Browsing by Subject "Branch and bound"

Now showing 1 - 7 of 7

Open Access
Bicriteria multiresource generalized assignment problem
(John Wiley & Sons, 2014) Karsu, O.; Azizoglu, M.
In this study,we consider a bicriteria multiresource generalized assignment problem. Our criteria are the total assignment load and maximum assignment load over all agents. We aim to generate all nondominated objective vectors and the corresponding efficient solutions. We propose several lower and upper bounds and use them in our optimization and heuristic algorithms. The computational results have shown the satisfactory behaviors of our approaches.
Open Access
A branch-and-bound algorithm for team formation on social networks
(Institute for Operations Research and the Management Sciences (INFORMS), 2021) Berktaş, Nihal; Yaman, Hande
The team formation problem (TFP) aims to construct a capable team that can communicate and collaborate effectively. The cost of communication is quantified using the proximity of the potential members in a social network. We study a TFP with two measures for communication effectiveness; namely, we minimize the sum of communication costs, and we impose an upper bound on the largest communication cost. This problem can be formulated as a constrained quadratic set covering problem. Our experiments show that a general purpose solver is capable of solving small and medium-sized instances to optimality. We propose a branch-and-bound algorithm to solve larger sizes: we reformulate the problem and relax it in such a way that it decomposes into a series of linear set covering problems, and we impose the relaxed constraints through branching. Our computational experiments show that the algorithm is capable of solving large-size instances, which are intractable for the solver. Summary of Contribution: This paper presents an exact algorithm for the Team Formation Problem (TFP), in which the aim is, given a project and its required skills, to construct a capable team that can communicate and collaborate effectively. This combinatorial opti mization problem is modeled as a quadratic set covering problem. The study provides a novel branch-and-bound algorithm where a reformulation of the problem is relaxed so that it decomposes into a series of linear set covering problems and the relaxed constraints are imposed through branching. The algorithm is able to solve instances that are intractable for commercial solvers. The study illustrates an efficient usage of algorithmic methods and modelling techniques for an operations research problem. It contributes to the field of computational optimization by proposing a new application as well as a new algorithm to solve a quadratic version of a classical combinatorial optimization problem.
Open Access
A finite concave minimization algorithm using branch and bound and neighbor generation
(Springer, 1994) Benson, H. P.; Sayin, S.
In this article we present a new finite algorithm for globally minimizing a concave function over a compact polyhedron. The algorithm combines a branch and bound search with a new process called neighbor generation. It is guaranteed to find an exact, extreme point optimal solution, does not require the objective function to be separable or even analytically defined, requires no nonlinear computations, and requires no determinations of convex envelopes or underestimating functions. Linear programs are solved in the branch and bound search which do not grow in size and differ from one another in only one column of data. Some preliminary computational experience is also presented.
Open Access
Match-up scheduling under a machine breakdown
(Elsevier, 1999) Aktürk, M. S.; Görgülü, E.
When a machine breakdown forces a modified flow shop (MFS) out of the prescribed state, the proposed strategy reschedules part of the initial schedule to match up with the preschedule at some point. The objective is to create a new schedule that is consistent with the other production planning decisions like material flow, tooling and purchasing by utilizing the time critical decision making concept. We propose a new rescheduling strategy and a match-up point determination procedure through a feedback mechanism to increase both the schedule quality and stability. The proposed approach is compared with alternative reactive scheduling methods under different experimental settings. © 1999 Elsevier Science B.V. All rights reserved.
Open Access
Optimization of transportation requirements in the deployment of military units
(Elsevier, 2007) Akgün, İ.; Tansel, B. Ç.
We study the deployment planning problem (DPP) that may roughly be defined as the problem of the planning of the physical movement of military units, stationed at geographically dispersed locations, from their home bases to their designated destinations while obeying constraints on scheduling and routing issues as well as on the availability and use of various types of transportation assets that operate on a multimodal transportation network. The DPP is a large-scale real-world problem for which analytical models do not exist. We propose a model for solving the problem and develop a solution methodology which involves an effective use of relaxation and restriction that significantly speeds up a CPLEX-based branch-and-bound. The solution times for intermediate-sized problems are around 1 h at maximum, whereas it takes about a week in the Turkish Armed Forces to produce a suboptimal feasible solution based on trial-and-error methods. The proposed model can be used to evaluate and assess investment decisions in transportation infrastructure and transportation assets as well as to plan and execute cost-effective deployment operations at different levels of planning.
Open Access
Optimization of transportation requirements in the deployment of military units
(2005) Akgün, İbrahim
We study the deployment planning problem (DPP) that may roughly be defined as the problem of the planning of the physical movement of military units, stationed at geographically dispersed locations, from their home bases to their designated destinations while obeying constraints on scheduling and routing issues as well as on the availability and use of various types of transportation assets that operate on a multimodal transportation network. The DPP is a large-scale real-world problem for which no analytical models are existent. In this study, we define the problem in detail and analyze it with respect to the academic literature. We propose three mixed integer programming models with the objectives of cost, lateness (the difference between the arrival time of a unit and its earliest allowable arrival time at its destination), and tardiness (the difference between the arrival time of a unit and its latest arrival time at its destination) minimization to solve the problem. The cost-minimization model minimizes total transportation cost of a deployment and is of use for investment decisions in transportation resources during peacetime and for deployment planning in cases where the operation is not imminent and there is enough time to do deliberate planning that takes costs into account. The lateness and tardiness minimization models are of min-max type and are of use when quick deployment is of utmost concern. The lateness minimization model is for cases when the given fleet of transportation assets is sufficient to deploy units within their allowable time windows and the tardiness minimization model is for cases when the given fleet is not sufficient. We propose a solution methodology for solving all three models. The solution methodology involves an effective use of relaxation and restriction that significantly speeds up a CPLEX-based branchand-bound. The solution times for intermediate sized problems are around one hour at maximum for cost and lateness minimization models and around two hours for the tardiness minimization model. Producing a suboptimal feasible solution based on trial and error methods for a problem of the same size takes about a week in the current practice in the Turkish Armed Forces. We also propose a heuristic that is essentially based on solving the models incrementally rather than at one step. Computational results show that the heuristic can be used to find good feasible solutions for the models. We conclude the study with comments on how to use the models in the realworld.
Open Access
Provably optimal sparse solutions to overdetermined linear systems with non-negativity constraints in a least-squares sense by implicit enumeration
(Springer, 2021-12) Aktaş, Fatih Selim; Ekmekcioglu, Ömer; Pinar, Mustafa Çelebi
Computing sparse solutions to overdetermined linear systems is a ubiquitous problem in several fields such as regression analysis, signal and image processing, information theory and machine learning. Additional non-negativity constraints in the solution are useful for interpretability. Most of the previous research efforts aimed at approximating the sparsity constrained linear least squares problem, and/or finding local solutions by means of descent algorithms. The objective of the present paper is to report on an efficient and modular implicit enumeration algorithm to find provably optimal solutions to the NP-hard problem of sparsity-constrained non-negative least squares. We focus on the problem where the system is assumed to be over-determined where the matrix has full column rank. Numerical results with real test data as well as comparisons of competing methods and an application to hyperspectral imaging are reported. Finally, we present a Python library implementation of our algorithm.