Constraint Programming Approach Research Articles

The container premarshalling problem under limited crane time: A constraint programming approach

This study addresses the premarshalling problem when the crane time is limited and a complete rearrangement of the bay is not possible. This issue has been neglected in the literature, but it is very common in practice. We show that the use of standard approaches often fails to yield good solutions and develop a model for the problem in two steps. First, a constraint programming model is proposed for premarshalling with crane time minimization objective. Then, this model is adapted to the new problem. An extensive computational study shows that the first model improves on the performance of the existing state-of-the-art integer programming model and that the model of the new problem obtains high quality solutions even in short running times.

Stable Matchings in Practice: A Constraint Programming Approach

We study a practical two-sided matching problem of allocating children to daycare centers, which has significant social implications. We are cooperating with several municipalities in Japan and our goal is to devise a reliable and trustworthy clearing algorithm to deal with the problem. In this paper, we describe the design of our new algorithm that minimizes the number of unmatched children while ensuring stability. We evaluate our algorithm using real-life data sets, and experimental results demonstrate that our algorithm surpasses the commercial software that currently dominates the market in terms of both the number of matched children and the number of blocking coalitions (measuring stability). Our findings have been reported to local governments, and some are considering adopting our proposed algorithm in the near future, instead of the existing solution. Moreover, our model and algorithm have broader applicability to other important matching markets, such as hospital-doctor matching with couples and school choice with siblings.

Network configuration distributed production scheduling problem: A constraint programming approach

Nowadays, many massive factories are forced to distribute their products in several manufacturing units. This issue has caused the emergence of a novel category of problems called distributed production scheduling, which is vital in today's growing world. In this paper, the distributed production scheduling problem by considering network configuration with two echelons is addressed. The first and second echelon factories have different job configurations and have a hybrid flow shop and a flexible job shop environment, respectively. For this problem, A bi-objective mixed integer linear programming (MILP) model is presented to minimize the maximum completion time of jobs and transportation costs between the selected factories in two echelons, respectively. Consequently, the epsilon constraint method is used to deal with this bi-objective model. In addition, since distributed scheduling problems are classified as NP-Hard problems, it is very challenging to solve them for large-sized instances. For this reason, a constraint programming model (CP) is also proposed. To evaluate the performance of the proposed MILP model and CP model, a total of 180 numerical instances are randomly generated in small, medium, and large sizes. The obtained results demonstrate the significant ability of the constraint programming approach in solving complex distributed scheduling problems even for large-sized instances with 30 jobs, 10 stages/operations for each job, 6 machines for each stage/operation, and 4 factories at each echelon in a reasonable time and proof that the CP model can outperform the MILP model in this problem.

A constraint programming approach for multi-objective tourist trip design problem with mandatory visits: A case study for İzmir Turkey

The Orienteering Problem (OP) is an optimization problem that finds the locations and routes that will return the highest profit/benefit, starting from the initial location of the traveler/vehicle, visiting these locations, and ending with the starting location of the tour within a given time or distance limit. There is no obligation to visit all locations in the problem structure. OP has many real-life applications, such as staff routing and disaster relief routing. In this study, OP with Time Windows (OPTW), an extension of OP, is discussed with hotel selection and mandatory visits. Although the main objective of OPTW is profit maximization, it is also essential to minimize the total travel time to complete the tour efficiently. For this reason, we consider the OPTW as a multi-objective problem. In the problem considered here, it is assumed that the profit/benefit, travel time between locations, service period, and time interval that each location can be visited are determined to be known. Within the scope of the study, first, a Mixed Integer Programming (MIP) model is prepared for the problem. Since the proposed mathematical model does not provide solutions in a reasonable time for large networks, the problem is solved by a Constraint Programming (CP) approach. Attractive tourist points of interest for Izmir, one of Turkey's major tourist cities, are determined, and the proposed method is applied to the real-life problem. The problem is modeled as Multi-Objective OPTW with MIP and CP and solved. Also, sensitivity analysis is performed by considering two different scenarios.

A Constraint Programming approach to solve the clustering problem in open-pit mine planning

A Constraint Programming approach to solve the clustering problem in open-pit mine planning

Constraint programming approaches to electric vehicle and robot routing problems

Constraint programming approaches to electric vehicle and robot routing problems

Constraint Programming Approach to Coverage-Path Planning for Autonomous Multi-UAV Infrastructure Inspection

This article presents a constraint modeling approach to global coverage-path planning for linear-infrastructure inspection using multiple autonomous UAVs. The problem is mathematically formulated as a variant of the Min–Max K-Chinese Postman Problem (MM K-CPP) with multi-weight edges. A high-level constraint programming language is used to model the problem, which enables model execution with different third-party solvers. The optimal solutions are obtained in a reasonable time for most of the tested instances and different numbers of vehicles involved in the inspection. For some graphs with multi-weight edges, a time limit is applied, as the problem is NP-hard and the computation time increases exponentially. Despite that, the final total inspection cost proved to be lower when compared with the solution obtained for the unrestricted MM K-CPP with single-weight edges. This model can be applied to plan coverage paths for linear-infrastructure inspection, resulting in a minimal total inspection time for relatively simple graphs that resemble real transmission networks. For more extensive graphs, it is possible to obtain valid solutions in a reasonable time, but optimality cannot be guaranteed. For future improvements, further optimization could be considered, or different models could be developed, possibly involving artificial neural networks.

Makespan Minimization for the Two-Stage Hybrid Flow Shop Problem with Dedicated Machines: A Comprehensive Study of Exact and Heuristic Approaches

This paper presents a comprehensive approach for minimizing makespan in the challenging two-stage hybrid flowshop with dedicated machines, a problem known to be strongly NP-hard. This study proposed a constraint programming approach, a novel heuristic based on a priority rule, and Tabu search procedures to tackle this optimization problem. The constraint programming model, implemented using a commercial solver, serves as the exact resolution method, while the heuristic and Tabu search explore approximate solutions simultaneously. The motivation behind this research is the need to address the complexities of scheduling problems in the context of two-stage hybrid flowshop with dedicated machines. This problem presents significant challenges due to its NP-hard nature and the need for efficient optimization techniques. The contribution of this study lies in the development of an integrated approach that combines constraint programming, a novel heuristic, and Tabu search to provide a comprehensive and efficient solution. The proposed constraint programming model offers exact resolution capabilities, while the heuristic and Tabu search provide approximate solutions, offering a balance between accuracy and efficiency. To enhance the search process, the research introduces effective elimination rules, which reduce the search space and simplify the search effort. This approach improves the overall optimization performance and contributes to finding high-quality solutions. The results demonstrate the effectiveness of the proposed approach. The heuristic approach achieves complete success in solving all instances for specific classes, showcasing its practical applicability. Furthermore, the constraint programming model exhibits exceptional efficiency, successfully solving problems with up to n=500 jobs. This efficiency is noteworthy compared to instances solved by other exact solution approaches, indicating the scalability and effectiveness of the proposed method.

Parallel Batch Processing for the Coating Problem

We solve a challenging scheduling problem with parallel batch processing and two-dimensional shelf strip packing constraints that arises in the tool coating field. Tools are assembled on so-called planetaries (batches) before they are loaded into coating machines to get coated. The assembling is not trivial and must fulfil specific constraints, which we refer to as shelf strip packing constraints. Further, each tool is associated with a starting time window s.t. tools can only be put on the same planetary if their time window overlap. The objective is to minimise the makespan and the number of required planetaries. Since the problem naturally decomposes into scheduling and packing parts, we tackle the problem with a two-phase logic-based Benders decomposition approach. The master problem assigns items to batches. The first phase solves as subproblem the packing problem by checking if the assignment is feasible, whereas the second phase solves the scheduling subproblem. The approach is compared with a monolithic mixed integer linear programming approach as well as a monolithic constraint programming approach. Experimental evaluation shows that our proposed approach outperforms the state-of-the-art benchmarks by solving more instances to optimality in a shorter time.

A constraint programming approach to a real-world workforce scheduling problem for multi-manned assembly lines with sequence-dependent setup times

For over five decades, researchers have presented various assembly line problems. Recently, assembly lines with multiple workers at each workstation have become very common in the literature. These lines are often found in the manufacturing of large vehicles, where workers at a workstation may perform their assigned tasks at the same time. Most research on multi-manned assembly lines focuses on balancing tasks and workers among workstations and scheduling tasks for workers. This study, however, concentrates on assigning tasks to workers already assigned to a specific workstation, rather than balancing the entire line. The problem was identified through an industrial case study at a large vehicle manufacturing company. The study presents two methods, one using mixed integer linear programming and the other using constraint programming, to minimise the number of workers required on a multi-manned assembly line with sequence-dependent setup times. The results of the computational experiments indicate that the constraint programming method performs better than the mixed integer linear programming method on several modified benchmark instances from the literature. The constraint programming model is also tested on the real-world scenario of our industrial case study and leads to significant improvements in the productivity of the workstations.

Solving the team orienteering problem with time windows and mandatory visits using a constraint programming approach

This paper presents a constraint programming (CP) approach for solving the team orienteering problem with time windows and mandatory visits (TOPTW-MV), which has many real-world implementations, such as tourist tour planning, routing technicians, and disaster relief routing. In the TOPTW-MV, a set of locations is given; some locations must be visited, while others are optional. For each location, the profit, service time, and service time window information are known. A fleet of homogeneous vehicles is available for visiting locations and collecting the profits. The objective in solving this problem is to create a set of vehicle routes that begin and end at a depot, visit mandatory locations exactly once and optional locations at most once, while observing other restrictions such as time windows and sequence-based travel times. The CP-based approach finds 99 of the best-known solutions and explores 64 new best-known solutions for the benchmark instances.

A competitive constraint programming approach for the group shop scheduling problem

In this paper, we propose a competitive Constraint Programming (CP) approach to solve the Group Shop Scheduling Problem (GSSP) under the makespan minimization criteria. Our contribution is two-fold: we provide a flexible mathematical formulation to solve the GSSP that can be used without change to solve other closed-related scheduling problems such as the Open Shop Scheduling Problem (OSSP), Job Shop Scheduling Problem (JSSP), and Mixed Shop Scheduling Problem (MSSP); and we improve several lower bounds and upper bounds from 130 classical GSSP instances from the literature. We evaluate our approach by comparing the performance with competitive methods mainly based on metaheuristics, where we were able to prove optimality in more than 85% of the instances in competitive running time, with a relative percentage deviation lower than 3% on average. In contrast to metaheuristics approaches, our CP method does not require calibrations of multiple parameters, several replicates for each instance, and complex computational coding to be competitive in both, solution quality and computational running times.

Credibility based chance constrained programming for parallel machine scheduling under linear deterioration and learning effects with considering setup times dependent on past sequences

The industry has expressed significant concern regarding the issue of parallel machines and the influence of learning and deterioration. This research investigates non-identical parallel machine scheduling, taking into account the simultaneous consideration of learning effects, deterioration, and past-sequence-dependent setup times. Due to the existence of uncertain parameters in real-world scenarios, the processing times and due dates are assumed to be triangular fuzzy numbers. A fuzzy nonlinear mathematical model with two objective functions is presented and solved using the fuzzy Chance Constraint Programming approach. The two objectives are the summation of earliness and tardiness, as well as makespan. To achieve an efficient near-optimal Pareto front for the problem, a hybrid NSGA-II and VNS multi-objective meta-heuristic is proposed and the results are discussed. Finally, the augmented ε-constraint method is utilized to address issues with small dimensions. The computational analysis demonstrates the effectiveness of this proposed algorithm in tackling problems, especially those with substantial dimensions.

Management of electronic ledger: a constraint programming approach for solving curricula scheduling problems

Management of electronic ledger: a constraint programming approach for solving curricula scheduling problems

A constraint programming approach for quantitative frequent pattern mining

A constraint programming approach for quantitative frequent pattern mining

Management of Electronic Ledger: A Constraint Programming Approach for Solving Curricula Scheduling Problems

Management of Electronic Ledger: A Constraint Programming Approach for Solving Curricula Scheduling Problems

A constraint programming approach for quantitative frequent pattern mining

A constraint programming approach for quantitative frequent pattern mining

A new two-stage constraint programming approach for open shop scheduling problem with machine blocking

In this paper, a variant of the open shop scheduling problem is considered in which the intermediate storage is forbidden among two adjacent production stages (zero buffer or machine blocking constraint). The performance measure is to minimise the maximal completion time of the jobs (makespan). Since this is an NP-hard problem, a two-stage constraint programming approach is proposed as a new exact method. Computational experiments were carried out on 222 literature problem instances in order to test the performance of the proposed algorithm. The relative deviation is adopted as the performance criteria. Computational results point to the ability of the proposed method to solve large-sized instances in comparison with the developed mixed-integer linear programming model and a simple constraint programming model, both with user cuts. In all set of instances, the proposed two-stage method performed better than benchmarking methods and integer programming models, with average relative deviation regarding objective values as lower as 12%. In addition, the results point to a competitive efficiency in computational times of the proposed method with less than 200 s in the most instances to obtain the optimal solution, in comparison to competitive metaheuristics from literature of the problem, for the tested test instances.

Minimum Scan Cover and Variants: Theory and Experiments

We consider a spectrum of geometric optimization problems motivated by contexts such as satellite communication and astrophysics. In the problem Minimum Scan Cover with Angular Costs , we are given a graph G that is embedded in Euclidean space. The edges of G need to be scanned, i.e., probed from both of their vertices. To scan their edge, two vertices need to face each other; changing the heading of a vertex incurs some cost in terms of energy or rotation time that is proportional to the corresponding rotation angle. Our goal is to compute schedules that minimize the following objective functions: (i) in Minimum Makespan Scan Cover (MSC-MS), this is the time until all edges are scanned; (ii) in Minimum Total Energy Scan Cover (MSC-TE), the sum of all rotation angles; and (iii) in Minimum Bottleneck Energy Scan Cover (MSC-BE), the maximum total rotation angle at one vertex. Previous theoretical work on MSC-MS revealed a close connection to graph coloring and the cut cover problem, leading to hardness and approximability results. In this article, we present polynomial-time algorithms for one-dimensional (1D) instances of MSC-TE and MSC-BE but NP-hardness proofs for bipartite 2D instances. For bipartite graphs in 2D, we also give 2-approximation algorithms for both MSC-TE and MSC-BE. Most importantly, we provide a comprehensive study of practical methods for all three problems. We compare three different mixed-integer programming and two constraint programming approaches and show how to compute provably optimal solutions for geometric instances with up to 300 edges. Additionally, we compare the performance of different meta-heuristics for even larger instances.

Scheduling of Multi-Robot Job Shop Systems in Dynamic Environments: Mixed-Integer Linear Programming and Constraint Programming Approaches

This paper investigates a dynamic scheduling problem within a job shop robotic cell, wherein multiple robotic arms are responsible for material handling in a U-shaped arrangement. Each robotic arm has access to specific workstations based on their distance in the cell layout. Therefore, a part may need to be exchanged between several robots according to its process plan. For this purpose, intermediate buffers are positioned between each pair of consecutive robots. Due to the dynamic nature of the problem, new jobs arrive at unpredictable times, which in turn necessitates rescheduling taking the system’s current state into account. To tackle this problem, firstly, a Mixed-Integer Linear Programming (MILP) model is devised. Secondly, three distinct Speed-up Constraints (SCs) derived from the problem’s inherent characteristics are designed and implemented to accelerate the MILP model’s solving procedure. Afterward, the problem is formulated using Constraint Programming (CP) approach. The performance of the CP model and the MILP model in presence of all possible combinations of the SCs are evaluated and compared through solving various random instances. Next, an analysis is performed on the buffers’ pick-up criterion and how it is affected by the problem’s size. Besides, the impact of changes in the robots’ speed on the productivity of the cell is assessed. Finally, the extent to which the rescheduling priority affects the output of the model is studied.