Mixed integer-linear formulations of cumulative scheduling constraints - A comparative study

This paper introduces two MILP models for the cumulative scheduling constraint and associated pre-processing filters. We compare standard solver performance for these models on three sets of problems and for two of them, where tasks have unitary resource consumption, we also compare them with two models based on a geometric placement constraint. In the experiments, the solver performance of one of the cumulative models, is clearly the best and is also shown to scale very well for a large scale industrial transportation scheduling problem

A New Multi-Resource cumulatives Constraint with Negative Heights

This paper presents a new cumulatives constraint which generalizes the original cumulative constraint in different ways. The two most important aspects consist in permitting multiple cumulative resources as well as negative heights for the resource consumption of the tasks. This allows modeling in an easy way new scheduling and planning problems. The introduction of negative heights has forced us to come up with new propagation algorithms and to revisit existing ones. The first propagation algorithm is derived from an idea called sweep which is extensively used in computational geometry; the second algorithm is based on a combination of sweep and constructive disjunction, while the last is a generalization of task intervals to this new context. A real-life timetabling problem originally motivated this constraint which was implemented within the SICStus finite domain solver and evaluated against different problem patterns

An Analysis of Arithmetic Constraints on Integer Intervals

Arithmetic constraints on integer intervals are supported in many constraint programming systems. We study here a number of approaches to implement constraint propagation for these constraints. To describe them we introduce integer interval arithmetic. Each approach is explained using appropriate proof rules that reduce the variable domains. We compare these approaches using a set of benchmarks. For the most promising approach we provide results that characterize the effect of constraint propagation. This is a full version of our earlier paper, cs.PL/0403016.Comment: 44 pages, to appear in 'Constraints' journa

Evaluation of Kermeta for Solving Graph-based Problems

Kermeta is a meta-language for specifying the structure and behavior of graphs of interconnected objects called models. In this paper,\ud we show that Kermeta is relatively suitable for solving three graph-based\ud problems. First, Kermeta allows the specification of generic model\ud transformations such as refactorings that we apply to different metamodels\ud including Ecore, Java, and Uml. Second, we demonstrate the extensibility\ud of Kermeta to the formal language Alloy using an inter-language model\ud transformation. Kermeta uses Alloy to generate recommendations for\ud completing partially specified models. Third, we show that the Kermeta\ud compiler achieves better execution time and memory performance compared\ud to similar graph-based approaches using a common case study. The\ud three solutions proposed for those graph-based problems and their\ud evaluation with Kermeta according to the criteria of genericity,\ud extensibility, and performance are the main contribution of the paper.\ud Another contribution is the comparison of these solutions with those\ud proposed by other graph-based tools

On Idle Energy Consumption Minimization in Production: Industrial Example and Mathematical Model

This paper, inspired by a real production process of steel hardening, investigates a scheduling problem to minimize the idle energy consumption of machines. The energy minimization is achieved by switching a machine to some power-saving mode when it is idle. For the steel hardening process, the mode of the machine (i.e., furnace) can be associated with its inner temperature. Contrary to the recent methods, which consider only a small number of machine modes, the temperature in the furnace can be changed continuously, and so an infinite number of the power-saving modes must be considered to achieve the highest possible savings. To model the machine modes efficiently, we use the concept of the energy function, which was originally introduced in the domain of embedded systems but has yet to take roots in the domain of production research. The energy function is illustrated with several application examples from the literature. Afterward, it is integrated into a mathematical model of a scheduling problem with parallel identical machines and jobs characterized by release times, deadlines, and processing times. Numerical experiments show that the proposed model outperforms a reference model adapted from the literature.Comment: Accepted to 9th International Conference on Operations Research and Enterprise Systems (ICORES 2020

Logic Programming Approaches for Representing and Solving Constraint Satisfaction Problems: A Comparison

Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the variables of the constraint satisfaction problem. On the other hand there are systems based on stable model semantics, abductive systems, and first order logic model generators which compute solutions as models of some theory. This paper compares these different approaches from the point of view of knowledge representation (how declarative are the programs) and from the point of view of performance (how good are they at solving typical problems).Comment: 15 pages, 3 eps-figure

Numerical Integration and Dynamic Discretization in Heuristic Search Planning over Hybrid Domains

In this paper we look into the problem of planning over hybrid domains, where change can be both discrete and instantaneous, or continuous over time. In addition, it is required that each state on the trajectory induced by the execution of plans complies with a given set of global constraints. We approach the computation of plans for such domains as the problem of searching over a deterministic state model. In this model, some of the successor states are obtained by solving numerically the so-called initial value problem over a set of ordinary differential equations (ODE) given by the current plan prefix. These equations hold over time intervals whose duration is determined dynamically, according to whether zero crossing events take place for a set of invariant conditions. The resulting planner, FS+, incorporates these features together with effective heuristic guidance. FS+ does not impose any of the syntactic restrictions on process effects often found on the existing literature on Hybrid Planning. A key concept of our approach is that a clear separation is struck between planning and simulation time steps. The former is the time allowed to observe the evolution of a given dynamical system before committing to a future course of action, whilst the later is part of the model of the environment. FS+ is shown to be a robust planner over a diverse set of hybrid domains, taken from the existing literature on hybrid planning and systems.Comment: 17 page