Constraint Programming Research Articles

Balancing the satisfaction of stakeholders in home health care coordination: a novel OptaPlanner CSP model

ABSTRACT Home Health Care Routing and Scheduling Problem (HHCRSP) has been widely investigated in operations research. In this paper, a model based on the Constraint Satisfaction Problem (CSP) is proposed, which is able to deal with daily HHCRSPs. Human factors are considered in our formulation of the problem and we seek a balance between the different stakeholders’ satisfaction criteria. The considered temporal constraints are soft and controlled by the stakeholders’ personalised tolerance and satisfaction rates. We will explain how this new Satisfaction-Oriented HHCRSP (SOH2CRSP) model is built and solved by using an open-source solver: the OptaPlanner. In order to examine the impact of human factors, a study will estimate the added value provided when satisfaction is considered in the problem formulation. The comparison is based on a use case derived from the dataset of an existing HHC organisation. The numerical results will show the benefits of our approach.

Designing microplate layouts using artificial intelligence

Microplates are indispensable in large-scale biomedical experiments but the physical location of samples and controls on the microplate can significantly affect the resulting data and quality metric values. We introduce a new method based on constraint programming for designing microplate layouts that reduces unwanted bias and limits the impact of batch effects after error correction and normalisation. We demonstrate that our method applied to dose-response experiments leads to more accurate regression curves and lower errors when estimating IC50/EC50, and for drug screening leads to increased precision, when compared to random layouts. It also reduces the risk of inflated scores from common microplate quality assessment metrics such as Z′ factor and SSMD. We make our method available via a suite of tools (PLAID) including a reference constraint model, a web application, and Python notebooks to evaluate and compare designs when planning microplate experiments.

Restoptr: an R package for ecological restoration planning

Ecological restoration is essential to curb the decline of biodiversity and ecosystems worldwide. Since the resources available for restoration are limited, restoration efforts must be cost‐effective to achieve conservation outcomes. Although decision support tools are available to aid in the design of protected areas, little progress has been made to provide such tools for restoration efforts. Here, we introduce therestoptrR package, a decision support tool designed to identify priority areas for ecological restoration. It uses constraint programming—an artificial intelligence technique—to identify optimal plans given ecological and socioeconomic constraints. Critically, it can identify strategic locations to enhance connectivity and reduce fragmentation across a broader landscape using complex landscape metrics. We illustrate its usage with a case study in New Caledonia. By applying this tool, we identified priority areas for restoration that could reverse forest fragmentation induced by mining activities in a specific area. We also found that relatively small investments could deliver large returns to restore connectivity. TherestoptrR package is a free and open‐source decision support tool available on the Comprehensive R Archive Network (https://cran.r-project.org/package=restoptr).

Constraint programming have been identifying as promising technique for efficiently solving discrete optimization problem

Constraint programming has roots in logic programming, where a model has both a declarative and a procedural interpretation. A model is declarative because its statements can be read as logical propositions that describe the problem, and it is procedural because the statements can be processed as instructions for how to find a solution. To make constraint programming material to practical problems one needs propagation algorithms that are both viable and proficient. The most incredible propagation algorithm for the alldifferent constraint, i.e. the one getting hyper-circular segment consistency, is to be sure extremely productive. The reason is that we can apply matching hypothesis from operations research. Likewise for the symmetric alldifferent constraint and the weighted alldifferent constraint powerful and effective propagation algorithms exist, again dependent on techniques from operations research. From this paper we show that some time alldifferent constraint is more easy way to solve the MIP. For this we will choose an auction strategy by which a company get more revenue.Despite this considerable progress, there remains great potential for further integration, with the concomitantimprovement in both modeling and solution method.

MAGNNETO: A Graph Neural Network-Based Multi-Agent System for Traffic Engineering

Current trends in networking propose the use of Machine Learning (ML) for a wide variety of network optimization tasks. As such, many efforts have been made to produce ML-based solutions for Traffic Engineering (TE), which is a fundamental problem in ISP networks. Nowadays, state-of-the-art TE optimizers rely on traditional optimization techniques, such as Local search, Constraint Programming, or Linear programming. In this paper, we present MAGNNETO, a distributed ML-based framework that leverages Multi-Agent Reinforcement Learning and Graph Neural Networks for distributed TE optimization. MAGNNETO deploys a set of agents across the network that learn and communicate in a distributed fashion via message exchanges between neighboring agents. Particularly, we apply this framework to optimize link weights in OSPF, with the goal of minimizing network congestion. In our evaluation, we compare MAGNNETO against several state-of-the-art TE optimizers in more than 75 topologies (up to 153 nodes and 354 links), including realistic traffic loads. Our experimental results show that, thanks to its distributed nature, MAGNNETO achieves comparable performance to state-of-the-art TE optimizers with significantly lower execution times. Moreover, our ML-based solution demonstrates a strong generalization capability to successfully operate in new networks unseen during training.

Integrated mixed-model assembly line balancing and parts feeding with supermarkets

In the automotive industry, decentralized in-house logistic areas called supermarkets are used for parts feeding to mixed-model assembly lines. In the literature, generally, the number of supermarkets and their locations are determined according to a previously balanced assembly line. As a result, supermarket locations have to be completely dependent on the line balance. There may be more than one solution that gives the same performance criterion value in the line balancing. Among these alternative solutions, it is more reasonable to use a solution that provides lower logistics costs than others. For this purpose, in this study, the mixed-model assembly line balancing problem and the supermarket location problem are considered simultaneously. Accordingly, in order to minimize the total costs of the assembly line and supermarkets, a mixed-integer mathematical model is developed, and the developed model is solved by using constraint programming (CP). In addition, a new approach based on Ant Colony Optimization (ACO) and Simulated Annealing (SA) is presented for large-sized problems. An illustrative example problem is solved using both the developed model and the proposed algorithm. The effectiveness of the proposed approach is tested through a new data set of test problems presented to the literature for a computational experiment. The experimental results show that the total costs are reduced meaningfully and a more realistic and applicable structure is achieved by the proposed approach.

Free energy subadditivity for symmetric random Hamiltonians

We consider a random Hamiltonian H:Σ→R defined on a compact space Σ that admits a transitive action by a compact group G. When the law of H is G-invariant, we show its expected free energy relative to the unique G-invariant probability measure on Σ, which obeys a subadditivity property in the law of H itself. The bound is often tight for weak disorder and relates free energies at different temperatures when H is a Gaussian process. Many examples are discussed, including branching random walks, several spin glasses, random constraint satisfaction problems, and the random field Ising model. We also provide a generalization to quantum Hamiltonians with applications to the quantum Sherrington–Kirkpatrick and Sachdev–Ye–Kitaev models.

Efficient and linear static approach for finding the memory leak in C

Code analysis has discovered that memory leaks are common in the C programming language. In the literature, there exist various approaches for statically analyzing and detecting memory leaks. The complexity and diversity of memory leaks make it difficult to find an approach that is both effective and simple. In embedded systems, costly resources like memory become limited as the system’s size diminishes. As a result, memory must be handled effectively and efficiently too. To obtain precise analysis, we propose a novel approach that works in a phase-wise manner. Instead of examining all possible paths for finding memory leaks, we use a program slicing to check for a potential memory leak. We introduce a source-sink flow graph (SSFG) based on source-sink properties of memory allocation-deallocation within the C code. To achieve simplicity in analysis, we also reduce the complexity of analysis in linear time. In addition, we utilize a constraint solver to improve the effectiveness of our approach. To evaluate the approach, we perform manual scanning on various test cases: link list applications, Juliet test cases, and common vulnerabilities and exposures found in 2021. The results show the efficiency of the proposed approach by preparing the SSFG with linear complexity.

Sistem Pakar Diagnosa Penyakit Skizofrenia Dengan Menerapkan Kombinasi Metode Constraint Satisfaction Problem (CSP) Dan Metode Certainty Factor

Psychiatric illness is a change in mental function that causes disturbances in ways of thinking, will, emotions, actions and social relations that can cause obstacles in carrying out social roles. One type of psychiatric disorder that is very often known by the public is schizophrenia. If schizophrenia is not followed up, it will have a lot of impact on Indonesian society. For this reason, we need a system that is designed to mimic the expertise of an expert in answering questions and solving a problem in accordance with the knowledge of an expert that is entered into a computer system. The development of artificial intelligence technology that has occurred has enabled expert systems to be applied in detecting diseases using programming languages. One of them is in providing information about various problems, especially psychiatric disorders or often called schizophrenia. The expert system method used is a combination of the Constraint Satisfaction Problem (CSP) and Certainty Factor (CF) methods, which is one of the solutions that can display the final results of several diagnoses of schizophrenia. With the facilities provided to users, it is possible to use this system according to their individual needs. Users are given the convenience of finding information about the symptoms of Schizophrenia and its prevention. This expert system was created using the Microsoft Visual Basic 2010 application.

Automated streamliner portfolios for constraint satisfaction problems

Constraint Programming (CP) is a powerful technique for solving large-scale combinatorial problems. Solving a problem proceeds in two distinct phases: modelling and solving. Effective modelling has a huge impact on the performance of the solving process. Even with the advance of modern automated modelling tools, search spaces involved can be so vast that problems can still be difficult to solve. To further constrain the model, a more aggressive step that can be taken is the addition of streamliner constraints, which are not guaranteed to be sound but are designed to focus effort on a highly restricted but promising portion of the search space. Previously, producing effective streamlined models was a manual, difficult and time-consuming task. This paper presents a completely automated process to the generation, search and selection of streamliner portfolios to produce a substantial reduction in search effort across a diverse range of problems. The results demonstrate a marked improvement in performance for both Chuffed, a CP solver with clause learning, and lingeling, a modern SAT solver.

Network Migration Problem: A Hybrid Logic-Based Benders Decomposition Approach

Telecommunication networks frequently face technological advancements and need to upgrade their infrastructure. Adapting legacy networks to the latest technology requires synchronized technicians responsible for migrating the equipment. The goal of the network migration problem is to find an optimal plan for this process. This is a defining step in the customer acquisition of telecommunications service suppliers, and its outcome directly impacts the network owners’ purchasing behavior. We propose the first exact method for the network migration problem, a logic-based Benders decomposition approach that benefits from a hybrid constraint programming–based column generation in its master problem and a constraint programming model in its subproblem. This integrated solution technique is applicable to any integer programming problem with similar structure, most notably the vehicle routing problem with node synchronization constraints. Comprehensive evaluation of our method over instances based on six real networks demonstrates the computational efficiency of the algorithm in obtaining quality solutions. We also show the merit of each incorporated optimization paradigm in achieving this performance. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Applications. Funding: This work was supported by Mitacs. SciNet is funded by the Canada Foundation for Innovation, the Government of Ontario, Ontario Research Fund–Research Excellence, and the University of Toronto. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoc.2023.1280 .

Max-3-Lin Over Non-abelian Groups with Universal Factor Graphs

The factor graph of an instance of a constraint satisfaction problem with n variables and m constraints is the bipartite graph between [m] and [n] describing which variable appears in which constraints. Thus, an instance of a CSP is completely determined by its factor graph and the list of predicates. We show optimal inapproximability of Max-3-LIN over non-Abelian groups (both in the perfect completeness case and in the imperfect completeness case), even when the factor graph is fixed. Previous reductions which proved similar optimal inapproximability results produced factor graphs that were dependent on the input instance. Along the way, we also show that these optimal hardness results hold even when we restrict the linear equations in the Max-3-LIN instances to the form xcdot ycdot z = g, where x, y, z are the variables and g is a group element. We use representation theory and Fourier analysis over non-Abelian groups to analyze the reductions.

The smallest hard trees

We find an orientation of a tree with 20 vertices such that the corresponding fixed-template constraint satisfaction problem (CSP) is NP-complete, and prove that for every orientation of a tree with fewer vertices the corresponding CSP can be solved in polynomial time. We also compute the smallest tree that is NL-hard (assuming L≠NL), the smallest tree that cannot be solved by arc consistency, and the smallest tree that cannot be solved by Datalog. Our experimental results also support a conjecture of Bulín concerning a question of Hell, Nešetřil and Zhu, namely that ‘easy trees lack the ability to count’. Most proofs are computer-based and make use of the most recent universal-algebraic theory about the complexity of finite-domain CSPs. However, further ideas are required because of the huge number of orientations of trees. In particular, we use the well-known fact that it suffices to study orientations of trees that are cores and show how to efficiently decide whether a given orientation of a tree is a core using the arc-consistency procedure. Moreover, we present a method to generate orientations of trees that are cores that works well in practice. In this way we found interesting examples for the open research problem to classify finite-domain CSPs in NL.

Solving the flexible job shop scheduling and lot streaming problem with setup and transport resource constraints

Statement of Removal Due to a technical issue, this article incorrectly published in the International Journal of Systems Science instead of the International Journal of Systems Science: Operations & Logistics. Therefore, this article has been removed from International Journal of Systems Science and republished in the International Journal of Systems Science:Operations & Logistics The article is now available in the link: https://doi.org/10.1080/23302674.2023.2221072 Article title: Solving the flexible job shop scheduling and lot streaming problemwith setup and transport resource constraints Authors: P. Yunusoglu & S. Topaloglu Yildiz Journal: International Journal of Systems Science Version of Record Published Online: 25 March 2023 DOI: http://doi.org/10.1080/00207721.2023.2192220

Mixed-Integer Programming vs. Constraint Programming for Shop Scheduling Problems: New Results and Outlook

Constraint programming (CP) has been recently in the spotlight after new CP-based procedures have been incorporated into state-of-the-art solvers, most notably the CP Optimizer from IBM. Classical CP solvers were only capable of guaranteeing the optimality of a solution, but they could not provide bounds for the integer feasible solutions found if interrupted prematurely due to, say, time limits. New versions, however, provide bounds and optimality guarantees, effectively making CP a viable alternative to more traditional mixed-integer programming (MIP) models and solvers. We capitalize on these developments and conduct a computational evaluation of MIP and CP models on 12 select scheduling problems. 1 We carefully chose these 12 problems to represent a wide variety of scheduling problems that occur in different service and manufacturing settings. We also consider basic and well-studied simplified problems. These scheduling settings range from pure sequencing (e.g., flow shop and open shop) or joint assignment-sequencing (e.g., distributed flow shop and hybrid flow shop) to pure assignment (i.e., parallel machine) scheduling problems. We present MIP and CP models for each variant of these problems and evaluate their performance over 17 relevant and standard benchmarks that we identified in the literature. The computational campaign encompasses almost 6,623 experiments and evaluates the MIP and CP models along five dimensions of problem characteristics, objective function, decision variables, input parameters, and quality of bounds. We establish the areas in which each one of these models performs well and recognize their conceivable reasons. The obtained results indicate that CP sets new limits concerning the maximum problem size that can be solved using off-the-shelf exact techniques. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.1287 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0326 ) at ( http://dx.doi.org/10.5281/zenodo.7541223 ).

An Integrated Risk Sensitive Crop Allocation Model with Pollination Intelligence Algorithm

A risk sensitive model for allocation of crops is considered in this work. The constructed model was designed to help farmers decision making process, thereby maximizing the use of agricultural land. Market price, cost of cultivation, yield of crops and climatic conditions were factors considered in the models. The theory of chance constraint programing was used to handle uncertainties that arise in crop planing. Data of known yield of crops were harvested and analyzed with the help of statistical tools. A class of Pollination Intelligence Algorithm was adopted to solve the model.

A CP-based approach for mining sequential patterns with quantities

This paper addresses the problem of mining sequential patterns (SPM) from data represented as a set ofsequences. In this work, we are interested in sequences of items in which each item is associated with its quantity.To the best of our knowledge, existing approaches don’t allow to handle this kind of sequences under constraints.In the other hand, several proposals show the efficiency of constraint programming (CP) to solve SPM problemdealing with several kind of constraints. However, in this paper, we propose the global constraint QSPM whichis an extension of the two CP-based approaches proposed in [5] and [7]. Experiments on real-life datasets showthe efficiency of our approach allowing to specify many constraints like size, membership and regular expressionconstraints.

PTAS for Sparse General-valued CSPs

We study polynomial-time approximation schemes (PTASes) for constraint satisfaction problems (CSPs) such as Maximum Independent Set or Minimum Vertex Cover on sparse graph classes. Baker’s approach gives a PTAS on planar graphs, excluded-minor classes, and beyond. For Max-CSPs, and even more generally, maximisation finite-valued CSPs (where constraints are arbitrary non-negative functions), Romero, Wrochna, and Živný [SODA’21] showed that the Sherali-Adams LP relaxation gives a simple PTAS for all fractionally-treewidth-fragile classes, which is the most general “sparsity” condition for which a PTAS is known. We extend these results to general-valued CSPs, which include “crisp” (or “strict”) constraints that have to be satisfied by every feasible assignment. The only condition on the crisp constraints is that their domain contains an element that is at least as feasible as all the others (but possibly less valuable). For minimisation general-valued CSPs with crisp constraints, we present a PTAS for all Baker graph classes—a definition by Dvořák [SODA’20] that encompasses all classes where Baker’s technique is known to work, except for fractionally-treewidth-fragile classes. While this is standard for problems satisfying a certain monotonicity condition on crisp constraints, we show this can be relaxed to diagonalisability —a property of relational structures connected to logics, statistical physics, and random CSPs.

Graph constraints refined for transitive relations

As a powerful modelling tool, Constraint Satisfaction Problems (CSPs) can be solved efficiently using various solving paradigms and can encapsulate various types of constraints in a single model. Graph constraints are one such type of constraint. Existing graph constraints are dedicated to solve classical problems, such as constrained path problems and subgraph extraction problems. However, in some scenarios modelled with CSPs, there are relations where a formal path is formed by selecting a set of vertices on a graph, and the shortest path between two neighbouring vertices on that path needs to be restricted. Such relations are known as transitive relations on the graph, which cannot be expressed by existing graph constraints. Although expressive table constraints can be used to express transitive relations, this approach significantly reduces the performance of using table constraints. Therefore, to express transitive relations on a graph that can be efficiently modelled and reasoned by various types of CSP solvers, we propose two new constraints and present propagation algorithms based on generalized arc consistency. Finally, we perform comparative experiments to demonstrate the correctness and efficiency of the proposed approach. The results of the experiments not only prove the correctness of the propagation algorithms but also show that our proposed approach of modelling directly using new constraints and then reasoning using proprietary propagation algorithms, is more efficient than translating relations into table constraints and then reasoning.

A symbolic algorithm for the case-split rule in solving word constraints with extensions

Case split is a core proof rule in current decision procedures for the theory of string constraints. Its use is the primary cause of the state space explosion in string constraint solving, since it is the only rule that creates branches in the proof tree. Moreover, explicit handling of the case split rule may cause recomputation of the same tasks in multiple branches of the proof tree. In this paper, we propose a symbolic algorithm that significantly reduces such a redundancy. In particular, we encode a string constraint as a regular language and proof rules as rational transducers. This allows us to perform similar steps in the proof tree only once, alleviating the state space explosion. We also extend the encoding to handle arbitrary Boolean combinations of string constraints, length constraints, and regular constraints. In our experimental results, we validate that our technique works in many practical cases where other state-of-the-art solvers fail to provide an answer; our Python prototype implementation solved over 50% of string constraints that could not be solved by the other tools.