In this paper we deal with a complex real world scheduling problem closely related to the wellknown Resource-Constrained Project Scheduling Problem (RCPSP). The problem concerns industrial test laboratories in which a large number of tests has to be performed by qualified personnel using specialised equipment, while respecting deadlines and other constraints. We present different constraint programming models and search strategies for this problem. Furthermore, we propose a Very Large Neighborhood Search approach based on our CP methods. Our models are evaluated using CP solvers and a MIP solver both on real-world test laboratory data and on a set of generated instances of different sizes based on the real-world data. Further, we compare the exact approaches with VLNS and a Simulated Annealing heuristic. We could find feasible solutions for all instances and several optimal solutions and we show that using VLNS we can improve upon the results of the other approaches. Literature OverviewThe Resource-Constrained Project Scheduling Problem (RCPSP) has been investigated by numerous researchers over the last decades. For a comprehensive overview over publications dealing with this problem and its many variants, we refer to surveys e.g. by Brucker et al. [10], Hartmann and Briskorn [11], or Mika et al. [12].Of particular interest for the problem treated in this work are various extensions to the classical RCPSP.Multi-Mode RCPSP (MRCPSP) formulations allow for activities that can be scheduled in one of several modes. This variant has been extensively studied since 1977 [13], we refer to the surveys by Wȩglarz et al. [14] and Hartmann and Briskorn [11]. A good example of a CP-Model for the MRCPSP was given by Szeredi and Schutt [6].Many formulations, including TLSP, make use of release dates, due dates, deadlines, or combinations of those. An example of this can be found in [15]. Further relevant extensions deal with multi-project formulations, including alternative objective functions (e.g. [16]). Usually, the objective in (variants of) RCPSP is the minimization of the total makespan [11]. However, also other objective values have been considered. Of particular relevance to TLSP are objectives based on total completion time and multi-objective formulations (both appear in e.g. [17]). Salewski

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While Answer-Set Programming (ASP) is a prominent approach to declarative problem solving, optimisation problems can still be a challenge for it. Large-Neighbourhood Search (LNS) is a metaheuristic for optimisation where parts of a solution are alternately destroyed and reconstructed that has high but untapped potential for ASP solving. We present a framework for LNS optimisation in answer-set solving, in which neighbourhoods can be specified either declaratively as part of the ASP encoding, or automatically generated by code. To effectively explore different neighbourhoods, we focus on multi-shot solving as it allows to avoid program regrounding. We illustrate the framework on different optimisation problems, some of which are notoriously difficult, including shift planning and a parallel machine scheduling problem from semi-conductor production which demonstrate the effectiveness of the LNS approach.

Paraconsistent logics constitute an important class of formalisms dealing with non-trivial reasoning from inconsistent premisses. In this paper, we introduce uniform axiomatisations for a family of nonmonotonic paraconsistent logics based on minimal inconsistency in terms of sequent-type proof systems. The latter are prominent and widely-used forms of calculi well-suited for analysing proof search. In particular, we provide sequent-type calculi for Priest's three-valued minimally inconsistent logic of paradox, and for four-valued paraconsistent inference relations due to Arieli and Avron. Our calculi follow the sequent method first introduced in the context of nonmonotonic reasoning by Bonatti and Olivetti, whose distinguishing feature is the use of a so-called rejection calculus for axiomatising invalid formulas. In fact, we present a general method to obtain sequent systems for any many-valued logic based on minimal inconsistency, yielding the calculi for the logics of Priest and of Arieli and Avron as special instances.

Automated scheduling solutions are tremendously important for the efficient operation of industrial laboratories. The Test Laboratory Scheduling Problem (TLSP) is an extension of the well-known Resource Constrained Project Scheduling Problem (RCPSP) and captures the specific requirements of such laboratories. In addition to several new scheduling constraints, it features a grouping phase, where the jobs to be scheduled are assembled from smaller units. In this work, we introduce an innovative scheduling system that allows the efficient and flexible generation of schedules for TLSP. It features a new Constraint Programming model that covers both the grouping and the scheduling aspect, as well as a hybrid Very Large Neighborhood Search that internally uses the CP model. Our experimental results on generated and real-world benchmark instances show that good results can be obtained even compared to settings which have a good grouping already provided, including several new best known solutions for these instances. Our algorithms for TLSP have been successfully implemented in a real-world industrial test laboratory. We provide a detailed description of the deployed system as well as additional useful soft constraints supported by the solvers and general lessons learned. This includes a discussion of the choice of soft constraint weights, with an analysis on the impact and relation of different objectives to each other. Our experiments show that some soft constraints complement each other well, while others require explicit trade-offs via their relative weights.