86 research outputs found
A linear programming based heuristic framework for min-max regret combinatorial optimization problems with interval costs
This work deals with a class of problems under interval data uncertainty,
namely interval robust-hard problems, composed of interval data min-max regret
generalizations of classical NP-hard combinatorial problems modeled as 0-1
integer linear programming problems. These problems are more challenging than
other interval data min-max regret problems, as solely computing the cost of
any feasible solution requires solving an instance of an NP-hard problem. The
state-of-the-art exact algorithms in the literature are based on the generation
of a possibly exponential number of cuts. As each cut separation involves the
resolution of an NP-hard classical optimization problem, the size of the
instances that can be solved efficiently is relatively small. To smooth this
issue, we present a modeling technique for interval robust-hard problems in the
context of a heuristic framework. The heuristic obtains feasible solutions by
exploring dual information of a linearly relaxed model associated with the
classical optimization problem counterpart. Computational experiments for
interval data min-max regret versions of the restricted shortest path problem
and the set covering problem show that our heuristic is able to find optimal or
near-optimal solutions and also improves the primal bounds obtained by a
state-of-the-art exact algorithm and a 2-approximation procedure for interval
data min-max regret problems
Regret Models and Preprocessing Techniques for Combinatorial Optimization under Uncertainty
Ph.DDOCTOR OF PHILOSOPH
Robust solutions to single and multi-period machine layout problems with interval flows
Ankara : Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 1997.Thesis (Master's) -- Bilkent University, 1997.Includes bibliographical references leaves 47-50.Design clecisous are genevcUly given in the early stages when there is a great
deal of inexactness in the data gathered. In this study, we consider the plant Uiyout
problem witli inexactness in material flow quantities with the aim of designing robust
layouts. Material flow quantities are assumed to lie in a priori specified intervals
based, for example, on low ¿md high demands. The robustness criterion we use is to
minimize the maximum I’egret. We extend our work to the multi-period case where
a distinction is made between reversible and irreversible layout decisions.Tüfekçi, Özgür AtillaM.S
A fast ILP-based Heuristic for the robust design of Body Wireless Sensor Networks
We consider the problem of optimally designing a body wireless sensor
network, while taking into account the uncertainty of data generation of
biosensors. Since the related min-max robustness Integer Linear Programming
(ILP) problem can be difficult to solve even for state-of-the-art commercial
optimization solvers, we propose an original heuristic for its solution. The
heuristic combines deterministic and probabilistic variable fixing strategies,
guided by the information coming from strengthened linear relaxations of the
ILP robust model, and includes a very large neighborhood search for reparation
and improvement of generated solutions, formulated as an ILP problem solved
exactly. Computational tests on realistic instances show that our heuristic
finds solutions of much higher quality than a state-of-the-art solver and than
an effective benchmark heuristic.Comment: This is the authors' final version of the paper published in G.
Squillero and K. Sim (Eds.): EvoApplications 2017, Part I, LNCS 10199, pp.
1-17, 2017. DOI: 10.1007/978-3-319-55849-3\_16. The final publication is
available at Springer via http://dx.doi.org/10.1007/978-3-319-55849-3_1
Information and decentralization in inventory, supply chain, and transportation systems
Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2006.Includes bibliographical references (p. 199-213).This thesis investigates the impact of lack of information and decentralization of decision-making on the performance of inventory, supply chain, and transportation systems. In the first part of the thesis, we study two extensions of a classic single-item, single-period inventory control problem: the "newsvendor problem." We first analyze the newsvendor problem when the demand distribution is only partially specified by some moments and shape parameters. We determine order quantities that are robust, in the sense that they minimize the newsvendor's maximum regret about not acting optimally, and we compute the maximum value of additional information. The minimax regret approach is scalable to solve large practical problems, such as those arising in network revenue management, since it combines an efficient solution procedure with very modest data requirements. We then analyze the newsvendor problem when the inventory decision-making is decentralized. In supply chains, inventory decisions often result from complex negotiations among supply partners and might therefore lead to a loss of efficiency (in terms of profit loss).(cont.) We quantify the loss of efficiency of decentralized supply chains that use price-only contracts under the following configurations: series, assembly, competitive procurement, and competitive distribution. In the second part of the thesis, we characterize the dynamic nature of traffic equilibria in a transportation network. Using the theory of kinematic waves, we derive an analytical model for traffic delays capturing the first-order traffic dynamics and the impact of shock waves. We then incorporate the travel-time model within a dynamic user equilibrium setting and illustrate how the model applies to solve a large network assignment problem.by Guillaume Roels.Ph.D
Algorithms for weighted coloring problems
In this thesis, we studied a generalization of vertex coloring problem (VCP). A classical VCP is an assignment of colors to the vertices of a given graph such that no two adjacent vertices receive the same color. The objective is to find a coloring with the minimum number of colors. In the first part of the thesis, we studied the weighted version of the problem, where vertices have non-negative weights. In a weighted vertex coloring problem (WVCP) the cost of each color depends on the weights of the vertices assigned to that color and equals the maximum of these weights. Furthermore, in WVCP, the adjacent vertices are assigned different colors, and the objective is to minimize the total cost of all the colors used. We studied WVCP and proposed an O(n^2 log n) time algorithm for binary trees. Additionally, we studied WVCP in cactus paths. We proposed sub-quadratic and quadratic time algorithms for cactus paths.
We studied a min-max regret version of the robust optimization where the weight of each vertex v is in the interval [w v , w v ]. The objective of is to find a coloring that has the minimum regret value. We proposed a linear time algorithm for robust coloring on bipartite graphs with uniform upper bound and arbitrary lower bound weights on the vertices. We also gave an integer linear programming (ILP) for the robust weighted vertex coloring problem (RWVCP). We solved a relaxation of the ILP formulation using column generation. We also gave an algorithm based on the branch and price method. Lastly, we performed experiments to study the quality of our algorithms.School of graduate studies, University of Lethbridge, PIMS, NSER
Models and algorithms for deterministic and robust discrete time/cost trade-off problems
Ankara : The Department of Management, Bilkent University, 2008.Thesis (Ph.D.) -- Bilkent University, 2008.Includes bibliographical references leaves 136-145Projects are subject to various sources of uncertainties that often negatively
impact activity durations and costs. Therefore, it is of crucial importance to develop
effective approaches to generate robust project schedules that are less vulnerable to
disruptions caused by uncontrollable factors. This dissertation concentrates on robust
scheduling in project environments; specifically, we address the discrete time/cost
trade-off problem (DTCTP).
Firstly, Benders Decomposition based exact algorithms to solve the deadline
and the budget versions of the deterministic DTCTP of realistic sizes are proposed.
We have included several features to accelerate the convergence and solve large
instances to optimality. Secondly, we incorporate uncertainty in activity costs. We
formulate robust DTCTP using three alternative models. We develop exact and
heuristic algorithms to solve the robust models in which uncertainty is modeled via
interval costs. The main contribution is the incorporation of uncertainty into a
practically relevant project scheduling problem and developing problem specific
solution approaches. To the best of our knowledge, this research is the first
application of robust optimization to DTCTP.
Finally, we introduce some surrogate measures that aim at providing an
accurate estimate of the schedule robustness. The pertinence of proposed measures is
assessed through computational experiments. Using the insight revealed by the
computational study, we propose a two-stage robust scheduling algorithm.
Furthermore, we provide evidence that the proposed approach can be extended to
solve a scheduling problem with tardiness penalties and earliness rewards.Hazır, ÖncüPh.D
Pilot3 D2.1 - Trade-off report on multi criteria decision making techniques
This deliverable describes the decision making approach that will be followed in Pilot3.
It presents a domain-driven analysis of the characteristics of Pilot3 objective function and optimisation framework. This has been done considering inputs from deliverable D1.1 - Technical Resources and Problem definition, from interaction with the Topic Manager, but most importantly from a dedicated Advisory Board workshop and follow-up consultation. The Advisory Board is formed by relevant stakeholders including airlines, flight operation experts, pilots, and other relevant ATM experts.
A review of the different multi-criteria decision making techniques available in the literature is presented. Considering the domain-driven characteristics of Pilot3 and inputs on how the tool could be used by airlines and crew. Then, the most suitable methods for multi-criteria optimisation are selected for each of the phases of the optimisation framework
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