recent studies demonstrate that aluminide coatings are beneficial to wear and erosion resistance and also that oxygen-active elements such as yttrium can remarkably improve this resistance. in this research, the micro-hardness of the aluminide coatings with and without yttrium on 1045 steel was investigated using a micro-mechanical probe. wear of the samples was measured using a pin-on-disk tri...

This paper presents a new method to pack convex polygons into bins (the nesting problem). To do this polygons are placed in rows within bins using a metaheuristic algorithm (simulated annealing) and by utilising the No Fit Polygon. We show that simulated annealing out performs hill climbing. The nesting algorithm is described in detail, along with various aspects that have been incorporated in ...

In this note we consider the problem of, given a sample, selecting the number of bins in a histogram. A loss function is introduced which reflects the idea that smooth distributions should have fewer bins than rough distributions. A stepwise Bayes rule, based on the Bayesian bootstrap, is found and is shown to be admissible. Some simulation results are presented to show how the rule works in pr...

Suppose now that instead of placing each ball in a single random bin, we choose d random bins for each ball, place it in the one that currently has fewest balls, and proceed in this manner sequentially for each ball. Clearly if d = n the maximum load will be optimal: dm/ne. But this requires global knowledge of the state of all bins. Today we will show that with d = 2 choices, the maximum load ...

For the Lego discrepancy with M bins, which is equivalent with a χ2-statistic with M bins, we present a procedure to calculate the moment generating function of the probability distribution perturbatively if M and N , the number of uniformly and randomly distributed data points, become large. Furthermore, we present a phase diagram for various limits of the probability distribution in terms of ...

This paper advocates the use of overlapping bins in histogram creation. It is shown how conventional histogram creation has an inherent quantisation that cause errors much like those in sampling with insufficient band limitation. The use of overlapping bins is shown to be the deterministic equivalent to dithering. Two applications of soft histograms are shown: Improved peak localisation in an e...

We consider online bin packing where in addition to the opening cost of each bin, the arriving items collect delay costs until their assigned bins are released (closed), and the open bins themselves collect holding costs. Besides being of practical interest, this problem generalises several previously unrelated online optimisation problems. We provide a general online algorithm for this problem...

In the bin covering problem there is a group L=(a1; : : : ; an) of items with sizes s̃(ai)∈ (0; 1), and the goal is to 6nd a packing of the items into bins to maximize the number of bins that receive items of total size at least 1. This is a dual problem to the classical bin packing problem. In this paper we present the 6rst asymptotic fully polynomial-time approximation scheme for the problem. ...

In this paper we introduce the Generalized Bin Packing Problem under Uncertainty, a new packing problem where, given a set of items characterized by volume and stochastic revenue and a set of bins characterized by volume and cost, we want to select a subset of items to be loaded into a subset of bins which maximizes the total profit, given by the difference between the expected total revenue of...

Three-dimensional orthogonal bin packing is a problem NP-hard in the strong sense where a set of boxes must be orthogonally packed into the minimum number of three-dimensional bins. We present a two-level tabu search for this problem. The first level aims to reduce the number of bins. The second optimizes the packing of the bins. This latter procedure is based on the Interval Graph representati...