“Almost-stable” matchings in the Hospitals / Residents problem with Couples

Manlove, David F.; McBride, Iain; Trimble, James

doi:10.1007/s10601-016-9249-7

Cited by 22 publications

(16 citation statements)

References 30 publications

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“…The two solvers that perform best on our benchmark set, the IBM Cplex CP and the Google OR-Tools CP-SAT solver, are compared in [19] on instances of the job shop scheduling problem. Another paper, which compares MIP and CP solvers, is [38], but it focuses on the hospitals/residents problem.…”

Section: Related Workmentioning

confidence: 99%

Cable tree wiring - benchmarking solvers on a real-world scheduling problem with a variety of precedence constraints

et al. 2021

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Cable trees are used in industrial products to transmit energy and information between different product parts. To this date, they are mostly assembled by humans and only few automated manufacturing solutions exist using complex robotic machines. For these machines, the wiring plan has to be translated into a wiring sequence of cable plugging operations to be followed by the machine. In this paper, we study and formalize the problem of deriving the optimal wiring sequence for a given layout of a cable tree. We summarize our investigations to model this cable tree wiring problem (CTW). as a traveling salesman problem with atomic, soft atomic, and disjunctive precedence constraints as well as tour-dependent edge costs such that it can be solved by state-of-the-art constraint programming (CP), Optimization Modulo Theories (OMT), and mixed-integer programming (MIP). solvers. It is further shown, how the CTW problem can be viewed as a soft version of the coupled tasks scheduling problem. We discuss various modeling variants for the problem, prove its NP-hardness, and empirically compare CP, OMT, and MIP solvers on a benchmark set of 278 instances. The complete benchmark set with all models and instance data is available on github and was included in the MiniZinc challenge 2020.

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Section: Related Workmentioning

confidence: 99%

Cable tree wiring - benchmarking solvers on a real-world scheduling problem with a variety of precedence constraints

et al. 2021

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“…These formulations have been extended to give ILP models for finding maximum size stable matchings in instances of SMTI and HRT [26,27]. ILP models have also been given for a common extension of HR that allows doctors to apply as couples, typically so that both members can be matched to hospitals that are geographically close [2,7,18,28,33]. Other techniques in the field include constraint programming, which has been applied to SM and its variants [14,15,32,35], and the use of SAT models and SAT solvers [7,15].…”

Section: Related Workmentioning

confidence: 99%

“…• Merging stability constraints (28) is not beneficial on these instances, as all algorithms that merge stability constraints have a worse average running compared to those that do not (e.g., 15.9 seconds on average for N5 versus 10.1 for N3, and 25.5 seconds for N9 versus 16.1 for N7). This can be explained by the fact that almost no gain is obtained in terms of number of constraints (e.g., 3465 for N5 versus 5014 for N3), but a significant loss is observed in terms of continuous relaxation value (e.g., 747.8 for N5 versus 744.5 for N3).…”

Section: Non Master List Instancesmentioning

confidence: 99%

“…Constraints (26) ensure that a doctor can only be assigned to a hospital that is not already filled by doctors that the hospital strictly prefers. Constraints (27) ensure that, if a hospital is full for doctors of rank at most k − 1, then it is also full for doctors of rank at most k. Constraints (28) ensure that the matching is stable by ruling out the existence of any blocking pair. More specifically, (28) ensure that, if a hospital j has space for doctors of rank k (i.e., z jk = 0), then all doctors i of the hospital with rank k − 1 were already accepted in j or in a hospital they consider equal or better than j (i.e., y d i,r d j (i) = 1).…”

Section: New Stability Constraints For Max-hrtmentioning

confidence: 99%

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Mathematical models for stable matching problems with ties and incomplete lists

Delorme

García

Gondzio

et al. 2019

European Journal of Operational Research

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We present new integer linear programming (ILP) models for N P-hard optimisation problems in instances of the Stable Marriage problem with Ties and Incomplete lists (SMTI) and its many-to-one generalisation, the Hospitals / Residents problem with Ties (HRT). These models can be used to efficiently solve these optimisation problems when applied to (i) instances derived from real-world applications, and (ii) larger instances that are randomlygenerated. In the case of SMTI, we consider instances arising from the pairing of children with adoptive families, where preferences are obtained from a quality measure of each possible pairing of child to family. In this case we seek a maximum weight stable matching. We present new algorithms for preprocessing instances of SMTI with ties on both sides, as well as new ILP models. Algorithms based on existing state-of-the-art models only solve 6 of our 22 real-world instances within an hour per instance, and our new models incorporating dummy variables and constraint merging, together with preprocessing and a warm start, solve all 22 instances within a mean runtime of a minute. For HRT, we consider instances derived from the problem of assigning junior doctors to foundation posts in Scottish hospitals. Here we seek a maximum size stable matching. We show how to extend our models for SMTI to HRT and reduce the average running time for real-world HRT instances by two orders of magnitude. We also show that our models outperform by a wide margin all known state-of-the-art models on larger randomly-generated instances of SMTI and HRT.

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“…This fact clearly illustrates the theoretical difficulty of dealing with predetermined groups of residents in matching problems. For matching with couples, several algorithms work well in practice [4], [31], and various optimization models have been employed [2], [6], [10], [18], [25]. However, to our knowledge, no previous studies have developed an effective algorithm for matching in groups.…”

Section: Introductionmentioning

confidence: 99%

Multi-objective Optimization Models for Many-to-one Matching Problems

Shimada

Yamazaki

Takano

2020

Journal of Information Processing

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This paper is concerned with many-to-one matching problems for assigning resident physicians (residents) to hospitals according to their preferences. The stable matching model aims at finding a stable matching, and the assignment game model involves maximizing the total utility. These two objectives however are generally incompatible. We focus on a case involving predetermined groups of residents who want to be matched in groups. To pursue these conflicting objectives simultaneously, we propose several multi-objective optimization models for many-to-one matching problems. We first derive a bi-objective optimization model for maximizing the total utility while minimizing the number of blocking pairs to promote stability. We next introduce a small-subgroup penalty, which will be minimized as the third objective for the purpose of matching in groups. Our multi-objective optimization models are formulated by means of the ε-constraint method as scalar objective mixed-integer optimization problems, which can be solved to optimality by using optimization software. The efficacy of our method is assessed through simulation experiments via comparison with the outcomes of two common matching algorithms: the deferred acceptance algorithm and Gale's top trading cycles algorithm. Our results highlight the potential of optimization models for computing good-quality solutions to a variety of difficult matching problems.

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“Almost-stable” matchings in the Hospitals / Residents problem with Couples

Cited by 22 publications

References 30 publications

Cable tree wiring - benchmarking solvers on a real-world scheduling problem with a variety of precedence constraints

Cable tree wiring - benchmarking solvers on a real-world scheduling problem with a variety of precedence constraints

Mathematical models for stable matching problems with ties and incomplete lists

Multi-objective Optimization Models for Many-to-one Matching Problems

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