2000) (Boccara, 2003) which consequently, is hard of being completely mastered from modelers coming from disperse domains like biology, ecology or even computer science. Among the existing formalisms, the agent-based or individual-based is increasing gradually the number of adepts in the recent years. The Individual-based modeling is a powerful methodology which is having more and more acceptance between researchers and practitioners of distinct branches from social to biological sciences, including specifically the modeling of ecological processes and microbial consortia studies. Certainly, one of the main reasons for the success of this approach is the relative simplicity for capturing micro-level properties, stochasticity and spatially complex phenomena without the requirement of a high level of mathematical background (Grimm and Railsback, 2005). But the counterpart of the ease for building complex and feature rich models, is the lack of a closed formal mathematical form of the model which implies that the study of these models cannot be attacked analytically.

We study a test-based population size adaptation (TBPSA) method, inspired from population control, in the noise-free multimodal case. In the noisy setting, TBPSA usually recommends, at the end of the run, the center of the Gaussian as an approximation of the optimum. We show that combined with a more naive recommendation, namely recommending the visited point which had the best fitness value so far, TBPSA is also powerful in the noise-free multimodal context. We demonstrate this experimentally and explore this mechanism theoretically: we prove that TBPSA is able to escape plateaus with probability one in spite of the fact that it can converge to local minima. This leads to an algorithm effective in the multimodal setting without resorting to a random restart from scratch.

This thesis describes work on two applications of probabilistic programming: the learning of probabilistic program code given specifications, in particular program code of one-dimensional samplers; and the facilitation of sequential Monte Carlo inference with help of data-driven proposals. The latter is presented with experimental results on a linear Gaussian model and a non-parametric dependent Dirichlet process mixture of objects model for object recognition and tracking. In Chapter 1 we provide a brief introduction to probabilistic programming. In Chapter 2 we present an approach to automatic discovery of samplers in the form of probabilistic programs. We formulate a Bayesian approach to this problem by specifying a grammar-based prior over probabilistic program code. We use an approximate Bayesian computation method to learn the programs, whose executions generate samples that statistically match observed data or analytical characteristics of distributions of interest. In our experiments we leverage different probabilistic programming systems to perform Markov chain Monte Carlo sampling over the space of programs. Experimental results have demonstrated that, using the proposed methodology, we can learn approximate and even some exact samplers. Finally, we show that our results are competitive with regard to genetic programming methods. In Chapter 3, we describe a way to facilitate sequential Monte Carlo inference in probabilistic programming using data-driven proposals. In particular, we develop a distance-based proposal for the non-parametric dependent Dirichlet process mixture of objects model. We implement this approach in the probabilistic programming system Anglican, and show that for that model data-driven proposals provide significant performance improvements. We also explore the possibility of using neural networks to improve data-driven proposals.

This paper tackles the age-old question of derivative free optimization in neural networks. This paper introduces AdaSwarm, a novel derivative-free optimizer to have similar or better performance to Adam but without "gradients". To support the AdaSwarm, a novel Particle Swarm Optimization Exponentially weighted Momentum PSO (EM-PSO), a derivative-free optimizer, is also proposed which tackles constrained and unconstrained single objective optimization problems and looks at applying the proposed momentum particle swarm optimization on benchmark test functions, engineering optimization problems and habitability scores for exoplanets which show speed and convergence of the technique. The EM-PSO is extended by approximating the gradient of a function at any point using the parameters of the particle swarm optimization. This is a novel technique to simulate gradient descent, an extremely popular method in the back-propagation algorithm, using the approximated gradients from the particle swarm optimization parameters. Mathematical proofs of gradient approximation by EM-PSO, thereby bypassing the gradient computation, are presented. The AdaSwarm is compared with various optimizers and the theory and algorithmic performance are supported by promising results.