Recent Improvements Using Constraint Integer Programming for Resource Allocation and Scheduling

Stefan, Heinz G.; Ku, Wen-Yang; Beck, J. Christopher

doi:10.1007/978-3-642-38171-3_2

Cited by 16 publications

(11 citation statements)

References 15 publications

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“…In the third relaxation, similar to the relaxations described in [32], a set of area relaxations based on the size and the minimum time required of each request is implemented. Each request is represented as a "job" to schedule.…”

Section: Mip Master Problemmentioning

confidence: 99%

Modelling and Solving the Senior Transportation Problem

Liu

Aleman

Beck

2018

Lecture Notes in Computer Science

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As the Canadian population ages, there is an increasing demand for senior transportation services that cannot be met by regular public transportation systems. This thesis aims to bring attention to the combinatorial optimization problem of senior transportation. By extending current vehicle routing problem knowledge and computational technologies, we construct novel problem definitions for the Senior Transportation Problem (STP) and the Senior Transportation Problem with Overbooking (STPOB) based on data provided by a partnering non-profit organization specializing in senior transportation services. Solution approaches including mixed integer programming, constraint programming, two logicbased Benders decompositions and a construction heuristic are developed and empirical analyses on both randomly generated datasets and real-life datasets are performed. Constraint programming demonstrates best results being able to solve to optimality large real-life instances of up to 270 vehicles with 385 requests for the STP and up to 210 vehicles with 320 requests for the STPOB under 600 seconds. This thesis would not have been possible without a number of people. I would like to use this space to express my gratitude towards them. Before all, I would like thank my supervisors Professor J. Christopher Beck and Professor Dionne M. Aleman for the boundless guidance, patience, support, as well as all the creative ideas throughout the past few years. Their persistence has inspired and pushed me to places and opportunities that I could not even have imagined previously. Not only have they advised me on technical expertise, they have shown me how interesting and fun research can be. I could not have imagined better mentors for my studies and research. I would like to thank my committee members, Professor Merve Bodur and Professor Chi-Guhn Lee for their time and feedback. Thanks to all the amazing people at TIDEL and morLAB for such a fun and amazing time that I would never forget in my life. They have made the sometimes dull student life shine in bright colours. Thanks to my parents for the unconditional love and support for me to pursue my dreams. Lastly, to Chong, my best friend and beloved husband, thank you for being always by my side to share the bitterness, keep me sane and make me laugh.

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Section: Mip Master Problemmentioning

confidence: 99%

Modelling and Solving the Senior Transportation Problem

Liu

Aleman

Beck

2018

Lecture Notes in Computer Science

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“…Mixed-integer programming (MIP) is a mathematical optimization approach for problems modeled as a set of decision variables taking on either continuous or integer values (hence "mixed"), constrained by linear constraints and with the goal of optimizing a linear objective function. MIP has been used widely for optimization since the 1950s, including many scheduling problems [12], [13], [19].…”

Section: A Mixed-integer Programmingmentioning

confidence: 99%

“…Constraint (12) sets the decision variable w j for all tasks, except recharge tasks, to be equal to 1, indicating that these tasks are required. Constraint (13) forces recharging tasks to be used in lexicographic order, breaking some of the symmetry in the model. Constraints (14) and (15) ensure that the start times of the tasks adhere to the user and task schedules where T represents all time points t in 0 ≤ t ≤ H and T j represents the time points during which task j can be scheduled to start.…”

Section: B Proposed Scheduling Modelsmentioning

confidence: 99%

“…In this paper, we focus on the application of existing, general-purpose scheduling technologies from the operations research (e.g., [12], [13]) and artificial intelligence (e.g., [14], [15]) literatures to robot task planning problems. Our hypothesis is that high-performance optimization techniques from these communities can be used to produce efficient, complete plans in run-times that are realistic for these applications.…”

Section: Introductionmentioning

confidence: 99%

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Mixed-Integer and Constraint Programming Techniques for Mobile Robot Task Planning

Booth

Tran

Nejat

et al. 2016

IEEE Robot. Autom. Lett.

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We investigate the use of optimization-based techniques to model and solve two real-world single robot task planning problems. In the first problem, a robot must plan a set of tasks, each with different temporal constraints. In the second problem, a socially interacting robot must plan a set of tasks while considering the schedules of multiple human users, as well as physical constraints including battery level. We apply existing mixed-integer programming and constraint programming techniques, yielding two exact methods for each problem. Numerical experiments show that both approaches produce better solutions in less time compared to techniques previously proposed for these problems. In order to confirm their physical utility, we implement the plans for the second problem in both simulated and real environments on Tangy, a socially interacting robot. We conclude that both mixed-integer programming and constraint programming are promising general approaches to robot task planning that should be considered when solving these problems.

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“…with A an integer m × n matrix, b ∈ Z m , w ∈ Z n , l, u ∈ (Z ∪ {±∞}) n . It is well known to be strongly NP-hard, but models many important problems in combinatorial optimization such as planning [30], scheduling [14], and transportation [4] and thus powerful generic solvers have been developed for it [27]. Still, theory is motivated to search for tractable special cases.…”

Section: Introductionmentioning

confidence: 99%

Evaluating and Tuning n -fold Integer Programming

Altmanová

Knop

Koutecký

2019

ACM J. Exp. Algorithmics

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In recent years, algorithmic breakthroughs in stringology, computational social choice, scheduling, etc., were achieved by applying the theory of so-called n-fold integer programming. An n-fold integer program (IP) has a highly uniform block structured constraint matrix. Hemmecke, Onn, and Romanchuk [Math. Programming, 2013] showed an algorithm with runtime ∆ O(rst+r 2 s) n 3 , where ∆ is the largest coefficient, r, s, and t are dimensions of blocks of the constraint matrix and n is the total dimension of the IP; thus, an algorithm efficient if the blocks are of small size and with small coefficients. The algorithm works by iteratively improving a feasible solution with augmenting steps, and n-fold IPs have the special property that augmenting steps are guaranteed to exist in a not-too-large neighborhood. However, this algorithm has never been implemented and evaluated.We have implemented the algorithm and learned the following along the way. The original algorithm is practically unusable, but we discover a series of improvements which make its evaluation possible. Crucially, we observe that a certain constant in the algorithm can be treated as a tuning parameter, which yields an efficient heuristic (essentially searching in a smaller-than-guaranteed neighborhood). Furthermore, the algorithm uses an overly expensive strategy to find a "best" step, while finding only an "approximately best" step is much cheaper, yet sufficient for quick convergence. Using this insight, we improve the asymptotic dependence on n from n 3 to n 2 log n.Finally, we tested the behavior of the algorithm with various values of the tuning parameter and different strategies of finding improving steps. First, we show that decreasing the tuning parameter initially leads to an increased number of iterations needed for convergence and eventually to getting stuck in local optima, as expected. However, surprisingly small values of the parameter already exhibit good behavior while significantly lowering the time the algorithm spends per single iteration. Second, our new strategy for finding "approximately best" steps wildly outperforms the original construction. ACM Subject ClassificationTheory of computation → Parameterized complexity and exact algorithms; Mathematics of computing → Solvers; Theory of computation → Discrete optimization Keywords and phrases n-fold integer programming, integer programming, analysis of algorithms, primal heuristic, local search Supplement Material https://github.com/katealtmanova/nfoldexperiment

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Recent Improvements Using Constraint Integer Programming for Resource Allocation and Scheduling

Cited by 16 publications

References 15 publications

Modelling and Solving the Senior Transportation Problem

Modelling and Solving the Senior Transportation Problem

Mixed-Integer and Constraint Programming Techniques for Mobile Robot Task Planning

Evaluating and Tuning n -fold Integer Programming

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