The Interchange Algorithms for Circuit Placement Problems

This paper discusses the applications of interchange procedures to solve circuit placement problems. A theoretical analysis to guage the quality of solutions is presented. Two interchange algorithms (Algo I and Algo II) are programmed and tested for moderate size placement problems. Algo II is an improved version of Algo I. On the basis of the limited computational results. Algo II seems to provide significant improvements without increased computation cost. The interchange procedure is widely utilized to find approximate solutions for combinatorial problems such as traveling salesman, facility locations, module placements, etc. There are many variations of the interchange procedure. However, the variations are generally limited to the procedure of selecting elements for possible exchanges. The different combinations (solutions) are systematically generated by interchanging only a few elements at a time. A combination which does not improve the value of some norm is rejected. A combination which improves the value of this norm is accepted and one tries to find another combination for further improvement. This is continued until one cannot improve the value of the norm. The search is terminated in a finite number of steps. Computational considerations limit the testing to only pairwise exchanges of elements. Thus, only a small subset of all the possible combinations are generated, and this generally results in suboptimum or local solutions. Even suboptimum solutions of very large problems (more than 100 nodes) can be computationally very expensive. Interchange procedures (as shown in Section 4) compete quite well with other heuristic techniques in regard to both computational time and quality of solutions.