Compiling graphical models has recently been under intense investigation, especially for probabilistic modeling and processing. We present here a novel data structure for compiling weighted graphical models (in particular, probabilistic models), called AND/OR Multi-Valued Decision Diagram (AOMDD). This is a generalization of our previous work on constraint networks, to weighted models. The AOMDD is based on the frameworks of AND/OR search spaces for graphical models, and Ordered Binary Decision Diagrams (OBDD). The AOMDD is a canonical representation of a graphical model, and its size and compilation time are bounded exponentially by the treewidth of the graph, rather than pathwidth as is known for OBDDs. We discuss a Variable Elimination schedule for compilation, and present the general APPLY algorithm that combines two weighted AOMDDs, and also present a search based method for compilation method. The preliminary experimental evaluation is quite encouraging, showing the potential of the AOMDD data structure.

Preferences play an important role in our everyday lives. CP-networks, or CP-nets in short, are graphical models for representing conditional qualitative preferences under ceteris paribus ("all else being equal") assumptions. Despite their intuitive nature and rich representation, dominance testing with CP-nets is computationally complex, even when the CP-nets are restricted to binary-valued preferences. Tractable algorithms exist for binary CP-nets, but these algorithms are incomplete for multi-valued CPnets. In this paper, we identify a class of multivalued CP-nets, which we call more-or-less CPnets, that have the same computational complexity as binary CP-nets. More-or-less CP-nets exploit the monotonicity of the attribute values and use intervals to aggregate values that induce similar preferences. We then present a search control rule for dominance testing that effectively prunes the search space while preserving completeness.

Stability analysis consists of identifying conditions under which the number of jobs in a system is guaranteed to remain bounded over time. To date, such long-run performance guarantees have not been available for periodic approaches to dynamic scheduling problems. However, stability has been extensively studied in queueing theory. In this paper, we introduce stability to the dynamic scheduling literature and demonstrate that stability guarantees can be obtained for methods that build the schedule for a dynamic problem by periodically solving static deterministic sub-problems. Specifically, we analyze the stability of two dynamic environments: a two-machine flow shop, which has received significant attention in scheduling research, and a polling system with a flow-shop server, an extension of systems typically considered in queueing. We demonstrate that, among stable policies, methods based on periodic optimization of static schedules may achieve better mean flow times than traditional queueing approaches.

We consider the problem of computing shortest paths subject to an additional resource constraint such as a hard limit on the (positive) height difference of the path. This is typically of interest in the context of bicycle route planning, or when energy consumption is to be limited. So far, the exact computation of such constrained shortest paths was not feasible on large networks; we show that state-of-the-art speed-up techniques for the shortest path problem, like contraction hierarchies, can be instrumented to solve this problem efficiently in practice despite the NP-hardness in general.

This paper provides an analysis of the efficacy of a known iterative improvement meta-heuristic approach from the AI area in solving the Blocking Job Shop Scheduling Problem (BJSSP) class of problems. The BJSSP is known to have significant fallouts on practical domains, and differs from the classical Job Shop Scheduling Problem (JSSP) in that it assumes that there are no intermediate buffers for storing a job as it moves from one machine to another; according to the BJSSP definition, each job has to wait on a machine until it can be processed on the next machine. In our analysis, two specific variants of the iterative improvement meta-heuristic are evaluated: (1) an adaptation of an existing scheduling algorithm based on the Iterative Flattening Search and (2) an off-the-shelf optimization tool, the IBM ILOG CP Optimizer, which implements Self-Adapting Large Neighborhood Search. Both are applied to a reference benchmark problem set and comparative performance results are presented. The results confirm the effectiveness of the iterative improvement approach in solving the BJSSP; both variants perform well individually and together succeed in improving the entire set of benchmark instances.

Existing ship scheduling approaches either ignore constraints on ship draft (distance between the waterline and the keel), or model these in very simple ways, such as a constant draft limit that does not change with time. However, in most ports the draft restriction changes over time due to variation in environmental conditions. More accurate consideration of draft constraints would allow more cargo to be scheduled for transport on the same set of ships. We present constraint programming (CP) and mixed integer programming (MIP) models for the problem of scheduling ships at a port with time-varying draft constraints so as to optimise cargo throughput at the port. We also investigate the effect of several variations to the CP model, including a model containing sequence variables, and a model with ordered inputs. Our model allows us to solve realistic instances of the problem to optimality in a very short time, and produces better schedules than both scheduling with constant draft, and manual scheduling approaches used in practice at ports.

This paper describes a polynomially-solvable sub-problem of temporal planning. Polynomiality follows from two assumptions. Firstly, by supposing that each sub-goal fluent can be established by at most one action, we can quickly determine which actions are necessary in any plan. Secondly, the monotonicity of sub-goal fluents allows us to express planning as an instance of STP≠ (Simple Temporal Problem, difference constraints). Our class includes temporally-expressive problems, which we illustrate with an example of chemical process planning.

Disjunctive scheduling is the problem of scheduling activities that must not overlap in time. Constraint-based techniques, such as edge finding and not first/not-last rules, have been a key element in successfully tackling large and complex disjunctive scheduling problems in recent years. In this work we investigate new propagation methods based on limited-width Multivalued Decision Diagrams (MDDs). We present theoretical properties of the MDD encoding and describe filtering and refinement operations that strengthen the relaxation it provides. Furthermore, we provide an efficient way to integrate the MDD-based reasoning with state-of-the-art propagation techniques for scheduling. Experimental results indicate that the MDD propagation can outperform existing domain filters especially when minimizing sequence dependent setup times, in certain cases by several orders of magnitude.

Temporal planning methods usually focus on the objective of minimizing makespan. Unfortunately, this misses a large class of planning problems where it is important to consider a wider variety of temporal and non-temporal preferences, making makespan lower-order concern. In this paper we consider modeling and reasoning with plan quality metrics that are not directly correlated with plan makespan, building on the planner POPF. We begin with the preferences defined in PDDL3, and present a mixed integer programming encoding to manage the the interaction between the hard temporal constraints for plan steps, and soft temporal constraints for preferences. To widen the support of metrics that can be expressed directly in PDDL, we then discuss an extension to soft-deadlines with continuous cost functions, avoiding the need to approximate these with several PDDL3 discrete-cost preferences. We demonstrate the success of our new planner on the benchmark temporal planning problems with preferences, showing that it is the state-of-the-art for such problems. We then analyze the benefits of reasoning with continuous (versus discretized) models of domains with continuous cost functions, showing the improvement in solution quality afforded through making the continuous cost function directly available to the planner.

This paper deals with planning domains that appear in computer games, especially when modeling intelligent virtual agents. Some of these domains contain only actions with no negative effects and are thus treated as easy from the planning perspective. We propose two new techniques to solve the problems in these planning domains, a heuristic search algorithm ANA* and a constraint-based planner RelaxPlan, and we compare them with the state-of-the-art planners, that were successful in IPC, using planning domains motivated by computer games.