How to Pack Trapezoids Exact and Evolutionary Algorithms
Abstract: The purposes of this paper are twofold. In the first, we describe an exact polynomial-time time algorithm for the pair sequencing problem and show how this method can be used to pack fixed fixed-height height trapezoids into a single bin such that interitem wastage is minim minimized. ized. We then go on to examine how this algorithm can be combined with bespoke evolutionary and local search methods for tackling the multiple-bin bin version of this problem problem-one one that is closely related to 1-D 1 bin packing. In the course of doing this, a number of ideas surrounding recombination, diversity, and genetic repair are also introduced and analyzed.