Constraint-Based Reasoning


Phase Transition Behavior of Cardinality and XOR Constraints

arXiv.org Artificial Intelligence

The runtime performance of modern SAT solvers is deeply connected to the phase transition behavior of CNF formulas. While CNF solving has witnessed significant runtime improvement over the past two decades, the same does not hold for several other classes such as the conjunction of cardinality and XOR constraints, denoted as CARD-XOR formulas. The problem of determining the satisfiability of CARD-XOR formulas is a fundamental problem with a wide variety of applications ranging from discrete integration in the field of artificial intelligence to maximum likelihood decoding in coding theory. The runtime behavior of random CARD-XOR formulas is unexplored in prior work. In this paper, we present the first rigorous empirical study to characterize the runtime behavior of 1-CARD-XOR formulas. We show empirical evidence of a surprising phase-transition that follows a non-linear tradeoff between CARD and XOR constraints.


How to improve supply chains with machine learning: 10 proven ways

#artificialintelligence

Bottom line: Enterprises are attaining double-digit improvements in forecast error rates, demand planning productivity, cost reductions and on-time shipments using machine learning today, revolutionising supply chain management in the process. Machine learning algorithms and the models they're based on excel at finding anomalies, patterns and predictive insights in large data sets. Many supply chain challenges are time, cost and resource constraint-based, making machine learning an ideal technology to solve them. From Amazon's Kiva robotics relying on machine learning to improve accuracy, speed and scale to DHL relying on AI and machine learning to power their Predictive Network Management system that analyses 58 different parameters of internal data to identify the top factors influencing shipment delays, machine learning is defining the next generation of supply chain management. Gartner predicts that by 2020, 95% of Supply Chain Planning (SCP) vendors will be relying on supervised and unsupervised machine learning in their solutions.


A new CP-approach for a parallel machine scheduling problem with time constraints on machine qualifications

arXiv.org Artificial Intelligence

This paper considers the scheduling of job families on parallel machines with time constraints on machine qualifications. In this problem, each job belongs to a family and a family can only be executed on a subset of qualified machines. In addition, machines can lose their qualifications during the schedule. Indeed, if no job of a family is scheduled on a machine during a given amount of time, the machine loses its qualification for this family. The goal is to minimize the sum of job completion times, i.e. the flow time, while maximizing the number of qualifications at the end of the schedule. The paper presents a new Constraint Programming (CP) model taking more advantages of the CP feature to model machine disqualifications. This model is compared with two existing models: an Integer Linear Programming (ILP) model and a Constraint Programming model. The experiments show that the new CP model outperforms the other model when the priority is given to the number of disqualifications objective. Furthermore, it is competitive with the other model when the flow time objective is prioritized.


Comparing Greedy Constructive Heuristic Subtour Elimination Methods for the Traveling Salesman Problem

arXiv.org Artificial Intelligence

This paper further defines the class of fragment constructive heuristics used to compute feasible solutions for the Traveling Salesman Problem into arc-greedy and node-greedy subclasses. Since these subclasses of heuristics can create subtours, two known methodologies for subtour elimination on symmetric instances are reviewed and are expanded to cover asymmetric problem instances. This paper introduces a third novel methodology, the Greedy Tracker, and compares it to both known methodologies. Computational results are generated across multiple symmetric and asymmetric instances. The results demonstrate the Greedy Tracker is the fastest method for preventing subtours for instances below 400 nodes. A distinction between fragment constructive heuristics and the subtour elimination methodology used to ensure the feasibility of resulting solutions enables the introduction of a new node-greedy fragment heuristic called Ordered Greedy.


Reflections on "Incremental Cardinality Constraints for MaxSAT"

arXiv.org Artificial Intelligence

To celebrate the first 25 years of the International Conference on Principles and Practice of Constraint Programming (CP) the editors invited the authors of the most cited paper of each year to write a commentary on their paper. This report describes our reflections on the CP 2014 paper "Incremental Cardinality Constraints for MaxSAT" and its impact on the Maximum Satisfiability community and beyond.


Building a constraint programming solver in Julia

#artificialintelligence

This is an ongoing series about: How to build a constraint solver? If you haven't read this post: Perfect as it is part 1;) More than 2 years ago I wrote a Sudoku solver in Python. I really enjoyed it and therefore I've spend some time to do the same in Julia just faster;) Then I wanted to build a whole constraint-programming solver in Julia. Well I actually still want to do it. It will be hard but fun.


A Commentary on "Breaking Row and Column Symmetries in Matrix Models"

arXiv.org Artificial Intelligence

The CP 2002 paper entitled "Breaking Row and Column Symmetries in Matrix Models" by Flener et al. [6] describes some of the first work for identifying and analyzing row and column symmetry in mat rix models and for efficiently and effectively dealing with such symmetry u sing static symmetry-breaking ordering constraints. This commentary provides a retrospective on that work and highlights some of the subsequent work on the topic.


Towards Improving Solution Dominance with Incomparability Conditions: A case-study using Generator Itemset Mining

arXiv.org Artificial Intelligence

Finding interesting patterns is a challenging task in data mining. Constraint based mining is a well-known approach to this, and one for which constraint programming has been shown to be a well-suited and generic framework. Dominance programming has been proposed as an extension that can capture an even wider class of constraint-based mining problems, by allowing to compare relations between patterns. In this paper, in addition to specifying a dominance relation, we introduce the ability to specify an incomparability condition. Using these two concepts we devise a generic framework that can do a batch-wise search that avoids checking incomparable solutions. We extend the ESSENCE language and underlying modelling pipeline to support this. We use generator itemset mining problem as a test case and give a declarative specification for that. We also present preliminary experimental results on this specific problem class with a CP solver backend to show that using the incomparability condition during search can improve the efficiency of dominance programming and reduces the need for post-processing to filter dominated solutions.


CSPLib: Twenty Years On

arXiv.org Artificial Intelligence

In 1999, we introduced CSPLib, a benchmark library for the constraints community. Our CP-1999 poster paper about CSPLib discussed the advantages and disadvantages of building such a library. Unlike some other domains such as theorem proving, or machine learning, representation was then and remains today a major issue in the success or failure to solve problems. Benchmarks in CSPLib are therefore specified in natural language as this allows users to find good representations for themselves. The community responded positively and CSPLib has become a valuable resource but, as we discuss here, we cannot rest.


SAT vs CSP: a commentary

arXiv.org Artificial Intelligence

In 2000, I published a relatively comprehensive study of mappings between propositional satisfiability (SAT) and constraint satisfaction problems (CSPs) [Wal00]. I analysed four different mappings of SAT problems into CSPs, and two of CSPs into SAT problems. For each mapping, I compared the impact of achieving arc-consistency on the CSP with unit propagation on the corresponding SAT problems, and lifted these results to CSP algorithms that maintain (some level of ) arc-consistency during search like FC and MAC, and to the Davis- Putnam procedure (which performs unit propagation at each search node). These results helped provide some insight into the relationship between propositional satisfiability and constraint satisfaction that set the scene for an important and valuable body of work that followed. I discuss here what prompted the paper, and what followed.