The idea is to minimize the occurrence of multiple objects from the same cluster in the same set. In the current paper, we study computational aspects of the method. First, we prove that the problem of finding the optimal clustering is NP-hard. Second, to numerically find a suitable clustering, we propose to use the genetic algorithm augmented by a renumbering procedure, a fast task-specific local search heuristic and an initial solution based on a simplified model. Third, in a simulation study, we demonstrate that our improvements of the standard genetic algorithm significantly enhance its computational performance.

In many risk-aware and multi-objective reinforcement learning settings, the utility of the user is derived from the single execution of a policy. In these settings, making decisions based on the average future returns is not suitable. For example, in a medical setting a patient may only have one opportunity to treat their illness. When making a decision, just the expected return -- known in reinforcement learning as the value -- cannot account for the potential range of adverse or positive outcomes a decision may have. Our key insight is that we should use the distribution over expected future returns differently to represent the critical information that the agent requires at decision time. In this paper, we propose Distributional Monte Carlo Tree Search, an algorithm that learns a posterior distribution over the utility of the different possible returns attainable from individual policy executions, resulting in good policies for both risk-aware and multi-objective settings. Moreover, our algorithm outperforms the state-of-the-art in multi-objective reinforcement learning for the expected utility of the returns.

The Rubik's Cube has been around for decades. I've toyed with the cube, probably in the very late '80s or early '90s, but never even imagined being able to solve one; from entirely shuffled, to perfectly ordered. But wouldn't it be satisfying if I could? Fortunately, the internet makes solving what was originally an architecture puzzle, doable for most of us. The world record for solving a cube has plummeted since 2000 from 20 seconds to under five, as pros and enthusiasts synthesized high-speed solutions and turn combinations (called algorithms) and shared them with the world.

$\alpha\mu$ is a search algorithm which repairs two defaults of Perfect Information Monte Carlo search: strategy fusion and non locality. In this paper we optimize $\alpha\mu$ for the game of Bridge, avoiding useless computations. The proposed optimizations are general and apply to other imperfect information turn-based games. We define multiple optimizations involving Pareto fronts, and show that these optimizations speed up the search. Some of these optimizations are cuts that stop the search at a node, while others keep track of which possible worlds have become redundant, avoiding unnecessary, costly evaluations. We also measure the benefits of parallelizing the double dummy searches at the leaves of the $\alpha\mu$ search tree.

Object rearrangement is a widely-applicable and challenging task for robots. Geometric constraints must be carefully examined to avoid collisions and combinatorial issues arise as the number of objects increases. This work studies the algorithmic structure of rearranging uniform objects, where robot-object collisions do not occur but object-object collisions have to be avoided. The objective is minimizing the number of object transfers under the assumption that the robot can manipulate one object at a time. An efficiently computable decomposition of the configuration space is used to create a "region graph", which classifies all continuous paths of equivalent collision possibilities. Based on this compact but rich representation, a complete dynamic programming primitive DFSDP performs a recursive depth first search to solve monotone problems quickly, i.e., those instances that do not require objects to be moved first to an intermediate buffer. DFSDP is extended to solve single-buffer, non-monotone instances, given a choice of an object and a buffer. This work utilizes these primitives as local planners in an informed search framework for more general, non-monotone instances. The search utilizes partial solutions from the primitives to identify the most promising choice of objects and buffers. Experiments demonstrate that the proposed solution returns near-optimal paths with higher success rate, even for challenging non-monotone instances, than other leading alternatives.

Persuasion is an important and yet complex aspect of human intelligence. When undertaken through dialogue, the deployment of good arguments, and therefore counterarguments, clearly has a significant effect on the ability to be successful in persuasion. Two key dimensions for determining whether an argument is good in a particular dialogue are the degree to which the intended audience believes the argument and counterarguments, and the impact that the argument has on the concerns of the intended audience. In this paper, we present a framework for modelling persuadees in terms of their beliefs and concerns, and for harnessing these models in optimizing the choice of move in persuasion dialogues. Our approach is based on the Monte Carlo Tree Search which allows optimization in real-time. We provide empirical results of a study with human participants showing that our automated persuasion system based on this technology is superior to a baseline system that does not take the beliefs and concerns into account in its strategy.

Machine learning (ML) has become a vital part in many aspects of our daily life. However, building well performing machine learning applications requires highly specialized data scientists and domain experts. Automated machine learning (AutoML) aims to reduce the demand for data scientists by enabling domain experts to build machine learning applications automatically without extensive knowledge of statistics and machine learning. This paper is a combination of a survey on current AutoML methods and a benchmark of popular AutoML frameworks on real data sets. Driven by the selected frameworks for evaluation, we summarize and review important AutoML techniques and methods concerning every step in building an ML pipeline. The selected AutoML frameworks are evaluated on 137 data sets from established AutoML benchmark suites.

Multiple known algorithmic paradigms (backtracking, local search and the polynomial method) only yield a 2n(1-1/O(k)) time algorithm for k-SAT in the worst case. For this reason, it has been hypothesized that the worst-case k-SAT problem cannot be solved in 2n(1-f(k)/k) time for any unbounded function f. This hypothesis has been called the "Super-Strong ETH", modelled after the ETH and the Strong ETH. It has also been hypothesized that k-SAT is hard to solve for randomly chosen instances near the "critical threshold", where the clause-to-variable ratio is such that randomly chosen instances are satisfiable with probability 1/2. We give a randomized algorithm which refutes the Super-Strong ETH for the case of random k-SAT and planted k-SAT for any clause-to-variable ratio. For example, given any random k-SAT instance F with n variables and m clauses, our algorithm decides satisfiability for F in  2n(1-c*log(k)/k) time with high probability (over the choice of the formula and the randomness of the algorithm). It turns out that a well-known algorithm from the literature on SAT algorithms does the job: the PPZ algorithm of Paturi, Pudlak, and Zane (1999).   The Unique k-SAT problem is the special case where there is at most one satisfying assignment. Improving prior reductions, we show that the Super-Strong ETHs for Unique k-SAT and k-SAT are equivalent. More precisely, we show the time complexities of Unique k-SAT and k-SAT are very tightly correlated: if Unique k-SAT is in  2n(1-f(k)/k) time for an unbounded f, then k-SAT is in 2n(1-f(k)/(2k)) time.

This process is called order picking, which may constitute about 50-65% of operating costs. Therefore order picking is considered the highest-priority area for productivity improvements (see De Koster et al. (2007)). In a traditional manual order picking system (also called a picker-to-parts system), the pickers spend 50% of their working time on the task of walking (see Tompkins (2010); for an overview of manual order picking systems see De Koster et al. (2007)). The unproductive working times require the picker-to-parts system to have a large workforce, especially for companies which have millions of small-sized items in large warehouses, such as the retailers Amazon, Alibaba, Zara, Zalando and Walmart. Many of them provide both brick-and-mortar stores and online shops to create a seamless shopping experience for customers (omnichannel flexibility). Due to the diversity of online shops, we concentrate on both single-line and multi-line small-sized orders. Especially during the COVID-19 pandemic, online grocery sales are growing threefold faster (see Fabric (2020)). There are increasing demands for alternative warehousing systems to increase the efficiency of order picking, for example, robot-based compact storage and retrieval systems and robotic mobile fulfillment systems (see more details in Azadeh et al. (2019)). Here we consider a relatively new warehousing concept that does not use expensive fixed hardware and can be easily and quickly implemented, called AGV-assisted picking (see Boysen et al. (2019), Azadeh et al. (2019)).

Evolutionary Algorithms are naturally inspired approximation optimisation algorithms that usually interfere with science problems when common mathematical methods are unable to provide a good solution or finding the exact solution requires an unreasonable amount of time using traditional exhaustive search algorithms. The success of these population-based frameworks is mainly due to their flexibility and ease of adaptation to the most different and complex optimisation problems. This paper presents a metaheuristic algorithm called Stochastic Fractal Search, inspired by the natural phenomenon of growth based on a mathematical concept called the fractal, which is shown to be able to explore the search space more efficiently. This paper also focuses on the algorithm steps and some example applications of engineering design optimisation problems commonly used in the literature being applied to the proposed algorithm.