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 4OR: A Quarterly Journal of Operations ResearchJournal Prestige (SJR): 0.825 Citation Impact (citeScore): 1Number of Followers: 10      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1619-4500 - ISSN (Online) 1614-2411 Published by Springer-Verlag  [2350 journals]
• Quasi-Newton methods for multiobjective optimization problems
Pages: 261 - 294
Abstract: Abstract This work is an attempt to develop multiobjective versions of some well-known single objective quasi-Newton methods, including BFGS, self-scaling BFGS (SS-BFGS), and the Huang BFGS (H-BFGS). A comprehensive and comparative study of these methods is presented in this paper. The Armijo line search is used for the implementation of these methods. The numerical results show that the Armijo rule does not work the same way for the multiobjective case as for the single objective case, because, in this case, it imposes a large computational effort and significantly decreases the speed of convergence in contrast to the single objective case. Hence, we consider two cases of all multi-objective versions of quasi-Newton methods: in the presence of the Armijo line search and in the absence of any line search. Moreover, the convergence of these methods without using any line search under some mild conditions is shown. Also, by introducing a multiobjective subproblem for finding the quasi-Newton multiobjective search direction, a simple representation of the Karush–Kuhn–Tucker conditions is derived. The H-BFGS quasi-Newton multiobjective optimization method provides a higher-order accuracy in approximating the second order curvature of the problem functions than the BFGS and SS-BFGS methods. Thus, this method has some benefits compared to the other methods as shown in the numerical results. All mentioned methods proposed in this paper are evaluated and compared with each other in different aspects. To do so, some well-known test problems and performance assessment criteria are employed. Moreover, these methods are compared with each other with regard to the expended CPU time, the number of iterations, and the number of function evaluations.
PubDate: 2018-09-01
DOI: 10.1007/s10288-017-0363-1
Issue No: Vol. 16, No. 3 (2018)

• Compact linearization for binary quadratic problems subject to assignment
constraints
• Authors: Sven Mallach
Pages: 295 - 309
Abstract: Abstract We introduce and prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints that has been proposed by Liberti (4OR 5(3):231–245, 2007, https://doi.org/10.1007/s10288-006-0015-3). The new conditions resolve inconsistencies that can occur when the original method is used. We also present a mixed-integer linear program to compute a minimally sized linearization. When all the assignment constraints have non-overlapping variable support, this program is shown to have a totally unimodular constraint matrix. Finally, we give a polynomial-time combinatorial algorithm that is exact in this case and can be used as a heuristic otherwise.
PubDate: 2018-09-01
DOI: 10.1007/s10288-017-0364-0
Issue No: Vol. 16, No. 3 (2018)

• Optimality and duality in constrained interval-valued optimization
• Authors: Do Van Luu; Tran Thi Mai
Pages: 311 - 337
Abstract: Abstract Fritz John and Karush–Kuhn–Tucker necessary conditions for local LU-optimal solutions of the constrained interval-valued optimization problems involving inequality, equality and set constraints in Banach spaces in terms of convexificators are established. Under suitable assumptions on the generalized convexity of objective and constraint functions, sufficient conditions for LU-optimal solutions are given. The dual problems of Mond–Weir and Wolfe types are studied together with weak and strong duality theorems for them.
PubDate: 2018-09-01
DOI: 10.1007/s10288-017-0369-8
Issue No: Vol. 16, No. 3 (2018)

• A supply chain perspective of synchromodality to increase the
sustainability of freight transportation
• Authors: Chuanwen Dong
Pages: 339 - 340
PubDate: 2018-09-01
DOI: 10.1007/s10288-017-0367-x
Issue No: Vol. 16, No. 3 (2018)

• The multiplicative weights update algorithm for mixed integer nonlinear
programming: theory, applications, and limitations
• Authors: Luca Mencarelli
Pages: 341 - 342
PubDate: 2018-09-01
DOI: 10.1007/s10288-018-0372-8
Issue No: Vol. 16, No. 3 (2018)

• Two-agent single-machine scheduling with cumulative deterioration
• Authors: Ren-Xia Chen; Shi-Sheng Li
Abstract: Abstract We address cumulative deterioration scheduling in which two agents compete to perform their respective jobs on a single machine. By cumulative deterioration we mean that the actual processing time of any job of the two agents is a linear increasing function of the total normal processing times of already processed jobs. Each agent desires to optimize some scheduling criterion that depends on the completion times of its own jobs only. We study several scheduling problems arising from different combinations of some regular scheduling criteria, including the maximum cost (embracing lateness and makespan as its special cases), the total completion time, and the (weighted) number of tardy jobs. The aim is to find an optimal schedule that minimizes the objective value of one agent while maintaining the objective value of the other agent not exceeding a fixed upper bound. For each problem under study, we design either a polynomial-time or a pseudo-polynomial-time algorithm to solve it.
PubDate: 2018-09-19
DOI: 10.1007/s10288-018-0388-0

• Recent studies of agent incentives in internet resource allocation and
pricing
• Authors: Yukun Cheng; Xiaotie Deng; Dominik Scheder
Abstract: Abstract Market makers choose and design market rules to serve certain objectives, such as to maximize revenue from the sales in the case of a single seller and multiple buyers. Given such rules, market participants play against each other to maximize their utility function values on goods acquired, possibly by hiding or misrepresenting their information needed in the implementation of market rules. Today’s Internet economy has changed the information collection process and may make some of the assumptions of market rule implementation obsolete. Here we make a fresh review of works on this challenge on the Internet where new economic systems operate.
PubDate: 2018-08-17
DOI: 10.1007/s10288-018-0385-3

• Cutting stock problems with nondeterministic item lengths: a new approach
to server consolidation
• Authors: John Martinovic; Markus Hähnel; Guntram Scheithauer; Waltenegus Dargie; Andreas Fischer
Abstract: Abstract Based on an application in the field of server consolidation, we consider the one-dimensional cutting stock problem with nondeterministic item lengths. After a short introduction to the general topic we investigate the case of normally distributed item lengths in more detail. Within this framework, we present two lower bounds as well as two heuristics to obtain upper bounds, where the latter are either based on a related (ordinary) cutting stock problem or an adaptation of the first fit decreasing heuristic to the given stochastical context. For these approximation techniques, dominance relations are discussed, and theoretical performance results are stated. As a main contribution, we develop a characterization of feasible patterns by means of one linear and one quadratic inequality. Based on this, we derive two exact modeling approaches for the nondeterministic cutting stock problem, and provide results of numerical simulations.
PubDate: 2018-07-18
DOI: 10.1007/s10288-018-0384-4

• Aggregated formulations, exact and heuristic algorithms for pickup and
delivery routing problems
• Authors: Bruno P. Bruck
PubDate: 2018-07-06
DOI: 10.1007/s10288-018-0382-6

• A note on posterior tight worst-case bounds for longest processing time
schedules
• Authors: Johnny C. Ho; Ivar Massabò; Giuseppe Paletta; Alex J. Ruiz-Torres
Abstract: Abstract This note proposes and analyzes a posterior tight worst-case bound for the longest processing time (LPT) heuristic for scheduling independent jobs on identical parallel machines with the objective of minimizing the makespan. It makes natural remarks on the well-known posterior worst-case bounds, and shows that the proposed bound can complement the well-known posterior bounds to synergistically achieve a better posterior worst-case bound for the LPT heuristic. Moreover, it gives some insight on LPT asymptotical optimality.
PubDate: 2018-06-16
DOI: 10.1007/s10288-018-0381-7

• Tactical production planning for physical and financial flows of supply
chain in a multi-site context
• Authors: Yuan Bian
PubDate: 2018-06-15
DOI: 10.1007/s10288-018-0379-1

• Evaluating groups with the generalized Shapley value
• Authors: Ramón Flores; Elisenda Molina; Juan Tejada
Abstract: Abstract Following the original interpretation of the Shapley value as a priori evaluation of the prospects of a player in a multi-person interaction situation, we intend to apply the Shapley generalized value (introduced formally in Marichal et al. in Discrete Appl Math 155:26–43, 2007) as a tool for the assessment of a group of players that act as a unit in a coalitional game. We propose an alternative axiomatic characterization which does not use a direct formulation of the classical efficiency property. Relying on this valuation, we also analyze the profitability of a group. We motivate this use of the Shapley generalized value by means of two relevant applications in which it is used as an objective function by a decision maker who is trying to identify an optimal group of agents in a framework in which agents interact and the attained benefit can be modeled by means of a transferable utility game.
PubDate: 2018-06-14
DOI: 10.1007/s10288-018-0380-8

• A Branch & Price algorithm for the minimum cost clique cover problem
in max-point tolerance graphs
• Authors: Luciano Porretta; Daniele Catanzaro; Bjarni V. Halldórsson; Bernard Fortz
Abstract: Abstract A point-interval $$(I_v, p_v)$$ is a pair constituted by an interval $$I_v$$ of $${\mathbb {R}}$$ and a point $$p_v \in I_v$$ . A graph $$G=(V,E)$$ is a Max-Point-Tolerance (MPT) graph if each vertex $$v\in V$$ can be mapped to a point-interval in such a way that (u, v) is an edge of G iff $$I_u \cap I_v \supseteq \{p_u, p_v\}$$ . MPT graphs constitute a superclass of interval graphs and naturally arise in genetic analysis as a way to represent specific relationships among DNA fragments extracted from a population of individuals. One of the most important applications of MPT graphs concerns the search for an association between major human diseases and chromosome regions from patients that exhibit loss of heterozygosity events. This task can be formulated as a minimum cost clique cover problem in a MPT graph and gives rise to a $${{\mathcal {N}}}{{\mathcal {P}}}$$ -hard combinatorial optimization problem known in the literature as the Parsimonious Loss of Heterozygosity Problem (PLOHP). In this article, we investigate ways to speed up the best known exact solution algorithm for the PLOHP as well as techniques to enlarge the size of the instances that can be optimally solved. In particular, we present a Branch&Price algorithm for the PLOHP and we develop a number of preprocessing techniques and decomposition strategies to dramatically reduce the size of its instances. Computational experiments show that the proposed approach is 10–30 $$\times$$ faster than previous approaches described in the literature, and suggest new directions for the development of future exact solution approaches that may prove of fundamental assistance in practice.
PubDate: 2018-06-07
DOI: 10.1007/s10288-018-0377-3

• Passenger robust timetables for dense railway networks
• Authors: Sofie Burggraeve
PubDate: 2018-06-01
DOI: 10.1007/s10288-017-0358-y

• Design and management of freight transport networks: intermodal transport
and externalities
• Authors: Martine Mostert
PubDate: 2018-06-01
DOI: 10.1007/s10288-017-0359-x

• Nonlinear optimization and support vector machines
• Abstract: Abstract Support Vector Machine (SVM) is one of the most important class of machine learning models and algorithms, and has been successfully applied in various fields. Nonlinear optimization plays a crucial role in SVM methodology, both in defining the machine learning models and in designing convergent and efficient algorithms for large-scale training problems. In this paper we present the convex programming problems underlying SVM focusing on supervised binary classification. We analyze the most important and used optimization methods for SVM training problems, and we discuss how the properties of these problems can be incorporated in designing useful algorithms.
PubDate: 2018-06-01
DOI: 10.1007/s10288-018-0378-2

• The inventory replenishment planning and staggering problem: a
bi-objective approach
• Authors: Fayez F. Boctor; Marie-Claude Bolduc
Abstract: Abstract To the best of our knowledge, this paper is the first one to suggest formulating the inventory replenishment problem as a bi-objective decision problem where, in addition to minimizing the sum of order and inventory holding costs, we should minimize the required storage space. Also, it develops two solution methods, called the exploratory method (EM) and the two-population evolutionary algorithm (TPEA), to solve the problem. The proposed methods generate a near-Pareto front of solutions with respect to the considered objectives. As the inventory replenishment problem have never been formulated as a bi-objective problem and as the literature does not provide any method to solve the considered bi-objective problem, we compared the results of the EM to three versions of the TPEA. The results obtained suggest that although the TPEA produces good near-Pareto solutions, the decision maker can apply a combination of both methods and choose among all the obtained solutions.
PubDate: 2018-06-01
DOI: 10.1007/s10288-017-0362-2

• New optimality conditions for unconstrained vector equilibrium problem in
terms of contingent derivatives in Banach spaces
• Authors: Tran Van Su
Abstract: Abstract This article presents necessary and sufficient optimality conditions for weakly efficient solution, Henig efficient solution, globally efficient solution and superefficient solution of vector equilibrium problem without constraints in terms of contingent derivatives in Banach spaces with stable functions. Using the steadiness and stability on a neighborhood of optimal point, necessary optimality conditions for efficient solutions are derived. Under suitable assumptions on generalized convexity, sufficient optimality conditions are established. Without assumptions on generalized convexity, a necessary and sufficient optimality condition for efficient solutions of unconstrained vector equilibrium problem is also given. Many examples to illustrate for the obtained results in the paper are derived as well.
PubDate: 2018-06-01
DOI: 10.1007/s10288-017-0360-4

• Nondominated Nash points: application of biobjective mixed integer
programming
• Authors: Hadi Charkhgard; Martin Savelsbergh; Masoud Talebian
Abstract: Abstract We study the connection between biobjective mixed integer linear programming and normal form games with two players. We first investigate computing Nash equilibria of normal form games with two players using single-objective mixed integer linear programming. Then, we define the concept of efficient (Pareto optimal) Nash equilibria. This concept is precisely equivalent to the concept of efficient solutions in multi-objective optimization, where the solutions are Nash equilibria. We prove that the set of all points in the payoff (or objective) space of a normal form game with two players corresponding to the utilities of players in an efficient Nash equilibrium, the so-called nondominated Nash points, is finite. We demonstrate that biobjective mixed integer linear programming, where the utility of each player is an objective function, can be used to compute the set of nondominated Nash points. Finally, we illustrate how the nondominated Nash points can be used to determine the disagreement point of a bargaining problem.
PubDate: 2018-06-01
DOI: 10.1007/s10288-017-0354-2

• Mathematical models and decomposition algorithms for cutting and packing
problems
• Authors: Maxence Delorme
PubDate: 2017-12-02
DOI: 10.1007/s10288-017-0365-z

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