Computational experiments with an asynchronous parallel branch and bound algorithm

In this paper we present an asynchronous branch and bound algorithm for execution on an MIMD system, state sufficient conditions to prevent the parallelism from degrading the performance of this algorithm, and investigate the consequences of having the algorithm executed by nonhomogeneous processing elements. We introduce the notions of perfect parallel time and achieved efficiency to empirically measure the effects of parallelism, because the traditional notions of speedup and processor utilization are not adequate for fully characterizing the actual execution of an asynchronous parallel branch and bound algorithm. Finally we present some computational results obtained for the symmetric traveling salesman problem

Optimal channel assignment and power control in wireless cellular networks

Wireless mobile communication is a fast growing field in current telecommunication industry. In a wireless cellular network, channel assignment is a mechanism that assigns channels to mobile users in order to establish a communication between a mobile terminal and a base station. It is important to determine an optimal allocation of channels that makes effective use of channels and minimizes call-blocking and call-dropping probabilities. Another important issue, the power control, is a problem of determining an optimal allocation of power levels to transmitters such that the power consumption is minimized while signal quality is maintained. In wireless mobile networks, channels and transmitter powers are limited resources. Therefore, efficient utilization of both those resources can significantly increase the capacity of network. In this thesis, we solve such optimizations by the hybrid channel assignment (HCA) method using integer linear programming (ILP). Two novel sets of ILP formulation are proposed for two different cases: Reuse Distance based HCA without power control, and Carrier-to-Interference Ratio based HCA combined with power control. For each of them, our experimental results show an improvement over other several approaches

A simulation tool for the performance evaluation of parallel branch and bound algorithms

Parallel computation offers a challenging opportunity to speed up the time consuming enumerative procedures that are necessary to solve hard combinatorial problems. Theoretical analysis of such a parallel branch and bound algorithm is very hard and empirical analysis is not straightforward because the performance of a parallel algorithm cannot be evaluated simply by executing the algorithm on a few parallel systems. Among the difficulties encountered are the noise produced by other users on the system, the limited variation in parallelism (the number of processors in the system is strictly bounded) and the waste of resources involved: most of the time, the outcomes of all computations are already known and the only issue of interest is when these outcomes are produced. We will describe a way to simulate the execution of parallel branch and bound algorithms on arbitrary parallel systems in such a way that the memory and cpu requirements are very reasonable. The use of simulation has only minor consequences for the formulation of the algorithm

Research trends in combinatorial optimization

Acknowledgments This work has been partially funded by the Spanish Ministry of Science, Innovation, and Universities through the project COGDRIVE (DPI2017-86915-C3-3-R). In this context, we would also like to thank the Karlsruhe Institute of Technology. Open access funding enabled and organized by Projekt DEAL.Peer reviewedPublisher PD

An effective line search for the subgradient method

One of the main drawbacks of the subgradient method is the tuning process to determine the sequence of steplengths. In this paper, the radar subgradient method, a heuristic method designed to compute a tuning-free subgradient steplength, is geometrically motivated and algebraically deduced. The unit commitment problem, which arises in the electrical engineering field, is used to compare the performance of the subgradient method with the new radar subgradient method.Peer ReviewedPostprint (published version