Linear and Integer Programming-Based Heuristics for Cost-Optimal Numeric Planning

Self Cite

We consider optimal numeric planning with numeric conditions consisting of linear expressions of numeric state variables and actions that increase or decrease numeric state variables by constant quantities. We build on previous research to introduce a new variant of the numeric hmax heuristic based on the delete-relaxed version of such planning tasks. Although our hmax heuristic is inadmissible, it yields a numeric version of the classical LM-cut heuristic which is admissible. Further, we prove that our LM-cut heuristic neither dominates nor is dominated by the existing numeric heuristic hmax(hbd). We show that admissibility also holds when integrating the numeric cuts into the operator-counting (OC) heuristic producing an admissible numeric version of the OC heuristic. Through experiments, we demonstrate that both these heuristics compete favorably with the state-of-the-art heuristics: in particular, while sometimes expanding more nodes than other heuristics, numeric OC solves 19 more problem instances than the next closest heuristic.

Section: Operator Countingmentioning

confidence: 99%

Section: Experimental Evaluationmentioning

confidence: 99%

Section: Comparison In the Oc Frameworkmentioning

confidence: 99%

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LM-cut and Operator Counting Heuristics for Optimal Numeric Planning with Simple Conditions

Kuroiwa

Shleyfman

Piacentini

et al. 2021

Self Cite

“…The OR and CP communities have each investigated solving optimization problems closely related to planning. Techniques developed in these fields are also utilized in existing planners as off-the-shelf solvers (Do and Kambhampati 2000;van den Briel and Kambhampati 2005;Piacentini et al 2018a), routines to solve sub-problems in decompositions (Benton, Coles, and Coles 2012), models to calculate heuristic values (Pommerening et al 2015;Piacentini et al 2018b), or as inference techniques customized for planning (Vidal and Geffner 2006). Motivated by CP's strong performance when applied to scheduling problems, we model QCC with qubits represented as capacitated resources and gate actions as tasks to be scheduled.…”

Section: Constraint Programming For Quantum Circuit Compilationmentioning

confidence: 99%

Comparing and Integrating Constraint Programming and Temporal Planning for Quantum Circuit Compilation

Booth

Beck

et al. 2018

Recently, the makespan-minimization problem of compiling a general class of quantum algorithms into near-term quantum processors has been introduced to the AI community. The research demonstrated that temporal planning is a strong approach for a class of quantum circuit compilation (QCC) problems. In this paper, we explore the use of constraint programming (CP) as an alternative and complementary approach to temporal planning. We extend previous work by introducing two new problem variations that incorporate important characteristics identified by the quantum computing community. We apply temporal planning and CP to the baseline and extended QCC problems as both stand-alone and hybrid approaches. Our hybrid methods use solutions found by temporal planning to warm start CP, leveraging the ability of the former to find satisficing solutions to problems with a high degree of task optionality, an area that CP typically struggles with. The CP model, benefiting from inferred bounds on planning horizon length and task counts provided by the warm start, is then used to find higher quality solutions. Our empirical evaluation indicates that while stand-alone CP is only competitive for the smallest problems, CP in our hybridization with temporal planning out-performs stand-alone temporal planning in the majority of problem classes.

“…The progress of methods for satisficing planning gave rise to the question 'can one plan optimally in presence of numeric variables in practice?'. The answer to this question was positive: recently, multiple admissible heuristics were proposed for numeric planning (Scala et al 2020(Scala et al , 2017Piacentini et al 2018b;Kuroiwa et al 2021). These heuristics, however, are limited to tasks with simple effects, i.e., each action increases or decreases the value of a numeric variable by a constant.…”

Section: Introductionmentioning

confidence: 99%

LM-Cut Heuristics for Optimal Linear Numeric Planning

Kuroiwa

Shleyfman

Beck

2022

Self Cite

While numeric variables play an important, sometimes central, role in many planning problems arising from real world scenarios, most of the currently available heuristic search planners either do not support such variables or impose heavy restrictions on them. In particular, most admissible heuristics are restricted to domains where actions can only change numeric variables by predetermined constants. In this work, we consider the setting of optimal numeric planning with linear effects, where actions can have numeric effects that assign the result of the evaluation of a linear formula. We extend a recent formulation of Numeric LM-cut for simple effects by adding conditional effects and second-order simple effects, allowing the heuristic to produce admissible estimates for tasks with linear numeric effects. Empirical comparison shows that the proposed LM-cut heuristics favorably compete with the currently available state-of-the-art heuristics and achieve significant improvement in coverage in the domains with second-order simple effects.