constraint programming based column generation is a hybrid optimization framework recently proposed ( Junker et al., 1999) that uses constraint programming to solve column generation subproblems. In the past, this fra...
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constraint programming based column generation is a hybrid optimization framework recently proposed ( Junker et al., 1999) that uses constraint programming to solve column generation subproblems. In the past, this framework has been used to solve scheduling problems where the associated graph is naturally acyclic and has done so very efficiently. This paper attempts to solve problems whose graph is cyclic by nature, such as routing problems, by solving the elementary shortest path problem with constraint programming. We also introduce new redundant constraints which can be useful in the general framework. The experimental results are comparable to those of the similar method in the literature ( Desrochers, Desrosiers, and Solomon, 1992) but the proposed method yields a much more flexible approach.
This paper presents constraint programming as a natural formalism for modelling problems, and as a flexible platform for solving them. CP has a range of techniques for handling constraints including several forms of p...
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This paper presents constraint programming as a natural formalism for modelling problems, and as a flexible platform for solving them. CP has a range of techniques for handling constraints including several forms of propagation and tailored algorithms for global constraints. It also allows linear programming to be combined with propagation and novel and varied search techniques which can be easily expressed in CP. The paper describes how CP can be used to exploit linear programming within different kinds of hybrid algorithm. In particular it can enhance techniques such as Lagrangian relaxation, Benders decomposition and column generation.
Flight-gate assignment problems are complex real world problems involving different constraints. Some of these constraints include plane-gate eligibility, assigning planes of the same airline and planes getting servic...
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Flight-gate assignment problems are complex real world problems involving different constraints. Some of these constraints include plane-gate eligibility, assigning planes of the same airline and planes getting service from the same ground handling companies to adjacent gates, buffers for changes in flight schedules, night stand flights, priority of some gates over others, and so on. In literature there are numerous models to solve this highly complicated problem and tackle its complexity. In this study, first, we propose two different integer programming models, namely, timetabling and assignment based models, and then a scheduling based constraint programming model to solve the problem to optimality. These models prove to be highly efficient in that the computational times are quite short. We also present the results for one day operation of an airport using real data. Finally, we present our conclusions based on our study along with the possible further research.
Elastic optical network (EON) is a novel optical technology introduced recently to provide flexible and multibitrate data transmission in the optical layer. Since many new network services including cloud computing an...
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Elastic optical network (EON) is a novel optical technology introduced recently to provide flexible and multibitrate data transmission in the optical layer. Since many new network services including cloud computing and content delivery networks are provisioned with the use of specialized data centers located in different network nodes, in place of one-to-one unicast transmission, the anycast transmission defined as one-toone-of-many gains much popularity as a quite simple way to improve network performance. Therefore, this article focuses on modeling and static optimization of anycast flows in EONs. In particular, a NP-hard Routing and Spectrum Allocation for Restoration of Anycast Flows (RSA/RAF) problem is formulated. Next, various optimization approaches are proposed to solve this problem, namely, integer linear programming (ILP) using branch and bound algorithm, constraint programming (CP), and various heuristic approaches. Extensive numerical experiments are run to evaluate and compare all proposed methods. The main conclusion is that in some cases the CP approach is more efficient than the ILP modeling. Moreover, the results show that the SA algorithm significantly outperforms other heuristic methods. (c) 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 66(4), 253-266 2015
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 M...
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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.
Ensuring truthfulness amongst self-interested agents bidding against one another in an auction can be computationally expensive when prices are determined using the Vickrey-Clarke-Groves (VCG) mechanism. This mechanis...
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Ensuring truthfulness amongst self-interested agents bidding against one another in an auction can be computationally expensive when prices are determined using the Vickrey-Clarke-Groves (VCG) mechanism. This mechanism guarantees that each agent's dominant strategy is to tell the truth, but it requires solving n + 1 optimization problems when the overall optimal solution involves n agents. This paper first examines a case-study example demonstrating how Operations Research techniques can be used to compute Vickrey prices efficiently. In particular, the case-study focuses on the Assignment Problem. We show how, in this case, Vickrey prices can be computed in the same asymptotic time complexity as that of the original optimization problem. This case-study can be seen as serving a pedagogical role in the paper illustrating how Operations Research techniques can be used for fast Vickrey pricing. We then propose a constraint programming approach that can be used in a more general context, where nothing is assumed about the nature of the constraints that must be satisfied or the structure of the underlying problem. In particular, we demonstrate how nogood learning can be used to improve the efficiency of constraint-based Vickrey pricing in combinatorial auctions.
This paper presents a constraint programming (CP) methodology to deal with the scheduling of flexible manufacturing systems (FMSs). The proposed approach, which consists of both a model and a search strategy, handles ...
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This paper presents a constraint programming (CP) methodology to deal with the scheduling of flexible manufacturing systems (FMSs). The proposed approach, which consists of both a model and a search strategy, handles several features found in industrial environments, such as limitations on number of tools in the system, lifetime of tools, as well as tool magazine capacity of machines. In addition, it tackles the problem in a integrated way by considering tool planning and allocation, machine assignment, part routing, and task timing decisions altogether in the approach. The formulation, which is able to take into account a variety of objective functions, has been successfully applied to the solution of test problems of various sizes and degrees of difficulty. (C) 2010 Elsevier Ltd. All rights reserved.
The modern constraint programming (CP) was adopted to minimize water scarcity and excessive water which are the critical issues in reservoir operation of Bhumibol Dam (BB) to solve consecutive droughts in the Chao Phr...
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The modern constraint programming (CP) was adopted to minimize water scarcity and excessive water which are the critical issues in reservoir operation of Bhumibol Dam (BB) to solve consecutive droughts in the Chao Phraya River Basin (CPYRB), Thailand. The situations of the severe droughts have been frequently occurred in a broad area of CPYRB due to an extremely low rainfall leading to unusually low water levels and inflow in major reservoirs. Therefore, multi-objective optimization was conducted to characterize the actual operation and physical reservoir system of BB Dam. Two different CP models with seasonal and yearly constraints were manipulated using MiniZinc programming language and the constraint solver IPOPT to find the optimal daily release scheme from 2000 to 2018 of BB Dam. The potential of downstream flow conditions was also considered to partially supply downstream water demand and store savable water in a reservoir for subsequent use during possible future droughts. The results reveal that CP models can diminish some extent of yearly reservoir release, while daily long-term release scheme conforms well with the actual operation particularly during dry and wet seasons in specific drought years. These mean that amount of reservoir water of approximately 47.12-103.83 MCM/year can be saved and stored in reservoir for subsequent use in CPYRB when CP models are deployed. This results in a reservoir storage increase of 7.10-7.94% at the end of the wet season for seasonal and yearly CP models, respectively. When potential side flow is considered, the increase climbs up to 10.49%. This envisages the higher possibility of supplying reservoir water for agricultural water needs over the dry season in the Greater Chao Phraya Irrigation Scheme. As the potential hydraulic head is subject to increased reservoir water storage, therefore, the increase in hydropower production is definitely found of ranging from + 6.10% to + 13.79% by these two sorts of CP models. In add
This paper is an introduction to Newton, a constraint programming language over nonlinear real constraints. Newton originates from an effort to reconcile the declarative nature of constraint logic programming (CLP) la...
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This paper is an introduction to Newton, a constraint programming language over nonlinear real constraints. Newton originates from an effort to reconcile the declarative nature of constraint logic programming (CLP) languages over intervals with advanced interval techniques developed in numerical analysis, such as the interval Newton method. Its key conceptual idea is to introduce the notion of box-consistency, which approximates arc-consistency, a notion well-known in artificial intelligence. Box-consistency achieves an effective pruning at a reasonable computation cost and generalizes some traditional interval operators. Newton has been applied to numerous applications in science and engineering, including nonlinear equation-solving, unconstrained optimization, and constrained optimization. It is competitive with continuation methods on their equation-solving benchmarks and outperforms the interval-based methods we are aware of on optimization problems.
In recent years, the multi-manned assembly line has become popular since the large-sized products allow more than one operator working simultaneously on the same product in a workstation. This line usually occurs in l...
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In recent years, the multi-manned assembly line has become popular since the large-sized products allow more than one operator working simultaneously on the same product in a workstation. This line usually occurs in large-size products such as cars, buses, trucks, and so on. The multi-manned assembly line offers several advantages, such as fewer number of workers/workstation and less cycle time to improve the performance of the system. However, it has been analyzed by a few papers in literature due to being a relatively new and complex problem. The current study aims to develop an efficient exact solution approach, constraint programming, to solve from small to large-size problems by minimizing the cycle time as a primary objective and the total number of workers as a secondary objective. First, two mixed-integer linear programming (MILP) models are proposed based on previous studies to solve the small test cases of the problem optimally. However, the models are not capable of solving the large-size test instances. Therefore, a constraint programming (CP) model is formulated to address both small and large-size data sets. The results of the CP model are compared with two MILP models and two heuristic algorithms available in the literature. The computational results indicate that the CP model discovers optimal solutions, approximately 90% of all the instances, and small optimality gaps in the remaining instances. It is useful to highlight that the CP model is highly concise and solved by a black-box, commercial solver. (c) 2020 Elsevier Ltd. All rights reserved.
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