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.

The Role of Motivational Strategies in the Upper Elementary Classroom : A systematic literature review about teacher strategies that promote self-confidence, motivation and a conducive learning environment

The aim of this literature review is to investigate which strategies teachers use to motivate pupils to communicate orally in English. The literature review also investigates how these teacher strategies affect pupils. The methodology used for this investigation is a systematic literature review. Various databases have been used when searching for literature. Scientific articles and theses have been searched for. They have also been read and analyzed before they have become a part of this review. The results indicate that some teachers feel insecure when speaking English. Therefore Swedish is spoken in many language classrooms. Teachers speaking in front of the class is the traditional way of teaching, and it does not seem to be a strategy who influences pupils positively. If teachers speak the target language among pupils they often get more motivated and focused pupils who feel comfortable speaking English. Young pupils are fast learners. By exposing them to the English language in early ages they receive great opportunities to learn a foreign language and strengthen their self-confidence. Drama, songs and rhymes are preferable strategies to use when teaching young learners. What position teachers decide to take in the classroom is also a significant element when teaching foreign languages.