IEEE TRANSACTIONS ON VLSI SYSTEMS, VOL. , NO. 1 Collaborative Multi-Objective Global Routing Hamid Shojaei, Student Member, IEEE, Azadeh Davoodi, Member, IEEE, Twan Basten, Senior Member, IEEE Abstract— This work presents a collaborative procedure for multi-objective global routing. Our procedure takes as input multiple global routing solutions, which are generated inde- pendently (e.g., by one router that runs in different modes concurrently, or by different routers running in parallel). It then performs multi-objective optimization based on Pareto algebra and quickly generates multiple global routing solutions with a tradeoff between the considered objectives. The user can control the number of generated solutions and the degree of exploring the tradeoff between them by constraining the maximum allowable degradation in each objective. This work then considers the following three multi-objective case studies: minimization of interconnect power and wirelength, minimization of routing congestion and wirelength, and minimization of wirelength with respect to the (finite-capacity) routing resources. The maximum allowable degradation in wirelength is specified in all cases. Our multi-objective procedure runs in only a few minutes for each of the ISPD 2008 benchmarks, even for the unroutable ones, which imposes a tolerable overhead in the design flow. In our simulations, we demonstrate the effectiveness of our procedure using five modern academic global routers. Index Terms— Global routing, Interconnect power, Multi- objective, Pareto Algebra, Congestion spreading. I. I NTRODUCTION G LOBAL Routing is increasingly gaining importance to combat obstacles such as timing and congestion when realizing complex systems in the nanometer design era. Ever since the release of large industrial benchmarks in the ISPD 2007 contest [11], new global routers have emerged which have pushed the boundaries to obtain higher solution quality and faster runtime [2], [3], [4], [5], [6], [9], [10], [13], [14], [18], [20], [21], [27], [28], [30], [23], [24]. Most recently, the work [29] proposes a multi-level global router with significant improvements both in wirelength and runtime. The global routing procedures can be divided into two cate- gories of concurrent and sequential procedures. The concurrent procedures consider simultaneous routing of all the nets [2], [5], [18], [27], [28], while the sequential ones impose an ordering to route the nets [3], [4], [9], [10], [13], [20], [21], [30]. Furthermore, the sequential techniques apply drastically different procedures for different steps such as net ordering, layer assignment, and route generation. These tools are inherently different in the underlying pro- cedures to tackle the routing problem. Each one provides An extended abstract of this paper was published in the 2010 International Symposium on Low Power Electronics and Design (ISLPED) [26]. The authors, Shojaei and Davoodi, are with the Department of Electrical and Computer Engineering, University of Wisconsin, Madison, WI 53706 USA (e- mail: shojaei@wisc.edu; adavoodi@wisc.edu), and the author, Twan Basten, is with the Department of Electrical Engineering, Eindhoven University of Technology & the Embedded Systems Institute, Eindhoven, The Netherlands (a.a.basten@tue.nl). This work was in part supported by the National Science Foundation under Award 0914981. Fig. 1. Overview of our collaborative multi-objective framework. exclusive features which result in distinct routing solutions compared to the other one. For example, [16] points out that for benchmark circuit adaptec1, compared to the tools FGR and BoxRouter, the tool MaizeRouter [15] tends to route the nets above the blockages and close to the edges of the chip. However, despite distinct routing solutions, the measured qualities such as wirelength are not very different among the majority of recent global routing tools. Distinction in the solutions provides opportunity for gener- ating a better one, for example when considering secondary objectives beyond wirelength. However, combining various routing procedures is difficult, if not impossible, since they may be incompatible (e.g., sequential versus concurrent). In this work, we show that it is possible to only combine these different solutions, which are reflective of these proce- dures in order to conduct multi-objective optimization beyond the traditional wirelength optimization. As shown in Figure 1, different solutions can be obtained by running different routing procedures in parallel which could be from different tools or by concurrently running the tool from the same vendor in different modes. Examples of different routing modes include optimizing wirelength, or routing overflow, or congestion. Our collaborative procedure is able to combine these solutions to perform multi-objective optimization. Each routing solution has a 3D route for each net, which may span multiple metal layers. Our procedure directly works with these 3D input routes to generate a a new 3D routing solution which has varying degrees of contributions of its different input solutions. It effectively explores the search space and tradeoff between the objectives and outputs multiple global routing solutions which provide a tradeoff set between the objectives. Some degree of control in exploring the tradeoff space is also possible; an upper bound on each objective can be specified and the number of generated solutions can be controlled. One feature of our procedure is its execution runtime which is consistently a few minutes for each of the ISPD 2008 benchmark circuits [12] including the unroutable benchmarks. Assuming the single-objective input procedures run indepen- dently in parallel, the additional runtime imposed by our pro-