On statistical bounds of heuristic solutions to location problems

Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region. 

GRASP and statistical bounds for heuristic solutions to combinatorial problems

The quality of a heuristic solution to a NP-hard combinatorial problem is hard to assess. A few studies have advocated and tested statistical bounds as a method for assessment. These studies indicate that statistical bounds are superior to the more widely known and used deterministic bounds. However, the previous studies have been limited to a few metaheuristics and combinatorial problems and, hence, the general performance of statistical bounds in combinatorial optimization remains an open question. This work complements the existing literature on statistical bounds by testing them on the metaheuristic Greedy Randomized Adaptive Search Procedures (GRASP) and four combinatorial problems. Our findings confirm previous results that statistical bounds are reliable for the p-median problem, while we note that they also seem reliable for the set covering problem. For the quadratic assignment problem, the statistical bounds has previously been found reliable when obtained from the Genetic algorithm whereas in this work they found less reliable. Finally, we provide statistical bounds to four 2-path network design problem instances for which the optimum is currently unknown.

Branch and Bound Algorithm for Multiprocessor Scheduling

The multiprocessor task graph scheduling problem has been extensively studied asacademic optimization problem which occurs in optimizing the execution time of parallelalgorithm with parallel computer. The problem is already being known as one of the NPhardproblems. There are many good approaches made with many optimizing algorithmto find out the optimum solution for this problem with less computational time. One ofthem is branch and bound algorithm.In this paper, we propose a branch and bound algorithm for the multiprocessor schedulingproblem. We investigate the algorithm by comparing two different lower bounds withtheir computational costs and the size of the pruned tree.Several experiments are made with small set of problems and results are compared indifferent sections.

QoS Evaluation of BandwidthSchedulers in IPTV Networks OfferedSRD Fluid Video Traffic

Internet protocol TV (IPTV) is predicted to be the key technology winner in the future. Efforts to accelerate the deployment of IPTV centralized model which is combined of VHO, encoders, controller, access network and Home network. Regardless of whether the network is delivering live TV, VOD, or Time-shift TV, all content and network traffic resulting from subscriber requests must traverse the entire network from the super-headend all the way to each subscriber's Set-Top Box (STB).IPTV services require very stringent QoS guarantees When IPTV traffic shares the network resources with other traffic like data and voice, how to ensure their QoS and efficiently utilize the network resources is a key and challenging issue. For QoS measured in the network-centric terms of delay jitter, packet losses and bounds on delay. The main focus of this thesis is on the optimized bandwidth allocation and smooth datatransmission. The proposed traffic model for smooth delivering video service IPTV network with its QoS performance evaluation. According to Maglaris et al [5] First, analyze the coding bit rate of a single video source. Various statistical quantities are derived from bit rate data collected with a conditional replenishment inter frame coding scheme. Two correlated Markov process models (one in discrete time and one incontinuous time) are shown to fit the experimental data and are used to model the input rates of several independent sources into a statistical multiplexer. Preventive control mechanism which is to be include CAC, traffic policing used for traffic control.QoS has been evaluated of common bandwidth scheduler( FIFO) by use fluid models with Markovian queuing method and analysis the result by using simulator andanalytically, Which is measured the performance of the packet loss, overflow and mean waiting time among the network users.

QoS evaluation of Bandwidth Schedulers in IPTV Networks Offered SRD Fluid Video Traffic

Internet protocol TV (IPTV) is predicted to be the key technology winner in the future. Efforts to accelerate the deployment of IPTV centralized model which is combined of VHO, encoders, controller, access network and Home network. Regardless of whether the network is delivering live TV, VOD, or Time-shift TV, all content and network traffic resulting from subscriber requests must traverse the entire network from the super-headend all the way to each subscriber's Set-Top Box (STB). IPTV services require very stringent QoS guarantees When IPTV traffic shares the network resources with other traffic like data and voice, how to ensure their QoS and efficiently utilize the network resources is a key and challenging issue. For QoS measured in the network-centric terms of delay jitter, packet losses and bounds on delay. The main focus of this thesis is on the optimized bandwidth allocation and smooth data transmission. The proposed traffic model for smooth delivering video service IPTV network with its QoS performance evaluation. According to Maglaris et al [5] first, analyze the coding bit rate of a single video source. Various statistical quantities are derived from bit rate data collected with a conditional replenishment inter frame coding scheme. Two correlated Markov process models (one in discrete time and one in continuous time) are shown to fit the experimental data and are used to model the input rates of several independent sources into a statistical multiplexer. Preventive control mechanism which is to be including CAC, traffic policing used for traffic control. QoS has been evaluated of common bandwidth scheduler( FIFO) by use fluid models with Markovian queuing method and analysis the result by using simulator and analytically, Which is measured the performance of the packet loss, overflow and mean waiting time among the network users.

Statistical bound of genetic solutions to quadratic assignment problems

Quadratic assignment problems (QAPs) are commonly solved by heuristic methods, where the optimum is sought iteratively. Heuristics are known to provide good solutions but the quality of the solutions, i.e., the confidence interval of the solution is unknown. This paper uses statistical optimum estimation techniques (SOETs) to assess the quality of Genetic algorithm solutions for QAPs. We examine the functioning of different SOETs regarding biasness, coverage rate and length of interval, and then we compare the SOET lower bound with deterministic ones. The commonly used deterministic bounds are confined to only a few algorithms. We show that, the Jackknife estimators have better performance than Weibull estimators, and when the number of heuristic solutions is as large as 100, higher order JK-estimators perform better than lower order ones. Compared with the deterministic bounds, the SOET lower bound performs significantly better than most deterministic lower bounds and is comparable with the best deterministic ones. 

Confidence in heuristic solutions?

Solutions to combinatorial optimization problems frequently rely on heuristics to minimize an objective function. The optimum is sought iteratively and pre-setting the number of iterations dominates in operations research applications, which implies that the quality of the solution cannot be ascertained. Deterministic bounds offer a mean of ascertaining the quality, but such bounds are available for only a limited number of heuristics and the length of the interval may be difficult to control in an application. A small, almost dormant, branch of the literature suggests using statistical principles to derive statistical bounds for the optimum. We discuss alternative approaches to derive statistical bounds. We also assess their performance by testing them on 40 test p-median problems on facility location, taken from Beasley’s OR-library, for which the optimum is known. We consider three popular heuristics for solving such location problems; simulated annealing, vertex substitution, and Lagrangian relaxation where only the last offers deterministic bounds. Moreover, we illustrate statistical bounds in the location of 71 regional delivery points of the Swedish Post. We find statistical bounds reliable and much more efficient than deterministic bounds provided that the heuristic solutions are sampled close to the optimum. Statistical bounds are also found computationally affordable.

Optimization heuristic solutions, how good can they be? : With empirical applications in location problems

Combinatorial optimization problems, are one of the most important types of problems in operational research. Heuristic and metaheuristics algorithms are widely applied to find a good solution. However, a common problem is that these algorithms do not guarantee that the solution will coincide with the optimum and, hence, many solutions to real world OR-problems are afflicted with an uncertainty about the quality of the solution. The main aim of this thesis is to investigate the usability of statistical bounds to evaluate the quality of heuristic solutions applied to large combinatorial problems. The contributions of this thesis are both methodological and empirical. From a methodological point of view, the usefulness of statistical bounds on p-median problems is thoroughly investigated. The statistical bounds have good performance in providing informative quality assessment under appropriate parameter settings. Also, they outperform the commonly used Lagrangian bounds. It is demonstrated that the statistical bounds are shown to be comparable with the deterministic bounds in quadratic assignment problems. As to empirical research, environment pollution has become a worldwide problem, and transportation can cause a great amount of pollution. A new method for calculating and comparing the CO2-emissions of online and brick-and-mortar retailing is proposed. It leads to the conclusion that online retailing has significantly lesser CO2-emissions. Another problem is that the Swedish regional division is under revision and the border effect to public service accessibility is concerned of both residents and politicians. After analysis, it is shown that borders hinder the optimal location of public services and consequently the highest achievable economic and social utility may not be attained.