Matheuristic Local Search for the Placement of Analog Integrated Circuits

TL;DR

This paper studies how to improve the results of the previous ILP model, first by introducing additional constraints and second by using matheuristics, and evaluates the revised approach on synthetically generated instances containing more than 200 independent rectangles and on real-life problems.

Abstract

The suboptimal physical design of the integrated circuits may not only increase the manufacturing costs due to the larger size of the chip but can also impact its performance by placing interconnected rectangular devices too far from each other. In the domain of Analog and Mixed-Signal Integrated Circuits (AMS ICs), placement automation is lacking behind its digital counterpart, mainly due to the variety of components and complex constraints the placement needs to satisfy. Integer Linear Programming (ILP) is a suitable approach to modeling the placement problem for AMS ICs. However, not even state-of-the-art solvers can create high-quality placements for large problem instances. In this paper, we study how to improve the results of our previous ILP model, first by introducing additional constraints and second by using matheuristics. Given the initial solution we obtain using our original ILP model, we use the solver to perform a local search. We try to improve the criterion by considering only a few spatially close rectangles while keeping the rest of the placement fixed. This local search approach enables us to significantly improve the quality of instances whose solution space we could not sufficiently explore before, even when the computation time reserved for the matheuristic is limited. Finally, we evaluate our revised approach on synthetically generated instances containing more than 200 independent rectangles and on real-life problems.

Figures (5)

• Figure 1: Example placement with critical constraints of the BCD technology icores23.
• Figure 2: Placement before and after ILP intensification. The black dot shows where the selection position $(x,y)$ was sampled. Rectangles modified during the process are highlighted. See the decrease in height after intensification.
• Figure 3: Comparison of final placements obtained by FDGD-ILP and MH-10 respectively, on instance from set $S_{200}^\mathrm{sym}$ with $c_C=1.0$. Both experiments' computation time was set to 2400 s.
• Figure 4: Value of criterion during optimization, for instance shown in Fig. \ref{['baseline_vs_mh']}. Black circles show when MH-10D performed diversification.
• Figure 5: Comparison of manual and automated placements, obtained for $c_C = 0.1$. Shown instance corresponds to the 14th row in Table \ref{['tab:realressize']}.