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.

Parameter estimation of Poisson generalized linear mixed models based on three different statistical principles : a simulation study

Generalized linear mixed models are flexible tools for modeling non-normal data and are useful for accommodating overdispersion in Poisson regression models with random effects. Their main difficulty resides in the parameter estimation because there is no analytic solution for the maximization of the marginal likelihood. Many methods have been proposed for this purpose and many of them are implemented in software packages. The purpose of this study is to compare the performance of three different statistical principles - marginal likelihood, extended likelihood, Bayesian analysis-via simulation studies. Real data on contact wrestling are used for illustration.

Testing the gravity p-median model empirically

Regarding the location of a facility, the presumption in the widely used p-median model is that the customer opts for the shortest route to the nearest facility. However, this assumption is problematic on free markets since the customer is presumed to gravitate to a facility by the distance to and the attractiveness of it. The recently introduced gravity p-median model offers an extension to the p-median model that account for this. The model is therefore potentially interesting, although it has not yet been implemented and tested empirically. In this paper, we have implemented the model in an empirical problem of locating vehicle inspections, locksmiths, and retail stores of vehicle spare-parts for the purpose of investigating its superiority to the p-median model. We found, however, the gravity p-median model to be of limited use for the problem of locating facilities as it either gives solutions similar to the p-median model, or it gives unstable solutions due to a non-concave objective function.

Influence of grinding operations on surface integrity and chloride induced stress corrosion cracking of stainless steels

Stainless steels were developed in the early 20th century and are used where both the mechanical properties of steels and corrosion resistance are required. There is continuous research to allow stainless steel components to be produced in a more economical way and be used in more harsh environments. A necessary component in this effort is to correlate the service performance with the production processes. The central theme of this thesis is the mechanical grinding process.  This is commonly used for producing stainless steel components, and results in varied surface properties that will strongly affect their service life. The influence of grinding parameters including abrasive grit size, machine power and grinding lubricant were studied for 304L austenitic stainless steel (Paper II) and 2304 duplex stainless steel (Paper I). Surface integrity was proved to vary significantly with different grinding parameters. Abrasive grit size was found to have the largest influence. Surface defects (deep grooves, smearing, adhesive/cold welding chips and indentations), a highly deformed surface layer up to a few microns in thickness and the generation of high level tensile residual stresses in the surface layer along the grinding direction were observed as the main types of damage when grinding stainless steels. A large degree of residual stress anisotropy is interpreted as being due to mechanical effects dominating over thermal effects. The effect of grinding on stress corrosion cracking behaviour of 304L austenitic stainless steel in a chloride environment was also investigated (Paper III). Depending on the surface conditions, the actual loading by four-point bend was found to deviate from the calculated value using the formula according to ASTM G39 by different amounts. Grinding-induced surface tensile residual stress was suggested as the main factor to cause micro-cracks initiation on the ground surfaces. Grinding along the loading direction was proved to increase the susceptibility to chloride-induced SCC, while grinding perpendicular to the loading direction improved SCC resistance. The knowledge obtained from this work can provide a reference for choosing appropriate grinding parameters when fabricating stainless steel components; and can also be used to help understanding the failure mechanism of ground stainless steel components during service.