Testing cyber-physical systems involves the execution of test cases on target-machines equipped with the latest release of a software control system. When testing industrial robots, it is common that the target machines need to share some common resources, e.g., costly hardware devices, and so there is a need to schedule test case execution on the target machines, accounting for these shared resources. With a large number of such tests executed on a regular basis, this scheduling becomes difficult to manage manually. In fact, with manual test execution planning and scheduling, some robots may remain unoccupied for long periods of time and some test cases may not be executed.
RCPSP has been addressed by both exact methods @cite_32 @cite_15 @cite_4 @cite_27 , as well as heuristic methods @cite_29 @cite_21 . Due to the vast amount of literature, we will focus on CP OR-methods most closely related to the work of this paper. The clear trend in both CP and OR is to solve such problems with hybrid approaches, like, for instance, the work by @cite_34 or @cite_6 . Furthermore, , a subfamily of RCPSP addressing unary resources (in our terms global resources), have been effectively solved, e.g. by lazy clause generation @cite_24 .
@cite_4 @cite_29 @cite_21 @cite_32 @cite_6 @cite_24 @cite_27 @cite_15 @cite_34
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We present a generic exact method for minimizing the project duration of the resource-constrained project scheduling problem with generalized precedence relations (Rcpsp max). This is a very general scheduling model with applications areas such as project management and production planning. Our method uses lazy clause generation, i.e., a hybrid of finite domain and Boolean satisfiability solving, in order to apply no-good learning and conflict-driven search to the solution generation. Our experiments show the benefit of lazy clause generation for finding an optimal solution and proving its optimality in comparison to other state-of-the-art exact and non-exact methods. In comparison to other methods, our method is able to find better solutions faster on the Rcpsp max benchmarks. Indeed, our method closes 573 open problem instances and generates better solutions in most of the remaining instances. Surprisingly, although ours is an exact method, it outperforms the published non-exact methods on these benchmarks in terms of the quality of solutions. Resource-constrained project scheduling with the objective of minimizing project duration (RCPSP) is one of the most studied scheduling problems. In this paper we consider the RCPSP with general temporal constraints and calendar constraints. Calendar constraints make some resources unavailable on certain days in the scheduling period and force activity execution to be delayed while resources are unavailable. They arise in practice from, e.g., unavailabilities of staff during public holidays and weekends. The resulting problems are challenging optimization problems. We develop not only four different constraint programming (CP) models to tackle the problem, but also a specialized propagator for the cumulative resource constraints taking the calendar constraints into account. This propagator includes the ability to explain its inferences so it can be used in a lazy clause generation solver. We compare these models, and different search strategies on a challenging set of benchmarks using a lazy clause generation solver. We close 83 of the open problems of the benchmark set, and show that CP solutions are highly competitive with existing Mip models of the problem. This paper considers heuristics for the well-known resource-constrained project scheduling problem (RCPSP). It provides an update of our survey which was published in 2000. We summarize and categorize a large number of heuristics that have recently been proposed in the literature. Most of these heuristics are then evaluated in a computational study and compared on the basis of our standardized experimental design. Based on the computational results we discuss features of good heuristics. The paper closes with some remarks on our test design and a summary of the recent developments in research on heuristics for the RCPSP. The Resource-constrained Project Scheduling Problem (Rcpsp), in which a schedule must obey the resource constraints and the precedence constraints between pairs of activities, is one of the most studied scheduling problems. An important variation of the problem (RcpspDc) is to find a schedule which maximises the net present value (discounted cash flow), when every activity has a given cash flow associated with it. Given the success of lazy clause generation (Lcg) approaches to solve Rcpsp with and without generalised precedence relations it seems worthwhile investigating Lcg's use on Rcpspdc. To do so, we must construct propagators for the net-present-value constraint that explain their propagation to the Lcg solver. In this paper we construct three different propagators for net-present-value constraints, and show how they can be used to rapidly solve RcpspDc.