Showing papers in "Journal of Mathematical Modelling and Algorithms in 2003"
TL;DR: The use of absorbing Markov chains is proposed to solve the capacity constrained transit network loading problem taking common lines into account, and also handles the common lines problem, where choice of route depends on frequency of arrivals.
Abstract: This paper proposes the use of absorbing Markov chains to solve the capacity constrained transit network loading problem taking common lines into account. The approach handles congested transit networks, where some passengers will not be able to board because of the absence of sufficient space. The model also handles the common lines problem, where choice of route depends on frequency of arrivals. The mathematical formulation of the problem is presented together with a numerical example.
132 citations
TL;DR: With the introduction of node labels, the formulation can exploit the route structure and hence attains efficiency in obtaining a cost minimizing transit network design.
Abstract: We consider the design of multiple transit lines in a network and present a mixed integer formulation for this multiple-route transit network design problem (MRTNDP). With the introduction of node labels, the formulation can exploit the route structure and hence attains efficiency in obtaining a cost minimizing transit network design.
83 citations
TL;DR: A cutting plane algorithm and a heuristic line search algorithm are proposed to solve the problem of delay minimization at isolated signal-controlled junctions as a Binary-Mix-Integer-Non-Linear Program (BMINLP).
Abstract: This paper presents a lane-based optimization method for minimizing delay at isolated signal-controlled junctions. The method integrates the design of lane markings and signal settings, and considers both traffic and pedestrian movements in a unified framework. While the capacity maximization and cycle length minimization problems are formulated as Binary-Mix-Integer-Linear-Programs (BMILPs) that are solvable by standard branch-and-bound routines, the problem of delay minimization is formulated as a Binary-Mix-Integer-Non-Linear Program (BMINLP). A cutting plane algorithm and a heuristic line search algorithm are proposed to solve this difficult BMINLP problem. The integer variables include the permitted movements on traffic lanes and successor functions to govern the order of signal displays, whereas the continuous variables include the assigned lane flows, common flow multiplier, cycle length, and starts and durations of green for traffic movements, lanes and pedestrian crossings. A set of constraints is set up to ensure the feasibility and safety of the resultant optimized lane markings and signal settings. A numerical example is given to demonstrate the effectiveness of the proposed methodology. The heuristic line search algorithm is more cost-effective in terms of both optimality of solution and computing time requirement.
61 citations
TL;DR: This paper has proposed an efficient incremental implementation of maximum flow problem after inserting an edge in the network G, which has the time complexity of O((Δn)2m), where Δn is the number of affected vertices and m is thenumber of edges in thenetwork.
Abstract: An incremental algorithm may yield an enormous computational time saving to solve a network flow problem. It updates the solution to an instance of a problem for a unit change in the input. In this paper we have proposed an efficient incremental implementation of maximum flow problem after inserting an edge in the network G. The algorithm has the time complexity of O((Δn)2m), where Δn is the number of affected vertices and m is the number of edges in the network. We have also discussed the incremental algorithm for deletion of an edge in the network G.
33 citations
TL;DR: A heuristic algorithm based on route/time-swapping process is proposed, which iteratively adjusts the route and departure time choices to reach closely to an extreme point of the minimization problem.
Abstract: This paper presents a formulation and solution algorithm for a composite dynamic user-equilibrium assignment problem with multi-user classes, in order to assess the impacts of Advanced Traveler Information Systems (ATIS) in general networks with queues. Suppose that users equipped with ATIS will receive complete information and hence be able to choose the best departure times and routes in a deterministic manner, while users not equipped with ATIS will have incomplete information and hence may make decisions on departure times and routes in a stochastic manner. This paper proposes a discrete-time, finite-dimensional variational inequality formulation that involves two criteria regarding the route and departure time choice behaviors, i.e., the deterministic dynamic user equilibrium and the nested logit-based stochastic dynamic user equilibrium. The formulation is then converted to an equivalent “zero-extreme value” minimization problem. A heuristic algorithm based on route/time-swapping process is proposed, which iteratively adjusts the route and departure time choices to reach closely to an extreme point of the minimization problem. A numerical example is used to demonstrate the effectiveness of the proposed approach for assessing the ATIS impacts such as changes in individual travel costs, departure times, route inflows, queuing peaks and total network travel cost.
25 citations
TL;DR: The NP-hardness of the general problem is established and polynomial algorithms for several special cases are presented and relating scheduling theory and graph theory appears to be an interesting and important concept.
Abstract: We consider the problem of minimizing the makespan on a batch processing machine, in which jobs are not all compatible. Only compatible jobs can be included into the same batch. This relation of compatibility is represented by a split graph. Jobs have release dates. The capacity of the batch processing machine is finite or infinite. The processing time of a batch is given by the processing time of the longest job in the batch. We establish the NP-hardness of the general problem and present polynomial algorithms for several special cases. Relating scheduling theory and graph theory appears to be an interesting and important concept.
19 citations
TL;DR: An optimal algorithm to solve the all-pairs shortest path problem on permutation graphs with n vertices and m edges which runs in O(n2) time is presented.
Abstract: In this paper we present an optimal algorithm to solve the all-pairs shortest path problem on permutation graphs with n vertices and m edges which runs in O(n2) time. Using this algorithm, the average distance of a permutation graph can also be computed in O(n2) time.
18 citations
TL;DR: This paper investigates the transit passenger origin–destination (O–D) estimation problem in congested transit networks where updated passenger counts and outdated O–D matrices are available and develops a new frequency-based stochastic user equilibrium (SUE) assignment model.
Abstract: This paper investigates the transit passenger origin–destination (O–D) estimation problem in congested transit networks where updated passenger counts and outdated O–D matrices are available. The bi-level programming approach is used for the transit passenger O–D estimation problem. The upper level minimizes the sum of error measurements in passenger counts and O–D matrices, and the lower level is a new frequency-based stochastic user equilibrium (SUE) assignment model that can determine simultaneously the passenger overload delays and passenger route choices in congested transit network together with the resultant transit line frequencies. The lower-level problem can be formulated as either a logit-type or probit-type SUE transit assignment problem. A heuristic solution algorithm is developed for solving the proposed bi-level programming model which is applicable to congested transit networks. Finally, a case study on a simplified transit network connecting Kowloon urban area and the Hong Kong International Airport is provided to illustrate the applications of the proposed bi-level programming model and solution algorithm.
17 citations
TL;DR: The nonlinear Schrodinger equation is of tremendous interest in both theory and applications as mentioned in this paper, and various regimes of pulse propagation in optical fibers are modeled by some form of the nonlinear SDE.
Abstract: The nonlinear Schrodinger equation is of tremendous interest in both theory and applications. Various regimes of pulse propagation in optical fibers are modeled by some form of the nonlinear Schrodinger equation.
13 citations
TL;DR: A branch-and-bound algorithm based on Lagrangian relaxation to solve the model of multi-level network optimization problems and results for randomly generated problems are presented showing the quality of the approach.
Abstract: Multi-level network optimization problems arise in many contexts such as telecommunication, transportation, and electric power systems. A model for multi-level network design is formulated as a mixed-integer program. The approach is innovative because it integrates in the same model aspects of discrete facility location, topological network design, and dimensioning. We propose a branch-and-bound algorithm based on Lagrangian relaxation to solve the model. Computational results for randomly generated problems are presented showing the quality of our approach. We also present and discuss a real world problem of designing a two-level local access urban telecommunication network and solving it with the proposed methodology.
13 citations
TL;DR: A new dual-based algorithm is presented for the feasibility problem in the case of strict relative constraints of Partially Clairvoyant Real-time scheduling systems and it is shown that the complexity of dispatching is logarithmically related to the complexity the schedulability problem.
Abstract: Real-time scheduling problems confront two issues not addressed by traditional scheduling models, viz., parameter variability and the existence of complex relationships constraining the executions of jobs. Accordingly, modeling becomes crucial in the specification of scheduling problems in such systems. In this paper, we analyze scheduling algorithms in Partially Clairvoyant Real-time scheduling systems and present a new dual-based algorithm for the feasibility problem in the case of strict relative constraints. We also study the problem of online dispatching in Partially Clairvoyant systems and show that the complexity of dispatching is logarithmically related to the complexity of the schedulability problem.
TL;DR: Functional enhancements to the WebCom metacomputer are described which give rise to dynamic reconfigurability and extendability of the computer platform.
Abstract: Functional enhancements to the WebCom metacomputer are described which give rise to dynamic reconfigurability and extendability of the computer platform. Component modules and interactions are described, with particular attention to the communications module that enables dynamic reconfigurability. The machines of the metacomputer can be configured to act in client/server or peer to peer mode on a number of interconnection topologies such as NOWs, Clusters or Grids. This paper addresses the dynamically extendable machine structure of WebCom facilitated by this new communications structure.
TL;DR: An optimization algorithm is presented which starts by utilizing the problem's special structure to determine the minimum workforce size and different workers are assigned to different days-off work patterns in order to minimize either the total number or the total cost of the workforce.
Abstract: A four-day workweek days-off scheduling problem is considered. Out of the three days off per week for each employee, either two or three days must be consecutive. An optimization algorithm is presented which starts by utilizing the problem's special structure to determine the minimum workforce size. Subsequently, workers are assigned to different days-off work patterns in order to minimize either the total number or the total cost of the workforce. Different procedures must be followed in assigning days-off patterns, depending on the characteristics of labor demands. In some cases, optimum days-off assignments are determined without requiring mathematical programming. In other cases, a workforce size constraint is added to the integer programming model, greatly improving computational performance.
TL;DR: The need for a more accurate modeling of the performance of systems whose functioning mainly dependant on external time parameters such as the number of requests during a particular time phase, led to a novel approach, taking into account the time parameters involved.
Abstract: The need for a more accurate modeling of the performance of systems whose functioning mainly dependant on external time parameters such as the number of requests during a particular time phase, led us to a novel approach, taking into account the time parameters involved. This is achieved through the evaluation of a performability indicator modeled by means of a two-phase cyclic nonhomogenous Markov chain considering periodical time-dependant arrival request probabilities and applied to a replicated database system. The computation of the performability indicator modeled by cyclic nonhomogeneous Markov chain requires the use of efficient computational methods by using explicit approximate inverse preconditioning methods.
TL;DR: This paper proposes an algorithm to predict networking loads on the computational Grid based on the Markov model, and the proposed algorithm is evaluated using an actual networking load to offer the most accurate predictions.
Abstract: The computational Grid is currently gaining in popularity, and it enables computers scattered all over the world to be connected by the Internet as if they are part of a large computational infrastructure. While the computational Grid gathers more and more computational resources and the number of the applications for the computational Grid is increasing, load balancing for the computational Grid is still not effective enough. Because the computers are connected by a wide area network on the computational Grid, the significant communication latency and the frequency of large wave throughputs make it difficult to achieve effective load balancing. Thus, in this paper, we propose an algorithm to predict networking loads on the computational Grid to make the use of computational resources more efficient. The proposed algorithm based on the Markov model is evaluated using an actual networking load. As a result, the Markov model based algorithm offers the most accurate predictions compared with the related work.
TL;DR: This paper designs and implements efficient and optimal parallel algorithms for Cholesky decomposition based on different data layouts and methods, and derives theoretical lower bounds on running time based on initial data layout and compares them against the algorithmic run-times.
Abstract: In this dissertation we consider design issues such as data, layout, data, dependency, communication scheduling, and parallel models in order to develop parallel algorithms for Cholesky decomposition. Our intention is to design efficient and portable parallel algorithms for large scale dense linear systems to be run in the distributed memory environment.
To consider the issue of portability, we utilize the well known LogP model for designing parallel algorithms and for performing theoretical run time analysis. We developed a contention free communication scheduling for the parallel algorithms in order to reduce the communication cost. To study the impact of data layout on performance, we designed the parallel algorithms based on column, row and block data distribution utilizing the fan-in and fan-out methods. Specifically we introduced panel size for 1D layouts and granularity size for 2D layouts for the task partitioning. To determine the efficiency of the parallel algorithms, we derived lower bound results and theoretical run time performance. The analysis on the parallel algorithms shows that parallel algorithms for 1D data layouts are optimal. However for 2D data layouts, the parallel algorithms are efficient, if not necessarily asymptotically optimal.
We then implemented the parallel algorithms using MPI. The experimental results show that fan-in outperforms fan-out for 2D layouts, especially for larger processor size. The performance for the 1D fan-out row-based parallel algorithm was no worse than that of the column-based parallel algorithms. This seems to refute the common notion that row-based parallel algorithms are not, as efficient as column-based parallel algorithms. The experimental results indicated that performance was impacted as panel size and/or granularity size varied. This provides insights that the constant factors for lower bound and run time performance call not be ignored.
TL;DR: A new precise formal definition of the term problem is suggested which is identified with an equivalence class of models describing it and a new definition is suggested for the size of a model which depends on the assumed encoding scheme.
Abstract: The meaning of the term ‘problem’ in operations research (OR) deviates from the understanding in the theoretical computer sciences: While an OR problem is often conceived to be stated or represented by model formulations, a computer-science problem can be viewed as a mapping from encoded instances to solutions. Such a computer-science problem turns out to be rather similar to an OR model formulation. This ambiguity may cause difficulties if the computer-science theory of computational complexity is applied in the OR context. In OR, a specific model formulation is commonly used in the analysis of the underlying problem and the results obtained for this model are simply lifted to the problem level. But this may lead to erroneous results, if the model used is not appropriate for such an analysis of the problem. To resolve this issue, we first suggest a new precise formal definition of the term problem which is identified with an equivalence class of models describing it. Afterwards, a new definition is suggested for the size of a model which depends on the assumed encoding scheme. Only models which exhibit a minimal size with respect to a ‘reasonable’ encoding scheme finally turn out to be suitable for the model-based complexity analysis of an OR problem. Therefore, the appropriate choice (or if necessary the construction) of a suitable representative of an OR problem becomes an important theoretical aspect of the modelling process.
TL;DR: The Discrete Lot-sizing and Scheduling Problem is analysed here in detail to demonstrate the difficulties which can arise if these aspects are neglected and to illustrate the new theoretical concept of a new minimal model for this problem.
Abstract: In Part I of this study, we suggest to identify an operations research (OR) problem with the equivalence class of models describing the problem and enhance the standard computer-science theory of computational complexity to be applicable to this situation of an often model-based OR context. The Discrete Lot-sizing and Scheduling Problem (DLSP) is analysed here in detail to demonstrate the difficulties which can arise if these aspects are neglected and to illustrate the new theoretical concept. In addition, a new minimal model is introduced for the DLSP which makes this problem eventually amenable to a rigorous analysis of its computational complexity.
TL;DR: This work conducts a comparable study on the properties and performance of the SAI preconditioners using the different sparsity patterns for solving some sparse linear systems.
Abstract: Sparse approximate inverse (SAI) techniques have recently emerged as a new class of parallel preconditioning techniques for solving large sparse linear systems on high performance computers. The choice of the sparsity pattern of the SAI matrix is probably the most important step in constructing an SAI preconditioner. Both dynamic and static sparsity pattern selection approaches have been proposed by researchers. Through a few numerical experiments, we conduct a comparable study on the properties and performance of the SAI preconditioners using the different sparsity patterns for solving some sparse linear systems.
TL;DR: The Weak-Integrity of a graph G is introduced as a new measure of stability in this sense and it is defined as Iw(G)=min S⊂V(G){S+me(G−S)}, where me(G+S) denotes the number of edges of the largest component of G−S.
Abstract: Connectivity has been used in the past to describe the stability of graphs. If two graphs have the same connectivity, then it does not distinguish between these graphs. That is, the connectivity is not a good measure of graph stability. Then we need other graph parameters to describe the stability. Suppose that two graphs have the same connectivity and the order (the number of vertices or edges) of the largest components of these graphs are not equal. Hence, we say that these graphs must be different in respect to stability and so we can define a new measure which distinguishes these graphs. In this paper, the Weak-Integrity of a graph G is introduced as a new measure of stability in this sense and it is defined as I w (G)=min S⊂V(G){S+m e (G−S)}, where m e (G−S) denotes the number of edges of the largest component of G−S. We give the weak-integrity of graphs obtained via various operations that are unary, such as powers, and binary, such as union, composition, product and corona.
TL;DR: An efficient algorithm is presented for the formation of suboptimal cycle bases of graphs corresponding to sparse cycle adjacency matrices, leading to theformation of highly sparse flexibility matrices.
Abstract: An efficient algorithm is presented for the formation of suboptimal cycle bases of graphs corresponding to sparse cycle adjacency matrices, leading to the formation of highly sparse flexibility matrices. The algorithm presented employs concepts from algebraic graph theory together with a Greedy-type algorithm to select cycles with small overlaps and uses a simple graph-theoretical method for controlling the independence of the selected cycles.