Journal Staff

This thesis concerns the development of novel feasible direction type algorithms for constrained nonlinear optimization. The new algorithms are based upon enhancements of the search direction determination and the line search steps. The Frank-Wolfe method is popular for solving certain structured linearly constrained nonlinear problems, although its rate of convergence is often poor. We develop improved Frank--Wolfe type algorithms based on conjugate directions. In the conjugate direction Frank-Wolfe method a line search is performed along a direction which is conjugate to the previous one with respect to the Hessian matrix of the objective. A further refinement of this method is derived by applying conjugation with respect to the last two directions, instead of only the last one. The new methods are applied to the single-class user traffic equilibrium problem, the multi-class user traffic equilibrium problem under social marginal cost pricing, and the stochastic transportation problem. In a limited set of computational tests the algorithms turn out to be quite efficient. Additionally, a feasible direction method with multi-dimensional search for the stochastic transportation problem is developed. We also derive a novel sequential linear programming algorithm for general constrained nonlinear optimization problems, with the intention of being able to attack problems with large numbers of variables and constraints. The algorithm is based on inner approximations of both the primal and the dual spaces, which yields a method combining column and constraint generation in the primal space.The articles are note published due to copyright rextrictions.</p

HEURISTIC AND OPTIMUM SOLUTIONS IN ALLOCATION PROBLEMS

In this paper we present some models and algoritms for solving some typical production planning and scheduling problems. We present the Resource-Constrained Project Scheduling Problem (RCPSP) and algorithms for the determination of maximal couplings with minimal arch length in the graph attached to an allocation problem, and for the determination of the solution of Dirichlet problem and of the potential-voltage problem which appear in a production planning. We develop a model for allocating work among potential VO partners, taking into account fixed and variable work costs and transportation costs.Dirichlet’s problem, conex graph, maximal coupling, RCPS problem, virtual organization, allocation problem

Linearly-Constrained Entropy Maximization Problem with Quadratic Costs and Its Applications to Transportation Planning Problems

Many transportation problems can be formulated as a linearly-constrained convex programming problem whose objective function consists of entropy functions and other cost-related terms. In this paper, we propose an unconstrained convex programming dual approach to solving these problems. In particular, we focus on a class of linearly-constrained entropy maximization problem with quadratic cost, study its Lagrangian dual, and provide a globally convergent algorithm with a quadratic rate of convergence. The theory and algorithm can be readily applied to the trip distribution problem with quadratic cost and many other entropy-based formulations, including the conventional trip distribution problem with linear cost, the entropy-based modal split model, and the decomposed problems of the combined problem of trip distribution and assignment. The efficiency and the robustness of this approach are confirmed by our computational experience

Metaheuristic approach to transportation scheduling in emergency situations

This paper compares two metaheuristic approaches in solving a constrained transportation scheduling problem, which can be found in transporting goods in emergency situations. We compared Greedy Search, Parameter-less Evolutionary Search and Ant-Stigmergy Algorithm. The transportation scheduling/allocation problem is NP-hard, and is applicable to different real-life situations with high frequency of loading and unloading operations; like in depots, warehouses and ports. To evaluate the efficiency of the presented approaches, they were tested with four tasks based on realistic data. Each task was evaluated using group and free transportation approach. The experiments proved that all tested algorithms are viable option in solving such scheduling problems, however some performing better than others on some tasks

GIS and Network Analysis

Both geographic information systems (GIS) and network analysis are burgeoning fields, characterised by rapid methodological and scientific advances in recent years. A geographic information system (GIS) is a digital computer application designed for the capture, storage, manipulation, analysis and display of geographic information. Geographic location is the element that distinguishes geographic information from all other types of information. Without location, data are termed to be non-spatial and would have little value within a GIS. Location is, thus, the basis for many benefits of GIS: the ability to map, the ability to measure distances and the ability to tie different kinds of information together because they refer to the same place (Longley et al., 2001). GIS-T, the application of geographic information science and systems to transportation problems, represents one of the most important application areas of GIS-technology today. While traditional GIS formulation's strengths are in mapping display and geodata processing, GIS-T requires new data structures to represent the complexities of transportation networks and to perform different network algorithms in order to fulfil its potential in the field of logistics and distribution logistics. This paper addresses these issues as follows. The section that follows discusses data models and design issues which are specifically oriented to GIS-T, and identifies several improvements of the traditional network data model that are needed to support advanced network analysis in a ground transportation context. These improvements include turn-tables, dynamic segmentation, linear referencing, traffic lines and non-planar networks. Most commercial GIS software vendors have extended their basic GIS data model during the past two decades to incorporate these innovations (Goodchild, 1998). The third section shifts attention to network routing problems that have become prominent in GIS-T: the travelling salesman problem, the vehicle routing problem and the shortest path problem with time windows, a problem that occurs as a subproblem in many time constrained routing and scheduling issues of practical importance. Such problems are conceptually simple, but mathematically complex and challenging. The focus is on theory and algorithms for solving these problems. The paper concludes with some final remarks.