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. 

A stopping rule while searching for optimal solution of facility-location

Solutions to combinatorial optimization, such as p-median problems of locating facilities, frequently rely on heuristics to minimize the objective function. The minimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. However, pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small branch of the literature suggests using statistical principles to estimate the minimum and use the estimate for either stopping or evaluating the quality of the solution. In this paper we use test-problems taken from Baesley's OR-library and apply Simulated Annealing on these p-median problems. We do this for the purpose of comparing suggested methods of minimum estimation and, eventually, provide a recommendation for practioners. An illustration ends the paper being a problem of locating some 70 distribution centers of the Swedish Post in a region.

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.

On processing GPS tracking data of car-movements in Borlänge, Sweden

The advancement of GPS technology enables GPS devices not only to be used as orientation and navigation tools, but also to track travelled routes. GPS tracking data provides essential information for a broad range of urban planning applications such as transportation routing and planning, traffic management and environmental control. This paper describes on processing the data that was collected by tracking the cars of 316 volunteers over a seven-week period. The detailed information is extracted. The processed data is further connected to the underlying road network by means of maps. Geographical maps are applied to check how the car-movements match the road network. The maps capture the complexity of the car-movements in the urban area. The results show that 90% of the trips on the plane match the road network within a tolerance.

Reliability of GPS based traffic data: an experimental evaluation

GPS tracking of mobile objects provides spatial and temporal data for a broad range of applications including traffic management and control, transportation routing and planning. Previous transport research has focused on GPS tracking data as an appealing alternative to travel diaries. Moreover, the GPS based data are gradually becoming a cornerstone for real-time traffic management. Tracking data of vehicles from GPS devices are however susceptible to measurement errors – a neglected issue in transport research. By conducting a randomized experiment, we assess the reliability of GPS based traffic data on geographical position, velocity, and altitude for three types of vehicles; bike, car, and bus. We find the geographical positioning reliable, but with an error greater than postulated by the manufacturer and a non-negligible risk for aberrant positioning. Velocity is slightly underestimated, whereas altitude measurements are unreliable.