A Heuristic Algorithm for Resource Allocation/Reallocation Problem

This paper presents a 1-opt heuristic approach to solve resource allocation/reallocation problem which is known as 0/1 multichoice multidimensional knapsack problem (MMKP). The intercept matrix of the constraints is employed to find optimal or near-optimal solution of the MMKP. This heuristic approach is tested for 33 benchmark problems taken from OR library of sizes upto 7000, and the results have been compared with optimum solutions. Computational complexity is proved to be (2) of solving heuristically MMKP using this approach. The performance of our heuristic is compared with the best state-of-art heuristic algorithms with respect to the quality of the solutions found. The encouraging results especially for relatively large-size test problems indicate that this heuristic approach can successfully be used for finding good solutions for highly constrained NP-hard problems

Nonlinear Symbolic Transformations for Simplifying Optimization Problems

The theory of nonlinear optimization traditionally studies numeric computations. However, increasing attention is being paid to involve computer algebra into mathematical programming. One can identify two possibilities of applying symbolic techniques in this field. Computer algebra can help the modeling phase by producing alternate mathematical models via symbolic transformations. The present paper concentrates on this direction. On the other hand, modern nonlinear solvers use more and more information about the structure of the problem through the optimization process leading to hybrid symbolic-numeric nonlinear solvers. This paper presents a new implementation of a symbolic simplification algorithm for unconstrained nonlinear optimization problems. The program can automatically recognize helpful transformations of the mathematical model and detect implicit redundancy in the objective function. We report computational results obtained for standard global optimization test problems and for other artificially constructed instances. Our results show that a heuristic (multistart) numerical solver takes advantage of the automatically produced transformations. New theoretical results will also be presented, which help the underlying method to achieve more complicated transformations

Analysis and Optimization of Chassis Movements in Transportation Networks with Centralized Chassis Processing Facilities

This work studies the concept of “Centralized Processing of Chassis,” and its potential impact on port drayage efficiency. The concept revolves around an off-dock terminal (or several off-dock terminals), referred to as Chassis Processing Facilities (CPFs). A CPF is located close to the port, where trucks will go to exchange chassis, thereby reducing traffic at the marine terminals and resulting in reduced travel times and reduced congestion. This work is divided into two major studies: one at the strategic planning level, and one at the operational level for individual trucking companies. In the first study, an analytical framework for modeling and optimization of chassis movements in transportation networks with CPFs is developed, and a case study in the Long Beach/Los Angeles (LB/LA) port area is performed. Comparisons between current practices at ports, in which chassis exchanges occur at marine terminals, and proposed practices, in which the exchanges happen at CPFs, are performed. The results of this study indicate that a reduction of total travel time by up to 20% can be achieved when using the CPFs. The study also shows that, in the LB/LA port area, the return on investment for establishing additional CPF locations decreases sharply for any more than three CPFs. Overall, the findings indicate that travel time can be significantly reduced through implementation of CPFs which has important implications in reducing negative environmental impacts of the port as well as operational costs for trucking companies. In the second study, scheduling of chassis and container movements is optimized at the operational level for individual trucking companies, when CPFs are available for use within a major metropolitan area. A multi-objective optimization problem is formulated in which the weighted combination of the total travel time for the schedules of all vehicles in the company fleet and the maximum work span across all vehicle drivers during the day is minimized. Time-varying dynamic models for the movements of chassis and containers are developed and used in the optimization process. The optimal solution is obtained through a genetic algorithm, and the effectiveness of the developed methodology is evaluated through a case study which once again focuses on the LB/LA port area. The case study uses a trucking company located in the Los Angeles region, which can utilize three candidate CPFs for exchange of chassis. The company assigns container movement tasks to its fleet of trucks, with warehouse locations spread across the region. In the simulation scenarios developed for the case study, the use of CPFs at the trucking company level, can provide improvements up to 30% (depending upon the specific scenario) over the cases not using any CPFs. It is found in this work that for typical cases where the number of jobs is much larger than the number of vehicles in the company fleet, the greatest benefit from CPF use would be in the cases where there are some significant job-to-job differences with respect to chassis usage and type. Lastly, in addition to the formulation and optimization for initially planning daily activities, the study further models the problem in a dynamic environment, in which traffic network parameters can change drastically from initial daily predictions. In order to perform the optimization in a dynamic formulation with varying noise levels, a method by which noise could be injected into the initial daily predictions is developed to support the model inputs for the case study and an incremental optimization approach is implemented. Results indicate that a modest potential benefit of approximately 2% may be expected if dynamic re-routing is performed. However, in practice it will be important to weigh the cost of the additional real-time queries required to enable the dynamic re-routing against the potential benefits for the specific company and job set in question prior to implementation

Semidefinite Facial Reduction for Low-Rank Euclidean Distance Matrix Completion

The main result of this thesis is the development of a theory of semidefinite facial reduction for the Euclidean distance matrix completion problem. Our key result shows a close connection between cliques in the graph of the partial Euclidean distance matrix and faces of the semidefinite cone containing the feasible set of the semidefinite relaxation. We show how using semidefinite facial reduction allows us to dramatically reduce the number of variables and constraints required to represent the semidefinite feasible set. We have used this theory to develop a highly efficient algorithm capable of solving many very large Euclidean distance matrix completion problems exactly, without the need for a semidefinite optimization solver. For problems with a low level of noise, our SNLSDPclique algorithm outperforms existing algorithms in terms of both CPU time and accuracy. Using only a laptop, problems of size up to 40,000 nodes can be solved in under a minute and problems with 100,000 nodes require only a few minutes to solve