Constraints - An International Journal最新文献

Constraint programming approaches to electric vehicle and robot routing problems 电动汽车和机器人路径问题的约束规划方法

Constraints - An International Journal Pub Date : 2023-09-01 DOI: 10.1007/s10601-023-09355-2

Kyle E. C. Booth

引用次数: 0

Complexity of minimum-size arc-inconsistency explanations 最小尺寸弧不一致解释的复杂性

Constraints - An International Journal Pub Date : 2023-09-01 DOI: 10.1007/s10601-023-09360-5

Christian Bessiere, Clément Carbonnel, Martin C. Cooper, Emmanuel Hebrard

{"title":"Complexity of minimum-size arc-inconsistency explanations","authors":"Christian Bessiere, Clément Carbonnel, Martin C. Cooper, Emmanuel Hebrard","doi":"10.1007/s10601-023-09360-5","DOIUrl":"https://doi.org/10.1007/s10601-023-09360-5","url":null,"abstract":"Explaining the outcome of programs has become one of the main concerns in AI research. In constraint programming, a user may want the system to explain why a given variable assignment is not feasible or how it came to the conclusion that the problem does not have any solution. One solution to the latter is to return to the user a sequence of simple reasoning steps that lead to inconsistency. Arc consistency is a well-known form of reasoning that can be understood by a human. We consider explanations as sequences of propagation steps of a constraint on a variable (i.e. the ubiquitous revise function in arc-consistency algorithms) that lead to inconsistency. We characterize several cases for which providing a shortest such explanation is easy: For instance when constraints are binary and variables have maximum degree two. However, these polynomial cases are tight. For instance, providing a shortest explanation is NP-hard when constraints are binary and the maximum degree is three, even if the number of variables is bounded. It remains NP-hard on trees, despite the fact that arc consistency is a decision procedure on trees. The problem is not even FPT-approximable unless the FPT $$ne $$ W[2] hypothesis is false.","PeriodicalId":127439,"journal":{"name":"Constraints - An International Journal","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135638325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Learn and route: learning implicit preferences for vehicle routing 学习和路线:学习车辆路线的隐性偏好

Constraints - An International Journal Pub Date : 2023-09-01 DOI: 10.1007/s10601-023-09363-2

Rocsildes Canoy, Víctor Bucarey, Jayanta Mandi, Tias Guns

{"title":"Learn and route: learning implicit preferences for vehicle routing","authors":"Rocsildes Canoy, Víctor Bucarey, Jayanta Mandi, Tias Guns","doi":"10.1007/s10601-023-09363-2","DOIUrl":"https://doi.org/10.1007/s10601-023-09363-2","url":null,"abstract":"Abstract We investigate a learning decision support system for vehicle routing, where the routing engine learns implicit preferences that human planners have when manually creating route plans (or routings ). The goal is to use these learned subjective preferences on top of the distance-based objective criterion in vehicle routing systems. This is an alternative to the practice of distinctively formulating a custom vehicle routing problem (VRP) for every company with its own routing requirements. Instead, we assume the presence of past vehicle routing solutions over similar sets of customers, and learn to make similar choices. The learning approach is based on the concept of learning a Markov model, which corresponds to a probabilistic transition matrix, rather than a deterministic distance matrix. This nevertheless allows us to use existing arc routing VRP software in creating the actual routings, and to optimize over both distances and preferences at the same time. For the learning, we explore different schemes to construct the probabilistic transition matrix that can co-evolve with changing preferences over time. Our results on randomly generated instances and on a use-case with a small transportation company show that our method is able to generate results that are close to the manually created solutions, without needing to characterize all constraints and sub-objectives explicitly. Even in the case of changes in the customer sets, our approach is able to find solutions that are closer to the actual routings than when using only distances, and hence, solutions that require fewer manual changes when transformed into practical routings.","PeriodicalId":127439,"journal":{"name":"Constraints - An International Journal","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135688398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Floating-point numbers round-off error analysis by constraint programming 约束编程的浮点数舍入误差分析

Constraints - An International Journal Pub Date : 2023-09-01 DOI: 10.1007/s10601-023-09354-3

Rémy Garcia

{"title":"Floating-point numbers round-off error analysis by constraint programming","authors":"Rémy Garcia","doi":"10.1007/s10601-023-09354-3","DOIUrl":"https://doi.org/10.1007/s10601-023-09354-3","url":null,"abstract":"Floating-point numbers are used in many applications to perform computations, often without the user’s knowledge. The mathematical models of these applications use real numbers that are often not representable on a computer. Indeed, a finite binary representation is not sufficient to represent the continuous and infinite set of real numbers. The problem is that computing with floating-point numbers often introduces a rounding error compared to its equivalent over real numbers. Knowing the order of magnitude of this error is essential in order to correctly understand the behaviour of a program. Many error analysis tools calculate an over-approximation of the errors. These over-approximations are often too coarse to effectively assess the impact of the error on the behaviour of the program. Other tools calculate an under-approximation of the maximum error, i.e., the largest possible error in absolute value. These under-approximations are either incorrect or unreachable. In this thesis, we propose a constraint system capable of capturing and reasoning about the error produced by a program that performs computations with floating-point numbers. We also propose an algorithm to search for the maximum error. For this purpose, our algorithm computes both a rigorous over-approximation and a rigorous under-approximation of the maximum error. An over-approximation is obtained from the constraint system for the errors, while a reachable under-approximation is produced using a generate-and-test procedure and a local search. Our algorithm is the first to combine both an over-approximation and an under-approximation of the error. Our methods are implemented in a solver, called FErA. Performance on a set of common problems is competitive: the rigorous enclosure produced is accurate and compares well with other state-of-the-art tools.","PeriodicalId":127439,"journal":{"name":"Constraints - An International Journal","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135347779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimization methods based on decision diagrams for constraint programming, AI planning, and mathematical programming 基于约束规划、人工智能规划和数学规划的决策图优化方法

Constraints - An International Journal Pub Date : 2023-09-01 DOI: 10.1007/s10601-023-09353-4

Margarita Paz Castro

引用次数: 0

CSP beyond tractable constraint languages 超越可处理约束语言的CSP

Constraints - An International Journal Pub Date : 2023-09-01 DOI: 10.1007/s10601-023-09362-3

Jan Dreier, Sebastian Ordyniak, Stefan Szeider

{"title":"CSP beyond tractable constraint languages","authors":"Jan Dreier, Sebastian Ordyniak, Stefan Szeider","doi":"10.1007/s10601-023-09362-3","DOIUrl":"https://doi.org/10.1007/s10601-023-09362-3","url":null,"abstract":"Abstract The constraint satisfaction problem (CSP) is among the most studied computational problems. While NP-hard, many tractable subproblems have been identified (Bulatov 2017, Zhuk 2017) Backdoors, introduced by Williams, Gomes, and Selman (2003), gradually extend such a tractable class to all CSP instances of bounded distance to the class. Backdoor size provides a natural but rather crude distance measure between a CSP instance and a tractable class. Backdoor depth, introduced by Mählmann, Siebertz, and Vigny (2021) for SAT, is a more refined distance measure, which admits the parallel utilization of different backdoor variables. Bounded backdoor size implies bounded backdoor depth, but there are instances of constant backdoor depth and arbitrarily large backdoor size. Dreier, Ordyniak, and Szeider (2022) provided fixed-parameter algorithms for finding backdoors of small depth into the classes of Horn and Krom formulas. In this paper, we consider backdoor depth for CSP. We consider backdoors w.r.t. tractable subproblems $$C_Gamma $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>Γ</mml:mi> </mml:msub> </mml:math> of the CSP defined by a constraint language $$varvec{Gamma }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>Γ</mml:mi> </mml:mrow> </mml:math> , i.e., where all the constraints use relations from the language $$varvec{Gamma }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>Γ</mml:mi> </mml:mrow> </mml:math> . Building upon Dreier et al.’s game-theoretic approach and their notion of separator obstructions, we show that for any finite, tractable, semi-conservative constraint language $$varvec{Gamma }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>Γ</mml:mi> </mml:mrow> </mml:math> , the CSP is fixed-parameter tractable parameterized by the backdoor depth into $$C_{varvec{Gamma }}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>Γ</mml:mi> </mml:mrow> </mml:msub> </mml:math> plus the domain size. With backdoors of low depth, we reach classes of instances that require backdoors of arbitrary large size. Hence, our results strictly generalize several known results for CSP that are based on backdoor size.","PeriodicalId":127439,"journal":{"name":"Constraints - An International Journal","volume":"142 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135688263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Learning to select SAT encodings for pseudo-Boolean and linear integer constraints 学习为伪布尔和线性整数约束选择SAT编码

Constraints - An International Journal Pub Date : 2023-09-01 DOI: 10.1007/s10601-023-09364-1

Felix Ulrich-Oltean, Peter Nightingale, James Alfred Walker

引用次数: 0

Reasoning and inference for (Maximum) satisfiability: new insights (最大)满意度的推理和推断:新的见解

Constraints - An International Journal Pub Date : 2023-09-01 DOI: 10.1007/s10601-023-09365-0

Mohamed Sami Cherif

引用次数: 0

Spacetime programming: a synchronous language for constraint search 时空编程:约束搜索的同步语言

Constraints - An International Journal Pub Date : 2023-09-01 DOI: 10.1007/s10601-023-09356-1

Pierre Talbot

引用次数: 2

Scheduling through logic-based tools 通过基于逻辑的工具进行调度

Constraints - An International Journal Pub Date : 2023-09-01 DOI: 10.1007/s10601-023-09357-0

Jordi Coll Caballero

引用次数: 0