A system for the compaction of two-dimensional irregular shapes based on simulated annealing

The problem of compacting a given number of 2-D shapes minimizing the area of the enclosing rectangle, i.e., minimizing the waste produced, often arises in the automotive industry, clothing manufacturing, steel construction, electronic engineering, and leather cutting. A simulated annealing approach for the compaction of 2-D irregular shapes is presented. The energy function is defined by considering three components: (1) a measure of the enclosing rectangle area; (2) a measure of the distances between each piece and the center of the board, weighted by parameters reflecting the desired width/height ratio of the enclosing rectangle; and (3) a measure of the quality (goodness) of local solutions. The results show that the annealing algorithm performs rather well when it deals with irregular pattern allocation, even though it leads to higher computation times than those needed to run some heuristic methods