Constraint Programming Methods Research Articles

Investigating constraint programming and hybrid methods for real world industrial test laboratory scheduling

AbstractIn this paper we deal with a complex real world scheduling problem closely related to the well-known Resource-Constrained Project Scheduling Problem (RCPSP). The problem concerns industrial test laboratories in which a large number of tests are performed by qualified personnel using specialised equipment, while respecting deadlines and other constraints. We present different constraint programming models and search strategies for this problem. Furthermore, we propose a Very Large Neighborhood Search approach based on our CP methods. Our models are evaluated using CP solvers and a MIP solver both on real-world test laboratory data and on a set of generated instances of different sizes based on the real-world data. Further, we compare the exact approaches with VLNS and a Simulated Annealing heuristic. We could find feasible solutions for all instances and several optimal solutions and we show that using VLNS we can improve upon the results of the other approaches.

An exact constraint programming method for the multi-manned assembly line balancing problem with assignment restrictions

This paper proposes an exact Constraint Programming (CP) method with an extensive focus on real-world constraints for the Multi-manned Assembly Line Balancing Problem with Assignment Restrictions (MALBP-AR). We perform an in-depth literature review to gather examples from real assembly lines and organize the AR regarding tasks, stations, workers, and mounting positions. Our study classifies the AR related to transformed resources and provides a general and unified model. We explore the concept of variable workplaces to dynamically assign workers to mounting positions and aggregate no overlap restrictions to avoid interference between workers. The classic MALBP model is extended by gradually incrementing the number of restrictions. The model variant found in the literature is herein called Partial MALBP-AR. Compared to the previous state-of-the-art Tabu Search Algorithm (TSA) for this problem, the Partial MALBP-AR found twelve additional optimality proofs. Besides the relevant results regarding solution quality, the CP method also has a satisfactory CPU performance. We also propose an entirely new set of AR and test these practical conditions with the so-called Extended MALBP-AR. Such an extended model, which covers all the AR presented here, reached optimality within the computational time limit for 36 out of 38 instances. The worst-case gap for an open instance is 8.20%. The results show a trade-off between the number of deemed restrictions and the computational performance. However, considering the detailed set of AR, we can obtain more representative solutions regarding the final balancing implementation compared to theoretical cases. The method can be used to design experiments, turning certain constraints on and off and allowing managers to evaluate different resource allocation scenarios.

Chance-Constrained optimal scheduling of power and hydrogen systems in power distribution network with significant photovoltaic and carbon offsetting strategies

The urgent need to address climate issues increases the significance of sustainable strategies in power networks. This study focuses on the optimal operation of a hydrogen-based microgrid incorporated with photovoltaics (PVs), time-of-use demand response (TOU-DR) program, distributed generation (DG) units, hydrogen fuel stations (HFSs), and battery storage units. Employing a multi-objective approach, the study aims to minimize emissions and system operation costs, being validated by implementing it on the IEEE 33-bus test network. To address the carbon emissions issue, the Power-to-gas (P-to-G) facility is utilized to capture and recycle CO2 pollutions. The implementation of a carbon trading market mechanism is also adopted to further enhance the generation capacity of the PV units and facilitate the achievement of sustainable development goals. Besides, the presence of uncertainties in renewable generation, demand, operational characteristics of hydrogen vehicles, and market prices pose challenges for the system operator, which is addressed by employing the chance constraint programming (CCP) method. Results show that using the P-to-G system has led to a 10 % emissions reduction. However, this is accompanied by a corresponding 25 % increase in operational costs. Additionally, when operating under the CCP constraints, the system's storage level has been increased by 10 % to ensure optimal performance.

Water–Food Nexus System Management under Uncertainty through an Inexact Fuzzy Chance Constraint Programming Method

This study discusses the planning of a regional-scale water–food nexus (WFN) system using an inexact fuzzy chance constraint programming (IFCCP) method. The IFCCP approach can handle uncertainties expressed as interval and fuzzy parameters, as well as the preferences of decision makers. An inexact fuzzy chance constraint programming-based water–food nexus (IFCCP-WFN) model has been developed for the City of Jinan with the consideration of various restrictions related to water and land availability, as well as food and vegetable demands. Solutions for the planting areas for different crops in different periods have been generated under the different preferences of decision makers. The water resource availability would be the priority factor affecting the WFN system under demanding conditions, in which wheat cultivation would be dominated by this factor under fuzzy confidence levels of 0.2 and 0.5, and the planting area of corn would be determined by this factor under high fuzzy confidence levels (e.g., 0.8). In addition, the reliability of irrigation would decrease with increasing fuzzy confidence levels under demanding conditions, limiting the planting areas for crops and leading to a decreasing trend of the system benefit. Adequate water resources would be available for irrigation under optimistic conditions, implying no significant contributions to the planting schemes. Nevertheless, increasing food loss rates would result in more planting areas to satisfy food requirements and thus a greater system benefit under advantageous conditions. Compared with the developed IFCCP-WFN model, the interval-linear-programming-based water–food nexus (ILP-WFN) model can merely reflect the lower and upper bounds of uncertain parameters and neglects the inherent distributional information within the fuzzy parameters. Thus, the ILP-WFN model is unable to reveal the inherent impacts of the fuzzy parameters on the resulting planting strategies.

Вбудування сімейства логічних мов із можливостями перепрограмування монадичної уніфікації в SCALA

The paper proposes a framework for embedding logic programming and constraint programming methods in Scala by building a logical object-oriented language around the unification of typed logic based on monads. Two types of API are considered — high-level for language embeddings and low-level for organization of the bidirectional flow of data during the execution of logic programs. Differences in the capabilities of logical mechanisms can be expressed as subclasses of the class of unification monad types. This design makes it possible to share the implementation of custom unification between different frameworks and to use other languages’ embeddings in Scala from the declarative side. The monadic API provides the application developer with a simple and intuitive tool to implement custom logic within the unification. Our frameworks provide a clear representation of logical deduction: Scala code is only used for ad hoc unification. But the overall goal execution is an external interpretation that can implement different strategies. This design provides modularity and good integration with the rest of the ecosystem.

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.

Project Portfolio Selection Considering the Fuzzy Chance Constraint of Water Environmental Restoration

The water environment restoration project portfolio (WERP) selection is discussed in this paper. By complying with the analysis of the project’s multidimensional property and operation mode, this paper develops the chance constraint and the management constraint of the WERP from the perspectives of public service and enterprise operation. In addition, the multi-objective mixed integer linear programming model is constructed by combining the expectation method and the fuzzy chance constraint programming method. The results demonstrate that: (1) Our proposed method successfully circumvents the occurrence of local objective optimization within a specific confidence interval, thereby achieving a balance between economic and water environment restoration objectives; (2) including fuzzy chance constraints in our proposed method significantly diminishes the risk of exceeding the WERP capacity, thereby ensuring the effectiveness of water environment restoration by adopting a market-based approach. However, further examination of the impact of various sub-projects in WERP is necessary, along with the integration of novel evolutionary algorithms to enhance the efficiency of our model.

Operating room scheduling by emphasising human factors and dynamic decision-making styles: a constraint programming method

ABSTRACT As the most crucial component of a hospital, the operating room (OR) is the primary source of revenue generation and expenditures. The hospital’s overall performance will be enhanced if this ward’s scheduling is accurate. This study investigates a multi-objective mixed-integer programming model for daily OR scheduling of inpatient surgeries. A major consideration is the setup time (e.g. cleaning, sterilising, and preparing the necessary OR equipment) for the OR when commencing additional surgeries in the same OR. The surgical staff’s performance, interaction quality, and compatibility level play a significant role in the surgery’s quality, success, and safety. As individuals’ decision-making styles vary depending on the situation, one of the objectives increases the compatibility of surgical team members by considering their primary and backup decision-making styles. Another objective is to maximise the efficiency of the surgical team. To this end, this paper employs the TOPSIS method to calculate each person’s efficiency level. The final objective is to minimise OR costs (including the opening and overtime cost of OR and wait time cost for each person). To address problem’s computational complexity, this paper develops a constraint programming (CP) method, and also a novel hybrid mixed-integer linear programming-CP method to solve the real-world instances.

Constraint programming for multi-line parallel partial disassembly line balancing problem with optional common stations

Due to the increased demand for efficient recycling systems for end-of-life (EOL) products, the role of disassembly lines in reverse supply chains has become crucial. Parallel disassembly lines can handle multi-type EOL products and consist of two or more lines. However, previous research has primarily focused on two-line disassembly systems and has not fully addressed the optionality of common stations. To address this gap, this study proposes three exact methods for optimizing multi-line parallel disassembly systems with optional common stations, partial disassembly mode, and AND/OR precedence relations. Firstly, a mixed-integer linear programming (MILP) model is formulated that optimizes three objectives: weighted line length, additional profits, and hazard evaluation. Secondly, two constraint programming (CP) models are developed with different solution methodologies to provide more extensive applications and efficient solutions. An illustrative example shows that production mode can significantly reduce line length and workstations, and computational results demonstrate that both CP methods outperform the MILP model in terms of solution quality and computational efficiency. Specifically, the CP-I method demonstrates a higher level of stability and efficiency in most instances, while the CP-II method excels in optimizing line length and station utilization. These results illustrate the potential for optimizing multi-line disassembly systems with optional common stations to enhance production flexibility in remanufacturing processes.

A joint chance constrained optimization algorithm with robust reconstruction for multi-echelon and multi-period closed-loop manufacturing adjustable system design under multi-source uncertainty

The complex electronic assembly scheduling problem under uncertainty poses a new challenge. The joint chance constraint programming method based on robust reconstruction is used to hedge the endogenous and external uncertainty in the closed-loop manufacturing scheduling model of multi-echelon and multi-product electronic assembly process under multi-source uncertainty in this study. The numerical cases of electronic factory in assembly and closed-loop manufacturing mode are studied, the sensitivity of cost to different types of uncertain parameters is analyzed. The results show that different types of uncertainty have different effects on economic benefits, and endogenous uncertainty has a greater impact on manufacturing costs. Decision makers can adjust the adjustable parameters according to external policies and economic situation to control the conservatism and economic benefits of the scheme, and at the same time reduce the demand for uncertain data and improve the efficiency of solution. The model provides a new sustainable production method for electronic assembly manufacturing practitioners, and makes the best production decision when weighing economic benefits and risks.

A Novel Constraint Programming Decomposition Approach for the Total Flow Time Fixed Group Shop Scheduling Problem

This work addresses a particular case of the group shop scheduling problem (GSSP) which will be denoted as the fixed group shop scheduling problem (FGSSP). In a FGSSP, job operations are divided into stages and each stage has a set of machines associated to it which are not shared with the other stages. All jobs go through all the stages in a specific order, where the operations of the job at each stage need to be finished before the job advances to the following stage, but operations within a stage can be performed in any order. This setting is common in companies such as leaf spring manufacturers and other automotive companies. To solve the problem, we propose a novel heuristic procedure that combines a decomposition approach with a constraint programming (CP) solver and a restart mechanism both to avoid local optima and to diversify the search. The performance of our approach was tested on instances derived from other scheduling problems that the FGSSP subsumes, considering both the cases with and without anticipatory sequence-dependent setup times. The results of the proposed algorithm are compared with off-the-shelf CP and mixed integer linear programming (MILP) methods as well as with the lower bounds derived from the study of the problem. The experiments show that the proposed heuristic algorithm outperforms the other methods, specially on large-size instances with improvements of over 10% on average.

An optimization model for water resources allocation in Dongjiang River Basin of Guangdong-Hong Kong-Macao Greater Bay Area under multiple complexities

In this research, an interval two-stage stochastic fuzzy-interval credibility constraint programming (ISFICP) method was developed for water resources allocation among multiple water users under complexities and uncertainties. The method could reflect the multiple complexities of water resources management, also trade-offs between the system benefits and violation risks. Dongjiang River (DJR) Basin, which supplies water to several core cities in south China such as Guangzhou, Shenzhen, and Hong Kong, was applied as the real demonstrative case. The water resources system of DJR Basin is particularly complex due to it is the primary source water for Guangdong-Hong Kong-Macao Greater Bay Area (GBA). Through considering multiple complexities and uncertainties of the water resources system, such as natural, economic, and social conditions, ISFICP was developed to obtain potential water-allocation schemes. Probabilistic distribution, fuzzy-interval sets (FIS), and discrete intervals were introduced to represent the multiple uncertainties associated with the multiple complexities. The results indicated that the model could provide practical schemes for local decision-makers under multiple scenarios such as flow levels, credibility levels, and recycling rates.

Подход к поиску глобального оптимума в задачах Constrained Clustering с привлечением оценок нескольких экспертов

An approach to solving the constrained clustering problem has been developed, based on the aggregation of data obtained as a result of evaluating the characteristics of clustered objects by several independent experts, and the analysis of alternative variants of clustering by constraint programming methods using original heuristics. Objects clusterized are represented as multisets, which makes it possible to use appropriate methods of aggregation of expert opinions. It is proposed to solve the constrained clustering problem as a constraint satisfaction problem. The main attention is paid to the issue of reducing the number and simplifying the constraints of the constraint satisfaction problem at the stage of its formalization. Within the framework of the approach, we have created: a) a method for estimating the optimal value of the objective function by hierarchical clustering of multisets, taking into account a priori constraints of the subject domain, and b) a method for generating additional constraints on the desired solution in the form of “smart tables”, based on the obtained estimate. The approach allows us to find the best partition in the problems of the class under consideration, which are characterized by a high dimension.

School Timetabling Optimisation Using Artificial Bee Colony Algorithm Based on a Virtual Searching Space Method

Although educational timetabling problems have been studied for decades, one instance of this, the school timetabling problem (STP), has not developed as quickly as examination timetabling and course timetabling problems due to its diversity and complexity. In addition, most STP research has only focused on the educators’ availabilities when studying the educator aspect, and the educators’ preferences and expertise have not been taken into consideration. To fill in this gap, this paper proposes a conceptual model for the school timetabling problem considering educators’ availabilities, preferences and expertise as a whole. Based on a common real-world school timetabling scenario, the artificial bee colony (ABC) algorithm is adapted to this study, as research shows its applicability in solving examination and course timetabling problems. A virtual search space for dealing with the large search space is introduced to the proposed model. The proposed approach is simulated with a large, randomly generated dataset. The experimental results demonstrate that the proposed approach is able to solve the STP and handle a large dataset in an ordinary computing hardware environment, which significantly reduces computational costs. Compared to the traditional constraint programming method, the proposed approach is more effective and can provide more satisfactory solutions by considering educators’ availabilities, preferences, and expertise levels.

Synergetic management of water-energy-food nexus system and GHG emissions under multiple uncertainties: An inexact fractional fuzzy chance constraint programming method

Management of water-food-energy nexus (WEFN) is of great importance to achieve the Sustainable Development Goals. The development of WEFN management strategies is challenged by extensive uncertainties in different system components. Also, agricultural activities would contribute a large portion of the total GHG emissions in many countries, which are affecting the promised carbon neutrality in future. In this study, an inexact fractional fuzzy chance constraint programming method was developed towards planning the water-food-energy nexus system under consideration of both uncertainties and greenhouse gases (GHG) emission. An inexact fractional fuzzy chance constraint programming-based water-energy-food nexus (IFFCCP-WEFN) model has been established under consideration of various restrictions and GHG emissions. Solutions of the planting areas for different crops in different periods have been generated. These results imply that the corn cultivation would be prioritized to satisfy cereal demand due to its relatively lower GHG emission intensity. But the residual resources, after satisfying cereal demand, would tend to be allocated to vegetable planting. Comparison has been conducted among the IFFCCP-WEFN model and WEFN models based the inexact fuzzy chance constraint programming approach with and without GHG emissions. The results indicate that, the results from IFFCCP-WEFN model would achieve a highest unit benefit and lowest total GHG emissions. The total GHG emissions can be 11% less at most than GHG emissions from the resulting crop structures of the other two comparable models. Consequently, the developed IFFCCP-WEFN model can help decision-makers identify the desirable planting structure for crops with a priority of low GHG emission rate. The major contributions in this study include (i) the inexact fractional fuzzy chance constraint programming method to deal with interval and fuzzy parameters, reflect decision makers’ preferences and handle conflicts among contradictory objectives, (ii) the IFFCCP-WEFN model to achieve a maximized unit benefit with respect GHG emissions

An exact solution method for multi-manned disassembly line design with AND/OR precedence relations

Specific government regulations for waste products and increasing environmental awareness are concerns for companies. Disassembly operations have become essential tools for green manufacturing and for reducing ecological hazards from waste electrical and electronic equipment. An effective and efficient line design may be vital to encourage companies to establish a disassembly center. The line-balancing problem is a critical issue in a disassembly center. Large products may allow simultaneous disassembly of parts using more than one operator at a workstation. However, multi-manned disassembly line balancing creates a more complicated problem. Thus, an efficient solution technique based on a constraint programming (CP) approach is proposed for multi-manned disassembly line balancing with AND/OR precedence relations to minimize cycle time as a primary objective and the total number of workers as a secondary objective. A mixed-integer linear programming (MILP) model based on previous studies was proposed to define the problem. A CP approach was developed for the first time to solve this problem. A genetic algorithm was used to show the relative performance of the CP method for large problems. The proposed CP approach demonstrates superior performance.

A new method for a class of parallel batch machine scheduling problem

This paper studies the scheduling problem of jobs with release times, non-identical sizes, and incompatible job families on unrelated parallel batch machines. The capacities of batch machines and the processing times of each job on the batch machines are different. The processing time of one batch is equal to the longest processing time of jobs in this batch. Different types of jobs are not allowed to be assigned into the same batch, which is known as incompatible job families. Mixed integer linear programming and constraint programming (CP) models are proposed. A new batch-based local search method is designed and an iterated greedy (IG) algorithm is developed to avoid unreasonable exchanging of jobs during the local search. Numerical results show that the CP method can obtain high quality solutions in the small-scale instances. For the large-scale instances, the IG algorithm with the new local search method has a competitive performance.

An inexact modeling approach for supporting water resources allocation under natural and social complexities in a border city of China and Myanmar

In this paper, an interval two-stage fuzzy credibility constraint programming (ITSFCCP) method is proposed to deal with multiple uncertainties that can be expressed as fuzzy sets, discrete intervals and probability distributions, which can be used for effectively reflect natural and social complexities of relevant decision-making processes. Lincang city of Yunnan province, which is located in the southwest border of China, is employed as the demonstrative case. It is a frontier window and an important channel for China to face the "radiation center" of Southeast and South Asia. Also, it is the intersection of the Tropic of Cancer and the Geographic Water Distribution Line between the Pacific and Indian Oceans. The city's water resources system is particularly unique due to its connection with Myanmar. Considering multiple uncertainties and complexities of the existing water resources system in the city, ITSFCCP is developed to optimize the allocation of water resources. The objective function of the model is the maximization of economic benefits of the water resources system. Fuzzy sets, discrete intervals and probability distribution were introduced to represent the multiple uncertainties associated with the natural and social complexities. Credibility levels were adopted to solve the complexity of multi-ethnic human society in Lincang. The results showed that the model could effectively deal with the uncertainties and complexities of Lincang's water resources system, and reflect the trade-offs between the system benefits and risks.

Application of random triangular and Gaussian type-2 fuzzy variable to solve fixed charge multi-item four dimensional transportation problem

In this paper, two types of hybrid random type-2 uncertain variables such as random type-2 triangular and random type-2 Gaussian fuzzy variables are used to express the uncertain parameters in a four-dimensional transportation problem. Here selling price, purchasing costs, transportation costs, fixed charges, sources, demands, capacities of conveyances are considered as hybrid random type-2 uncertain parameters. The objective function of the proposed model is de-randomized using the expected value method and the constraints of the model are de-randomized using the probability chance constraint programming method. After that, the proposed model is de-fuzzified by CV based reduction technique. These two reduced crisp problems are solved by Generalized Reduced Gradient (GRG) technique using LINGO 14.0 software. The models are numerically illustrated. Some sensitivity analyses are also presented. Conventional solid (3D) and general (2D) transportation problems are derived as particular cases.

Tabu search and constraint programming-based approach for a real scheduling and routing problem

Constraint programming method (CPM) has gained much attention in the last years since it proved a great efficiency to model and solve many combinatorial problems like scheduling, assignment and routing problems. In this paper, we first present a CPM model for a real scheduling and routing problem (SRP) faced by a company of water and electricity distribution. The problem aims to minimise the total distance travelled by the company's technicians to the clients' locations in order to carry out some services. To solve the studied SRP three CPM-based solution methods are proposed: an exact method (branch and prune), a local search meta-heuristic and a hybrid algorithm which combine tabu search and constraint programming method. The proposed solution methods have been tested using three sets of instances. The two first sets are generated randomly, they represent small and large scale instances, while the third one contain the real instances provided by the company with which we are working. The results obtained by the three methods show clearly the superiority of the hybrid algorithm over the two others methods.