Abstract
A problem of optimizing locations of many rectangular pieces for efficiently utilizing a sheet is considered. The object is to minimize the amount of waste. This problem which is called the nesting problem is important in industrial applications, but it's NP hard. This problem is considered in two stages of the ordering the pieces and the selecting locations of the pieces using the order. In this paper, we propose a new greedy algorithm, called ridgeline method for selecting the optimal locations in the second stage. The order of the pieces strongly affects the performance of the method. Therefore, methods of meta-heuristics, i.e., local search, simulated annealing, tabu search and genetic algorithms, to optimize the order in the first stage are considered. Two options in genetic algorithms are used. These methods of meta heuristics as well as random ordering are compared using simulations experiments. The result shows that the simulated annealing is better than the other meta-heuristics.
