Surrogate dual search in nonlinear integer programming.

Wang, Chongyu.Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.Includes bibliographical references (leaves 74-78).Abstract also in Chinese.Abstract --- p.1Abstract in Chinese --- p.3Acknowledgement --- p.4Contents --- p.5List of Tables --- p.7List of Figures --- p.8Chapter 1. --- Introduction --- p.9Chapter 2. --- Conventional Dynamic Programming --- p.15Chapter 2.1. --- Principle of optimality and decomposition --- p.15Chapter 2.2. --- Backward dynamic programming --- p.17Chapter 2.3. --- Forward dynamic programming --- p.20Chapter 2.4. --- Curse of dimensionality --- p.23Chapter 3. --- Surrogate Constraint Formulation --- p.26Chapter 3.1. --- Surrogate constraint formulation --- p.26Chapter 3.2. --- Singly constrained dynamic programming --- p.28Chapter 3.3. --- Surrogate dual search --- p.29Chapter 4. --- Distance Confined Path Algorithm --- p.34Chapter 4.1. --- Yen´ةs algorithm for the kth shortest path problem --- p.35Chapter 4.2. --- Application of Yen´ةs method to integer programming --- p.36Chapter 4.3. --- Distance confined path problem --- p.42Chapter 4.4. --- Application of distance confined path formulation to integer programming --- p.50Chapter 5. --- Convergent Surrogate Dual Search --- p.59Chapter 5.1. --- Algorithm for convergent surrogate dual search --- p.62Chapter 5.2. --- "Solution schemes for (Pμ{αk,αβ)) and f(x) = αk" --- p.63Chapter 5.3. --- Computational Results and Analysis --- p.68Chapter 6. --- Conclusions --- p.72Bibliography --- p.7

An Optimised Shortest Path Algorithm for Network Rotuting & SDN: Improvement on Bellman-Ford Algorithm

Network routing algorithms form the backbone of data transmission in modern network architectures, with implications for efficiency, speed, and reliability. This research aims to critically investigate and compare three prominent routing algorithms: Bellman-Ford, Shortest Path Faster Algorithm (SPFA), and our novel improved variant of Bellman-Ford, the Space-efficient Cost-Balancing Bellman-Ford (SCBF). We evaluate the performance of these algorithms in terms of time and space complexity, memory utilization, and routing efficacy, within a simulated network environment. Our results indicate that while Bellman-Ford provides consistent performance, both SPFA and SCBF present improvements in specific scenarios with the SCBF showing notable enhancements in space efficiency. The innovative SCBF algorithm provides competitive performance and greater space efficiency, potentially making it a valuable contribution to the development of network routing protocols. Further research is encouraged to optimize and evaluate these algorithms in real-world network conditions. This study underscores the continuous need for algorithmic innovation in response to evolving network demands

A GIS based multi-modal multiple optimal path transit advanced traveler information system

A method for the design and use of a Transit Advanced Traveler Information System (TATIS) using an off-the-shelf Geographic Information System (GIS) is developed in this thesis. The research design included: 1) representing multi-modal transit networks in a digital form with schedule databases; 2) development of a multiple optimal path algorithm that takes into account walking transfers using published time schedules; 3) incorporating user preferences and penalties in the algorithm; 4) development of a user-interface with suitable output capabilities; 5) using the prototype for sample inquiries giving performance measures. This prototype was developed using the Arc/Info GIS developed by ESRI, Inc. The principal results of the research demonstrated the effectiveness and robustness of the TATIS prototype with respect to the five previously mentioned issues. Areas of future improvement and research focus on performance measures and added functionality

On optimal and near-optimal algorithms for some computational graph problems

PhD ThesisSome computational graph problems are considered in this thesis and algorithms for solving these problems are described in detail. The problems can be divided into three main classes, namely, problems involving partially ordered sets, finding cycles in graphs, and shortest path problems. Most of the algorithms are based on recursive procedures using depth-first search. The efficiency of each algorithm is derived and it can be concluded that the majority of the proposed algorithms are either optimal and near-optimal within a constant factor. The efficiency of the algorithms is measured by the time and space requirements for their implementation.Conselho Nacional de Pesquisas,Brazil: Universidade Federal do Rio de Janeiro, Brazil

Exact rotamer optimization for computational protein design

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (leaves 235-244).The search for the global minimum energy conformation (GMEC) of protein side chains is an important computational challenge in protein structure prediction and design. Using rotamer models, the problem is formulated as a NP-hard optimization problem. Dead-end elimination (DEE) methods combined with systematic A* search (DEE/A*) have proven useful, but may not be strong enough as we attempt to solve protein design problems where a large number of similar rotamers is eligible and the network of interactions between residues is dense. In this thesis, we present an exact solution method, named BroMAP (branch-and-bound rotamer optimization using MAP estimation), for such protein design problems. The design goal of BroMAP is to be able to expand smaller search trees than conventional branch-and-bound methods while performing only a moderate amount of computation in each node, thereby reducing the total running time. To achieve that, BroMAP attempts reduction of the problem size within each node through DEE and elimination by energy lower bounds from approximate maximurn-a-posteriori (MAP) estimation. The lower bounds are also exploited in branching and subproblem selection for fast discovery of strong upper bounds. Our computational results show that BroMAP tends to be faster than DEE/A* for large protein design cases. BroMAP also solved cases that were not solvable by DEE/A* within the maximum allowed time, and did not incur significant disadvantage for cases where DEE/A* performed well. In the second part of the thesis, we explore several ways of improving the energy lower bounds by using Lagrangian relaxation. Through computational experiments, solving the dual problem derived from cyclic subgraphs, such as triplets, is shown to produce stronger lower bounds than using the tree-reweighted max-product algorithm.(cont.) In the second approach, the Lagrangian relaxation is tightened through addition of violated valid inequalities. Finally, we suggest a way of computing individual lower bounds using the dual method. The preliminary results from evaluating BroMAP employing the dual bounds suggest that the use of the strengthened bounds does not in general improve the running time of BroMAP due to the longer running time of the dual method.by Eun-Jong Hong.Ph.D