Showing papers on "Assignment problem published in 2010"
01 Jan 2010
TL;DR: This paper has always been one of my favorite “children,” combining as it does elements of the duality of linear programming and combinatorial tools from graph theory.
Abstract: This paper has always been one of my favorite “children,” combining as it does elements of the duality of linear programming and combinatorial tools from graph theory. It may be of some interest to tell the story of its origin.
3,108 citations
14 May 2010
TL;DR: A solution to the combinatorial assignment problem by proposing two new criteria of outcome fairness, the maximin share guarantee and envy bounded by a single good, which weaken well-known criteria to accommodate indivisibilities and formalize why dictatorships are unfair.
Abstract: Impossibility theorems suggest that the only efficient and strategyproof mechanisms for the problem of combinatorial assignment - e.g., assigning schedules of courses to students - are dictatorships. Dictatorships are mostly rejected as unfair: for any two agents, one chooses all their objects before the other chooses any. Any solution will involve compromise amongst efficiency, incentive and fairness considerations.This paper proposes a solution to the combinatorial assignment problem. It is developed in four steps. First, I propose two new criteria of outcome fairness, the maximin share guarantee and envy bounded by a single good, which weaken well-known criteria to accommodate indivisibilities; the criteria formalize why dictatorships are unfair. Second, I prove existence of an approximation to Competitive Equilibrium from Equal Incomes in which (i) incomes are unequal but arbitrarily close together; (ii) the market clears with error, which approaches zero in the limit and is small for realistic problems. Third, I show that this Approximate CEEI satisfies the fairness criteria. Last, I define a mechanism based on Approximate CEEI that is strategyproof for the zero-measure agents economists traditionally regard as price takers. The proposed mechanism is calibrated on real data and is compared to alternatives from theory and practice: all other known mechanisms are either manipulable by zero-measure agents or unfair ex-post, and most are both manipulable and unfair.
421 citations
TL;DR: An Improved Genetic Algorithm to solve the Distributed and Flexible Job-shop Scheduling problem is proposed and has been compared with other algorithms for distributed scheduling and evaluated with satisfactory results on a large set of distributed-and-flexible scheduling problems derived from classical job-shop scheduling benchmarks.
252 citations
TL;DR: In this article, a heuristic algorithm which combines tabu search methods and mathematical programming techniques is proposed to solve the problem of berth assignment and quay crane assignment in container terminals, which aims to maximize the total value of chosen QC profiles and minimize the housekeeping costs generated by transshipment flows between ships.
Abstract: In this paper we integrate at the tactical level two decision problems arising in container terminals: the berth allocation problem, which consists of assigning and scheduling incoming ships to berthing positions, and the quay crane assignment problem, which assigns to incoming ships a certain QC profile (i.e. number of quay cranes per working shift). We present two formulations: a mixed integer quadratic program and a linearization which reduces to a mixed integer linear program. The objective function aims, on the one hand, to maximize the total value of chosen QC profiles and, on the other hand, to minimize the housekeeping costs generated by transshipment flows between ships. To solve the problem we developed a heuristic algorithm which combines tabu search methods and mathematical programming techniques. Computational results on instances based on real data are presented and compared to those obtained through a commercial solver.
198 citations
TL;DR: A bi-level network optimization model is formulated, in which the upper level aims at optimizing the network evacuation performance subject to the lane-reversal and crossing-elimination constraints and the lower level conveys a cell transmission-based dynamic traffic assignment problem.
Abstract: This paper discusses a dynamic evacuation network optimization problem that incorporates lane reversal and crossing elimination strategies. These two lane-based planning strategies complement one another by increasing capacity in specific directions through the evacuation network. A bi-level network optimization model is formulated, in which the upper level aims at optimizing the network evacuation performance subject to the lane-reversal and crossing-elimination constraints and the lower level conveys a cell transmission-based dynamic traffic assignment problem. An integrated Lagrangian relaxation and tabu search method is devised for approximating optimal problem solutions through an iterative optimization-evaluation process. The numerical results of implementing the developed modeling and solution approach to a synthetic network and a real-world example application justify its theoretical and practical value.
196 citations
TL;DR: This work proposes a set of simple iterated greedy local search based metaheuristics that produce solutions of very good quality in a very short amount of time that are better than the current state-of-the-art methodologies by a statistically significant margin.
163 citations
TL;DR: This paper presents the Tree of Hubs Location Problem, a network hub location problem with single assignment where a fixed number of hubs have to be located, with the particularity that it is required that the hubs are connected by means of a tree.
150 citations
TL;DR: Using the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D), the DPAP is decomposed into a set of scalar subproblems that are classified based on their objective preference and tackled in parallel by using neighborhood information and problem-specific evolutionary operators, in a single run.
125 citations
TL;DR: The results suggest that the MOGA can help correct suboptimal class responsibility assignment decisions and perform far better than simpler alternative heuristics such as hill climbing and a single-objective GA.
Abstract: In the context of object-oriented analysis and design (OOAD), class responsibility assignment is not an easy skill to acquire. Though there are many methodologies for assigning responsibilities to classes, they all rely on human judgment and decision making. Our objective is to provide decision-making support to reassign methods and attributes to classes in a class diagram. Our solution is based on a multi-objective genetic algorithm (MOGA) and uses class coupling and cohesion measurement for defining fitness functions. Our MOGA takes as input a class diagram to be optimized and suggests possible improvements to it. The choice of a MOGA stems from the fact that there are typically many evaluation criteria that cannot be easily combined into one objective, and several alternative solutions are acceptable for a given OO domain model. Using a carefully selected case study, this paper investigates the application of our proposed MOGA to the class responsibility assignment problem, in the context of object-oriented analysis and domain class models. Our results suggest that the MOGA can help correct suboptimal class responsibility assignment decisions and perform far better than simpler alternative heuristics such as hill climbing and a single-objective GA.
125 citations
TL;DR: A generalization of the two phase method to solve multi-objective integer programmes with p>2 objectives to the assignment problem with three objectives, where experimental results show the efficiency of the method.
113 citations
TL;DR: Computational experiments show that Absalom is a very promising exact solution approach although the additional assignment restrictions complicate the problem considerably and necessitate a relaxation of some components of Salome.
TL;DR: Results suggest that swapping flows between shortest and longest route segments consistently outperforms other RMP solution techniques, and the relative performance of the algorithms is consistent with the analysis.
Abstract: This paper studies a class of bush-based algorithms (BA) for the user equilibrium (UE) traffic assignment problem, which promise to produce highly precise solutions by exploiting acyclicity of UE flows. Each of the two building blocks of BA, namely the construction of acyclic sub-networks (bush) and the solution of restricted master problems (RMP), is examined and further developed. Four Newton-type algorithms for solving RMP, which can be broadly categorized as route flow and origin flow based, are presented, of which one is newly developed in this paper. Similarities and differences between these algorithms, as well as the relevant implementation issues are discussed in great details. A comprehensive numerical study is conducted using both real and randomly generated networks, which reveals that the relative performance of the algorithms is consistent with the analysis. In particular, the results suggest that swapping flows between shortest and longest route segments consistently outperforms other RMP solution techniques.
TL;DR: A successful heuristic approach is presented, based on an ILP formulation in which the seat requirement constraints are stated in a “strong” form, derived from the description of the convex hull of the variant of the knapsack polytope arising when the sum of the variables is restricted not to exceed two.
Abstract: We face a real-world train-unit assignment problem for an operator running trains in a regional area. Given a set of timetabled train trips, each with a required number of passenger seats, and a set of train units, each with a given number of available seats, the problem calls for an assignment of the train units to the trips, possibly combining more than one train unit for a given trip, that fulfills the seat requests. With respect to analogous case studies previously faced in the literature, ours is characterized by the fairly large number of distinct train-unit types available (in addition to the fairly large number of trips to be covered). As a result, although there is a wide margin of improvement over the solution used by the practitioners (as our results show), even only finding a solution of the same value is challenging in practice. We present a successful heuristic approach, based on an ILP formulation in which the seat requirement constraints are stated in a “strong” form, derived from the description of the convex hull of the variant of the knapsack polytope arising when the sum of the variables is restricted not to exceed two. Computational results on real-world instances are reported, showing the effectiveness of the proposed approach.
TL;DR: In this article, a variable neighborhood search (VNS) algorithm is proposed to solve the flexible job shop scheduling problem (FJSP), which allows an operation of each job to be executed by any machine out of a set of available machines.
Abstract: The flexible job-shop scheduling problem (FJSP) is a generalisation of the classical job-shop scheduling problem which allows an operation of each job to be executed by any machine out of a set of available machines. FJSP consists of two sub-problems which are assigning each operation to a machine out of a set of capable machines (routing sub-problem) and sequencing the assigned operations on the machines (sequencing sub-problem). This paper proposes a variable neighbourhood search (VNS) algorithm that solves the FJSP to minimise makespan. In the process of the presented algorithm, various neighbourhood structures related to assignment and sequencing problems are used for generating neighbouring solutions. To compare our algorithm with previous ones, an extensive computational study on 181 benchmark problems has been conducted. The results obtained from the presented algorithm are quite comparable to those obtained by the best-known algorithms for FJSP.
TL;DR: This paper studies the dynamic user optimal (DUO) traffic assignment problem considering simultaneous route and departure time choice, formulated as a discrete variational inequality (DVI), with an embeded LWR-consistent mesoscopic dynamic network loading model to encapsulate traffic dynamics.
Abstract: This paper studies the dynamic user optimal (DUO) traffic assignment problem considering simultaneous route and departure time choice. The DUO problem is formulated as a discrete variational inequality (DVI), with an embeded LWR-consistent mesoscopic dynamic network loading (DNL) model to encapsulate traffic dynamics. The presented DNL model is capable of capturing realistic traffic phenomena such as queue spillback. Various VI solution algorithms, particularly those based on feasible directions and a line search, are applied to solve the formulated DUO problem. Two examples are constructed to check equilibrium solutions obtained from numerical algorithms, to compare the performance of the algorithms, and to study the impacts of traffic interacts across multiple links on equilibrium solutions.
TL;DR: A novel global harmony search algorithm (NGHS) is used to solve the task assignment problem, and the NGHS algorithm has demonstrated higher efficiency than the improved harmonysearch algorithm (IHS) on finding the near optimal task assignment.
TL;DR: In this article, the authors considered a single-machine scheduling problem with the effects of learning and deterioration and showed that the problem remains polynomially solvable under the proposed model.
01 Jun 2010
TL;DR: A distributed version of the Hungarian Method for the assignment problem is developed and comes up with a global optimum solution in O(n3) cumulative time (O(n2) for each robot), with O( n3) number of messages exchanged among the n robots.
Abstract: In this work we address the Multi-Robot Task Allocation Problem (MRTA). We assume that the decision making environment is decentralized with as many decision makers (agents) as the robots in the system. To solve this problem, we developed a distributed version of the Hungarian Method for the assignment problem. The robots autonomously perform different substeps of the Hungarian algorithm on the base of the individual and the information received through the messages from the other robots in the system. It is assumed that each robot agent has an information regarding its distance from the targets in the environment. The inter-robot communication is performed over a connected dynamic communication network and the solution to the assignment problem is reached without any common coordinator or a shared memory of the system. The algorithm comes up with a global optimum solution in O(n3) cumulative time (O(n2) for each robot), with O(n3) number of messages exchanged among the n robots.
TL;DR: Computational results show that GA is promising in finding good solutions in very shorter times and can be substituted in the place of MIP model.
TL;DR: Stability of user equilibrium (UE) route flow solutions with respect to inputs to a traffic assignment problem, namely the travel demand and parameters in the link cost function, are studied.
Abstract: This paper studies stability of user-equilibrium (UE) route flow solutions with respect to inputs to a traffic assignment problem, namely the travel demand and parameters in the link cost function. It shows, under certain continuity and strict monotonicity assumptions on the link cost function, that the UE link flow is a continuous function of the inputs, that the set of UE route flows is a continuous multifunction of the inputs, and that the UE route flow selected to maximize an objective function with certain properties is a continuous function of the inputs. The maximum entropy UE route flow is an example of the last. On the other hand, a UE route flow arbitrarily generated in a standard traffic assignment procedure may not bear such continuity property, as demonstrated by an example in this paper.
TL;DR: In this paper, a correlated storage location assignment problem by considering the production bill of material (BOM) information is considered, and a mathematical model is formulated and a multi-stage heuristic is proposed.
Abstract: This paper deals with a correlated storage location assignment problem by considering the production bill of material (BOM) information. Due to the large number of parts in a BOM, the picking capacity constraint is considered. A mathematical model is formulated and a multi-stage heuristic is proposed. The heuristic relaxes the close interrelationships within the original problem through an improvement algorithm and an iterated approach to incorporate the effect of BOM splitting. In order to evaluate the performance of the heuristic, numerical experimentation is conducted in a single-block-multi-aisles warehouse, by using a randomly generated data set.
TL;DR: In this paper, a tabu search algorithm is proposed to improve the solution for medium and large sized problems in an automated storage/retrieval system with duration-of-stay based shared storage policy.
Abstract: Storage location assignment and interleaving policy are two closely related problems in warehousing management. This paper addresses the location assignment and interleaving problem at the same time in an automated storage/retrieval system with duration-of-stay based shared storage policy. Based on the heuristics for single command operation, a two-step procedure is developed to solve the problem. A tabu search algorithm is proposed to improve the solution for medium and large sized problems. The computational results indicate that the tabu search algorithm is effective in finding high quality solutions, and efficient in solving large sized problems.
13 Jun 2010
TL;DR: It is shown that there is no feasible algorithm to find the optimal Hadoop task assignment unless P = NP, and a flow-based algorithm is presented that computes assignments that are optimal to within an additive constant.
Abstract: In recent years Google's MapReduce has emerged as a leading large-scale data processing architecture. Adopted by companies such as Amazon, Facebook, Google, IBM and Yahoo! in daily use, and more recently put in use by several universities, it allows parallel processing of huge volumes of data over cluster of machines. Hadoop is a free Java implementation of MapReduce. In Hadoop, files are split into blocks and replicated and spread over all servers in a network. Each job is also split into many small pieces called tasks. Several tasks are processed on a single server, and a job is not completed until all the assigned tasks are finished. A crucial factor that affects the completion time of a job is the particular assignment of tasks to servers. Given a placement of the input data over servers, one wishes to find the assignment that minimizes the completion time. In this paper, an idealized Hadoop model is proposed to investigate the Hadoop task assignment problem. It is shown that there is no feasible algorithm to find the optimal Hadoop task assignment unless P = NP. Assignments that are computed by the round robin algorithm inspired by the current Hadoop scheduler are shown to deviate from optimum by a multiplicative factor in the worst case. A flow-based algorithm is presented that computes assignments that are optimal to within an additive constant.
TL;DR: A cutting plane algorithm working in the space of the variables of the basic formulation of the Generalized Assignment Problem, whose core is an exact separation procedure for the knapsack polytopes induced by the capacity constraints is proposed.
Abstract: The Generalized Assignment Problem is a well-known NP-hard combinatorial optimization problem which consists of minimizing the assignment costs of a set of jobs to a set of machines satisfying capacity constraints Most of the existing algorithms are of a Branch-and-Price type, with lower bounds computed through Dantzig---Wolfe reformulation and column generation
In this paper we propose a cutting plane algorithm working in the space of the variables of the basic formulation, whose core is an exact separation procedure for the knapsack polytopes induced by the capacity constraints We show that an efficient implementation of the exact separation procedure allows to deal with large-scale instances and to solve to optimality several previously unsolved instances
TL;DR: Simulation results demonstrate that the proposed algorithm can provide the same system capacity with less backhaul resources so that, under backhaul bottleneck situations, a better overall network performance is effectively achieved.
Abstract: Existing base station (BS) assignment methods in cellular networks are mainly driven by radio criteria since it is assumed that the only limiting resource factor is on the air interface. However, as enhanced air interfaces have been deployed, and mobile data and multimedia traffic increases, a growing concern is that the backhaul of the cellular network can become the bottleneck in certain deployment scenarios. In this paper, we extend the BS assignment problem to cope with possible backhaul congestion situations. A backhaul-aware BS assignment problem is modeled as an optimization problem using a utility-based framework, imposing constraints on both radio and backhaul resources, and mapped into a Multiple-Choice Multidimensional Knapsack Problem (MMKP). A novel heuristic BS assignment algorithm with polynomial time is formulated, evaluated and compared to classical schemes based exclusively on radio conditions. Simulation results demonstrate that the proposed algorithm can provide the same system capacity with less backhaul resources so that, under backhaul bottleneck situations, a better overall network performance is effectively achieved.
01 Jan 2010
TL;DR: In this article, a cell-based variant of the Merchant-Nemhauser (M-N) model is proposed for the system optimum (SO) dynamic traffic assignment (DTA) problem.
Abstract: Using a simple piecewise linear exit-flow function, a cell-based variant of the Merchant-Nemhauser (M-N) model is proposed for the system optimum (SO) dynamic traffic assignment (DTA) problem. Once augmented with additional constraints to capture cross-cell interactions, the model becomes a linear program that embeds a relaxed cell transmission model (CTM) for traffic propagation. The proposed cell-based M-N model is different from the existing CTM-based SO-DTA models in that (1) it does not require intersections to be standard merge and diverge; and 2) it does not directly solve for cell-to-cell flows. Generally, the proposed model has a simpler constraint structure and is easier to construct. Path marginal costs are defined using a recursive formula that involves a subset of multipliers from the linear program. This definition is then employed to interpret the necessary condition, which is a dynamic extension of the Wardrop's second principle. An algorithm is presented to solve the flow holding back problem that is known to exist in many existing SO-DTA models. A numerical experiment is conducted to verify the proposed model and algorithm.
TL;DR: Aij has been considered to be trapezoidal and triangular numbers denoted by aij which are more realistic and general in nature than the fuzzy numbers considered in this paper.
Abstract: th job to the i th person. The cost is usually deterministic in nature. In this paper aij has been considered to be trapezoidal and triangular numbers denoted by aij which are more realistic and general in nature. Robust’s ranking method [10] has been used for ranking the fuzzy numbers. The fuzzy assignment problem has been transformed into crisp assignment problem in the linear programming problem form and solved by using Hungarian method; Numerical examples show that the fuzzy ranking method offers an effective tool for handling the fuzzy assignment problem.
03 May 2010
TL;DR: This paper presents two task-allocation strategies for a multi-robot transportation system based on a centralized planner that uses domain knowledge to solve the assignment problem in linear time and individual robots make rule-based allocation decisions using only locally obtainable information and single value communication.
Abstract: In this paper we present two task-allocation strategies for a multi-robot transportation system. The first strategy is based on a centralized planner that uses domain knowledge to solve the assignment problem in linear time. In contrast in the second strategy, individual robots make rule-based allocation decisions using only locally obtainable information and single value communication. Both methods are tested and analysed in simulation experiments. We show that the rule-based method performs well but the lack of information has to be paid for with increased energy consumption.
01 Jan 2010
TL;DR: A hybrid genetic algorithm to solve a multi-depot homogenous locomotive assignment problem with time windows that is efficient and solves the problem in a polynomial time is presented.
Abstract: This paper presents a hybrid genetic algorithm to solve a multi-depot homogenous locomotive assignment problem with time windows. The locomotive assignment problem is to assign a set of homogeneous locomotives locating in a set of dispersed depots to a set of pre-schedules trains that are supposed to be serviced in pre-specified hard/soft time windows. A mathematical model is presented, using vehicle routing problem with time windows (VRPTW) for formulation of the problem. A cluster-first, route-second approach is used to inform the multi-depot locomotive assignment to a set of single depot problems and after that we solve each problem independently. Each single depot problem is solved heuristically by a hybrid genetic algorithm that in which Push Forward Insertion Heuristic (PFIH) is used to determine the initial solution and @l-interchange mechanism is used for neighborhood search and improving method. A medium sized numerical example with different scenarios is presented and examined to more clarification of the approach as well as to check capabilities of the model and algorithm. Also some of the results are compared with the solutions produced by branch & bound technique to determine validity and quality of the model. The experiments with a set of 15 completely random generated instance problems indicate that this algorithm is efficient and solves the problem in a polynomial time.
TL;DR: A new approach for solving the generalized assignment problem (GAP) is proposed that combines the exact branch & bound approach with the heuristic strategy of tabu search (TS) to produce a hybrid algorithm for solving GAP.