2009 International Conference on Advances in Recent Technologies in Communication and Computing
Application Metaheuristic Technique for Solving VLSI Global Routing Problem I. Hameem Shanavas
R.K.Gnanamurthy
Lecturer, Department of Electronics & Communication, Vivekanandha College of Engineering for Women, Tamil Nadu, India. email:
[email protected]
Professor, Department of Electronics & Communication, Vivekanandha College of Engineering for Women, Tamil Nadu, India. email:
[email protected]
Abstract –― Routing is an important and computationally intensive step in the VLSI physical design cycle. It is the process of interconnecting the cells that have been assigned positions as a solution of the placement problem. Global routing is a design action that precedes local routing and follows placement. Global routing decides about the distribution of the interconnections across the available routing channels. Then, all required connections can be established by solving the local routing problem in each channel separately. The combination of evolutionary algorithms with local search is named “Memetic Algorithms”. These methods are inspired by models of natural systems that combine the evolutionary adaptation of a population with individual learning within the lifetimes of its members. In the context of heuristic optimization, a meme is taken to represent a learning or development strategy. Thus a memetic model of adaptation exhibits the plasticity of individuals that a strictly genetic model fails to capture. This paper deals with application of memetic algorithms to solve the problem of global routing. More particularly the emphasis is on the topics of wire length minimization and reduction of channel capacitances, and congestion estimation which are of utmost priority in any global routing scenario.
II. PROBLEM DESCRIPTION In this paper we are mainly deal with congestion problems because it leads the cost function .routing has become more difficult. Routing can fail to complete or can take an unacceptably long time discusses these issues in the context of routability-driven placement. Optimization of congestion in global routing problems is NP-hard; thus, it is unlikely that there can be any efficient algorithm that guarantees success. In this paper, we extend a well known heuristic approach, improving the quality of global routing solutions substantially, with minimal impact to run time. We consider over-the-cell routing in this paper, using the grid based model that has been used in recent works. Using the benchmarks provided by the authors of we are able to obtain average wire length reductions of 15.1% and 65.2% reduction in an “over-congestion” metric. In addition to improved routing quality, our new tool is also substantially faster; on some benchmarks, there is nearly an order of magnitude difference in run time. here introducing a feedback loop to each rip-up and reroute iteration, in order to inform the maze router of congested areas that should be avoided. The congested areas are determined in two ways. Static predictions about congestion are given by a probabilistic algorithm, and dynamic information about congestion is obtained from previous iterations of the rip-up and reroute process.
Keywords –― Combinatorial Optimization, Memetic Algorithms, VLSI global routing, local search, congestion estimation
I.
III. GLOBAL ROUTING WITH CONGESTION PREDICTION Our routing approach extends previous work through the introduction of a congestion prediction method; this influences the routing of Individual connections, improving the solution quality. In this section, we first describe the routing method of [1] in more detail. We then present our method of predicting congestion. The routing costs are influenced by the congestion estimates; o u r o b j ecti ve i s t o d i s p e r s e r o utes from areas we expect to be congested.
INTRODUCTION
In the VLSI physical design process having the following steps partitioning, floor planning, placement, routing, compaction. All VLSI problems are basically difficult to optimize so we called these problems are NPhard problems. Routing is nothing but connection between the two or more modules with wires. In the design process routing problem also difficult to optimize .routing process is normally split into two categories that’s global routing and detail routing. Global routing is previous step to detailed routing processes. While going to routing have to meet the lot of constraints. The objectives of global routing are minimize the area, minimize the wire length, minimize the critical path, and predict the cost function also, etc…the main issue in the global routing is congestion estimation and cost function prediction. In this global routing congestion is directly proportional to the cost function.
978-0-7695-3845-7/09 $26.00 $25.00 © 2009 IEEE DOI 10.1109/ARTCom.2009.80
A. Basic Routing Approach The basic approach in our routing tool is well known, we follow the general outline of Linsker [1]. We first decompose multi-pin nets into sets of point to point connections, and then route each connection. We rip-up and reroute each edge, in order, for a number of iterations, we find that solution quality converges quickly, and that 915
large numbers of iterations seldom improve quality. As is done in most global routing tools, we monitor the number of routes using any particular edge in our routing graph, and use this to adjust routing cost. We consider this to be an extremely important issue in the construction of an effective global routing tool. It was observed that having routing cost increase linearly with congestion was far more effective than having a “step” cost function these observations were confirmed. Despite this, several recent global routers have routing cost which increases abruptly when the number of routes on a graph edge reaches the edge capacity. The routing cost functions are illustrated in Figure 1.
(a)
is the consideration of congestion estimates as part of the routing cost function. C. Probabilistic Congestion Estimation Routing demand can be estimated by enumerating simple paths between endpoints for each wire. The demand for any given routing graph edge is based on the total number of possible routes, and the number that use the graph edge. D. Dynamic Congestion Estimation In addition to the “static” congestion estimate, we also utilize a “dynamic” estimate. After each iteration of rip-up and reroute, we use the actual routing to identify congested areas. Each routed connection contributes to the demand for one or more of the routing graph edges. The demand of wire wi for graph edge ej is pdynamic (wi,ej)=1. This demand is “unit cost” because there is only a single
(b)
Figure 1: In rip-up and reroute approaches, routing cost is a function of the demand for graph edges. In many recent works, cost increases abruptly when demand reaches (or approaches) capacity (a); in the routing tool by Linsker, routing cost is a linear function of demand (b). During ripup and reroute, the connections routed in the early stages will have difficulty in being rerouted, because of the added wire length. If routing cost increases smoothly as we approach the capacity limits of a resource, routes in moderately congested regions will shift towards lightly congested regions. Because the moderately Congested regions have less demand; routes in heavily congested regions can shift towards areas that were previously moderately congested. All routes are subject to rip-up and reroute; it is necessary to move routes in moderate congested areas into lightly congested ones, in order to have room for routes in heavily congested areas to move into moderately congested ones. We would compare this effect to “erosion;” all routing shifts away from the congestion peaks, equalizing resource usage and reducing the maximum congestion values. If the routing cost function steps up abruptly when resource capacities are reached, there is little incentive for routes in uncontested area to “move out of the way.” When the routing cost increases abruptly, route l e n g t h s c a n a l s o i n c r e a s e s u b s t a n t i a l l y ; rather than passing through a congested region, a route may detour significantly. These results in higher routing resource demand, which can in turn lead to higher congestion.
E. Amplification of Congestion Estimation We use the “static” and “dynamic” congestion estimates to influence routing cost; prior to use, however, we amplify them. Motivation for this comes from the following observations • In heavily congested areas, we have a strong desire to push routes to other areas. Routing in congested areas should cost substantially more than uncongested areas. • In lightly congested and moderately congested areas, we would wish to avoid introducing routing detours. Routing cost should not be increased in this case. To amplify the congestion estimates, we apply a relatively simple scaling factor. For any given wire wi in a dynamic congestion estimate, we consider the estimated demand along all routing edges used by the wire. If no routing edge has demand greater than 80% of capacity, we set the amplification factor α(wi) to 0. If a routing edge has demand greater than 1.2 of capacity, α (wi) is set to 1.2. Otherwise, α (wi) is set to 1. The amplified dynamic demand for routing edge ej is dynamic (ej) =∑wi α (wi) × p (wi, ej) The static amplified demand is calculated in a similar manner.
B. Congestion Estimation and Amplification Prior to initial routing, the method of Linsker has no indication as to where congestion is to be expected; thus, the first routes may pass through areas that will have high demand, even when there are viable alternatives. During ripup and reroute, the sub-optimal routings of some wires impacts the routes considered for others; our objective with congestion estimation is to minimize the number of poorly routed connections in the early stages of routing, and to provide an effective tie-breaking method when there are multiple routes with similar cost. Our main contribution
IV. MEMETIC ALGORITHM Genetic Algorithms are not well suited for fine-tuning structures which are close to optimal solutions. Incorporation of local improvement operators into the recombination step of a Genetic Algorithm is essential if a competitive Genetic Algorithm is desired. Memetic algorithms (MAs) are evolutionary algorithms (EAs) that apply a separate local search process to refine individuals. Under different contexts and situations, MAs are also known as hybrid EAs, genetic local searchers. Combining global and local search is a strategy used by many successful global optimization approaches, and MAs have in
path.
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fact been recognized as a powerful algorithmic paradigm for evolutionary computing. In particular, the relative advantage of MAs over EAs is quite consistent on complex search spaces. pop
have a similar guiding value as well. V. CONCLUSION In this paper, we focus on improving congestion in global routing, using the current over-the-cell routing model. Our work improves a classic routing approach by integrating congestion estimates with the routing. By amplifying estimated congestion, we can target “problem” areas without introducing detours in uncongested regions .Compared to recent global routing work; our new approach produces excellent results. The method is also surprisingly fast, even when compared to tools that perform pattern routing. Improving routing congestion is a significant concern for large and dense designs. If routing fails, the design team must modify the placement, or possibly increase the chip size to introduce additional routing resources. In fixed- die design, if there is additional space available, the impact of increased routing area will generally be limited to increased wire length and power consumption. If additional space is not available, routing failure may increase the cost of a design substantially.
Repeat μ times
Start population
Generate Random
new sorted pop
Raw solution Apply Local Improver
Pick the best Solution Store in Population
Store in Population New
pop
Fig 2: A possible re-starting procedure for the population. The top = pµ agents in the population are kept, and the remaining ¹ i ¼ are generated from scratch.
ACKNOWLEDGEMENT It is to note here that this topic-specific article for the easy reference of VLSI Routing Problem. Author Hameem Shanavas.I thank the management of Vivekanandha College of Engineering for Women, India to conduct his research in this arena and also he worked under the Guidance of Dr.R.K.Gnanamurthy, the Eminent Professor in India.
A. Minimizing epitasis Epitasis can be defined as the non- adaptive influence on the guiding function of combining several information units. Clearly, the higher this non-additive influence, the lower the absolute relevance to find individual information units. B. Minimizing fitness variance The fitness variance for a certain information unit is the Variance of the values returned by the guiding function, measured across a representative subset of taken from the parents. In either case, similarly to mutation, performing the combination of information in a problemoriented way is crucial for the performance of the algorithm. This description of recombination has introduced a crucial concept, namely, relevant features. Consider that a certain solution can contain a high number of atomic information units, but only some of them are directly linked with quality.. The definition of operators manipulating the relevant features is one of the key aspects in the design of MAs. There have been several attempts for quantifying how good a certain set of information units is for representing solutions for specific problems.
REFERENCES [1]
Ralph Linsker. “An iterative - improvement Penalty – function driven wire routing system” IBM Journal of Research and Development, pp 613–624, September 1984. [2] R.T. Hadsell and H.Madden “Improved global routing through congestion estimation” In Proc..Design Automation Conf, 2003. [3] P.Moscato and C.Cotta “Memetic algorithm” University of Malaga, Spain, September 2005. [4] Shawki Areibi, Medhat Moussa and Hussein Abdullah “A Comparison of Genetic/Memetic Algorithms and Other Heuristic Search Techniques” University of Guelph, Ontario [5] C.Albrecht “Global routing by new approximation algorithms for multi commodity flow”IEEE Trans…on Computer-Aided Design of integrated Circuits and Systems, May2001. [6] Hu.J and Sapatnekar.S.S “Performance driven global routing through gradual refinement” IEEE Int. Conf.on Comp Design, 2001, pp.481483 [7] Jing.T,Hong.X,Bao.H,Cai,“A unified timing and congestion optimizing algorithm for standard cell global routing” Asia And South Pacific Design Automation conf.2001,pp.834-839 [8] Hu,J and Sapatnekar.S.S “A timing- constrained algorithm for Simultaneous global routing of multiple nets”,IEEE Int Conf. on Computer-Aided Design, 2000, pp.99-103 [9] Lin S.P and ChangY.W “A novel frame work for multilevel Routing considering routability and performance”Int. Conf.on ComputerAided Design, 2002, pp.44-50 [10] P.Moscato and C.Cotta “A gentle introduction to memetic algorithms” and F.Glover and G.Kochen-Berger “Handbook of Metaheuristics” BostonMA, 2003.
C. Maximizing fitness correlation In this case a certain reproductive operator is assumed, and the correlation in the values of the guiding function for parents and offspring is measured. If the fitness correlations are high, good solutions are likely to produce optimal solutions, and thus the search will gradually shift toward the most promising regions of the search space. since the reproductive operators will create new solutions by manipulating these features, the offspring is likely to
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