Answer Set Programming (ASP) is a powerful tool for solving real-world problems. However, many problems involve numeric values and complex constraints beyond the capabilities of standard ASP solvers. Hybrid solvers like CLINGCON and CLINGO[DL] address this by using specialized methods for specific constraints. However, these solvers lack a strong theoretical foundation. This issue has first been addressed by introducing the Logic of Here-and-There with constraints (HT_c) as an extension of the Logic of Here-and-There (HT) and its non-monotone extension Equilibrium Logic. Nowadays, HT serves as a logical foundation for ASP and has facilitated a broader understanding of this paradigm. The idea is that HTC (and other extensions) play an analogous role for hybrid ASP. There remain many open questions about these logics regarding their fundamental characteristics as well as their practical use in solvers, ie. how they can guide the implementation. Having a formal understanding of these hybrid logics is also needed to better understand the inherent structure of the (real-world) problems they are applied to and to improve their representations in ASP. As an example of an application of ASP we use product configuration.

We analyze how symmetries can be used to compress structures (also known as interpretations) onto a smaller domain without loss of information. This analysis suggests the possibility to solve satisfiability problems in the compressed domain for better performance. Thus, we propose a 2-step novel method: (i) the sentence to be satisfied is automatically translated into an equisatisfiable sentence over a ``lifted'' vocabulary that allows domain compression; (ii) satisfiability of the lifted sentence is checked by growing the (initially unknown) compressed domain until a satisfying structure is found. The key issue is to ensure that this satisfying structure can always be expanded into an uncompressed structure that satisfies the original sentence to be satisfied. We present an adequate translation for sentences in typed first-order logic extended with aggregates. Our experimental evaluation shows large speedups for generative configuration problems. The method also has applications in the verification of software operating on complex data structures. Our results justify further research in automatic translation of sentences for symmetry reduction.

The configuration of radar networks is a complex problem that is often performed manually by experts with the help of a simulator. Different numbers and types of radars as well as different locations that the radars shall cover give rise to different instances of the radar configuration problem. The exact modeling of these instances is complex, as the quality of the configurations depends on a large number of parameters, on internal radar processing, and on the terrains on which the radars need to be placed. Classic optimization algorithms can therefore not be applied to this problem, and we rely on "trial-and-error" black-box approaches. In this paper, we study the performances of 13 black-box optimization algorithms on 153 radar network configuration problem instances. The algorithms perform considerably better than human experts. Their ranking, however, depends on the budget of configurations that can be evaluated and on the elevation profile of the location. We therefore also investigate automated algorithm selection approaches. Our results demonstrate that a pipeline that extracts instance features from the elevation of the terrain performs on par with the classical, far more expensive approach that extracts features from the objective function.

In this paper, we apply incremental answer set solving to product configuration. Incremental answer set solving is a step-wise incremental approach to Answer Set Programming (ASP). We demonstrate how to use this technique to solve product configurations problems incrementally. Every step of the incremental solving process corresponds to a predefined configuration action. Using complex domain-specific configuration actions makes it possible to tightly control the level of non-determinism and performance of the solving process. We show applications of this technique for reasoning about product configuration, like simulating the behavior of a deterministic configuration algorithm and describing user actions.

This is a preliminary work on configuration knowledge representation which serves as a foundation for building interactive configuration systems in Answer Set programming (ASP). The major concepts of the product configuration problem are identified and discussed with a bike configuration example. A fact format is developed for expressing product knowledge that is domain-specific and can be mapped from other systems. Finally, a domain-independent ASP encoding is provided that represents the concepts in the configuration problem.

Algorithms typically come with tunable parameters that have a considerable impact on the computational resources they consume. Too often, practitioners must hand-tune the parameters, a tedious and error-prone task. A recent line of research provides algorithms that return nearly-optimal parameters from within a finite set. These algorithms can be used when the parameter space is infinite by providing as input a random sample of parameters. This data-independent discretization, however, might miss pockets of nearly-optimal parameters: prior research has presented scenarios where the only viable parameters lie within an arbitrarily small region. We provide an algorithm that learns a finite set of promising parameters from within an infinite set. Our algorithm can help compile a configuration portfolio, or it can be used to select the input to a configuration algorithm for finite parameter spaces. Our approach applies to any configuration problem that satisfies a simple yet ubiquitous structure: the algorithm's performance is a piecewise constant function of its parameters. Prior research has exhibited this structure in domains from integer programming to clustering. For these types of combinatorial problems, this is the first configuration algorithm beyond exhaustive search whose output provably competes with the best parameters from an infinite space.

Cellular network configuration plays a critical role in network performance. In current practice, network configuration depends heavily on field experience of engineers and often remains static for a long period of time. This practice is far from optimal. To address this limitation, online-learning-based approaches have great potentials to automate and optimize network configuration. Learning-based approaches face the challenges of learning a highly complex function for each base station and balancing the fundamental exploration-exploitation tradeoff while minimizing the exploration cost. Fortunately, in cellular networks, base stations (BSs) often have similarities even though they are not identical. To leverage such similarities, we propose kernel-based multi-BS contextual bandit algorithm based on multi-task learning. In the algorithm, we leverage the similarity among different BSs defined by conditional kernel embedding. We present theoretical analysis of the proposed algorithm in terms of regret and multi-task-learning efficiency. We evaluate the effectiveness of our algorithm based on a simulator built by real traces.

Department of Computer Science Carnegie-Mellon University Pittsburgh, Pennsylvania 15221 RI is a rule-based program that configures VAX-I 1 computer systems. Given a customer's purchase order, it determines what, if any, substitutions and additions have to be made to the order to make it consistent and complete and produces a numnber of diagrams showing the spatial and logical relationships among the 90 or so components that typically constitute a system. The program has been used on a regular basis by Digital Equipment Corporation's manufacturing organization since January of 1980. Rl has sufficient knowledge of the configuration domain and of the pecularities of the various configuration constraints that at each step in the configuration process, it simply recognizes what to do; thus it requires little search in order to configure a computer system. The approach RI takes to the configuration task and the way its knowledge is represented has been described elsewhere [McDermott 80a, MC Dermott 80b].

The development of problem solvers for configuration tasks is one of the most successful and mature application areas of artificial intelligence. The provision of tailored products, services, and systems requires efficient engineering and design processes where configurators play a crucial role. Because one of the core competencies of Siemens is to provide such highly engineered and customized systems, ranging from solutions for medium-sized and small businesses up to huge industrial plants, the efficient implementation and maintenance of configurators are important goals for the success of many departments. For more than 25 years the application of constraint-based methods has proven to be a key technology in order to realize configurators at Siemens. This article summarizes the main aspects and insights we have gained looking back over this period. In particular, we highlight the main technology factors regarding knowledge representation, reasoning, and integration which were important for our achievement. Finally we describe selected key application areas where the business success vitally depends on the high productivity of configuration processes.

In their nature configuration problems are combinatorial (optimization) problems. In order to find a configuration a solver has to instantiate a number of components of a some type and each of these components can be used in a relation defined for a type. Therefore, many solutions of a configuration problem have symmetric ones which can be obtained by replacing some component of a solution by another one of the same type. These symmetric solutions decrease performance of optimization algorithms because of two reasons: a) they satisfy all requirements and cannot be pruned out from the search space; and b) existence of symmetric optimal solutions does not allow to prove the optimum in a feasible time.