Based on the problems defined in previous sections and application of metaheuristics in circuit analysis and optimization, the contributions of the thesis and motivation of the pro- posed work are presented in this section.
• Power distribution network analysis using metaheuristics
– One of the major concerns in today’s CMOS VLSI design is reliable on-chip power delivery. As semiconductor technology continues to scale down day-by- day, different process variabilities in silicon keep on manifest themselves affecting the chip performance. One of the critical process induced variations come from worst-case voltage fluctuations (hotspots) across power rails of a chip. These fluc- tuations have become more significant with increase in size of power distribution networks. Thus, it is necessary to locate the hotspots accurately throughout the power distribution network for efficient design verification by using suitable com- puting environment and a methodology.
– The objective is to design a parallel and scalable power distribution network anal- ysis tool, which can locate the hotspots across the power distribution network
1.8 Motivations and contributions of the thesis
state and transient analyses on very large power distribution networks (having more than 30 million nodes) using minimum number of computations and mem- ory with acceptable accuracy loss.
– We present two techniques based on random walk (two-step random walk (TSRW)) and river formation dynamics (RFD) methods to analyze large power distribution networks. The effectiveness of both techniques are analyzed by running several experiments on GPU. Experimental results show that both the proposed TSRW and RFD methods accelerate the analysis to achieve remarkable speedups with acceptable loss in accuracy (less than 5%).
• Power distribution network design optimization using metaheuristics
– In general, power distribution network (PDN) analysis is performed as a perfunc- tory signoff procedure as it is employed at a later stage within the design flow to enable designers to correct major PDN-related issues, such as IR drop, L(di/dt) noise, electromigration issues, etc [3,6]. As described in section 1.3, with increase in size of the power distribution network, the number of nodes affected by IR drop also increases nonlinearly. Therefore, it is necessary to minimize IR drop by re- designing the power distribution network. Further, as IR drop depends on the wire width of power rails, minimizing the IR drop also affects the area of the power distribution network.
– Secondly, to avoid the occurrence of any major PDN problems, the designers over- constrain the designs by extending their margins and routability. Due to this over- designing, overall power distribution area becomes too congested for a placement and routing engine to predict the amount of routing and it requires manual efforts to slice the wire area of the PDN and to complete the routing. This process of de- sign slicing relies on designer’s know-how and past design experience. However, it may result in false errors due to boundary effects and the degree of uncertainty in current directions. Therefore, minimizing the wire area of the entire PDN is
more complicated and the number of design variables can be huge with large scale PDNs.
– To minimize the wire area of the PDN, an optimization framework is presented based on river formation dynamics (RFD) heuristic. The framework is utilized to size the widths of power distribution network for very large-scale designs so that the wire area required by power rails is minimized. Both the area minimization problem and IR drop problem are transformed into two single objective optimiza- tion problems subject to various design constraints, such as electromigration con- straints. The minimization process is carried out for both the problems using RFD method. The random probabilistic search strategy of RFD is employed to advance through stringent design requirements to minimize the wire area and IR drop of an over-designed power distribution network.
– Later, we modify the RFD method (MRFD) to analyze the design of several power distribution networks (minimization of IR drop and area of power distribution networks). Additional nature-inspired factors, liketransverse slope statisticsand sediment transport rateare incorporated to formulate a generalized model of RFD.
The generalized model is proved to control flow of the water drops to ensure better convergence and stability of the MRFD method.
– Finally, experimental results are demonstrated to show performance of the pro- posed generalized model of RFD on both standard single objective test functions, and industry standard power distribution network benchmarks. It is observed that both RFD and MRFD frameworks show competitive performance with respect to other peer algorithms (both direct methods and metaheuristics) in optimizing power distribution network benchmarks.
• Analog/RF circuit design optimization using metaheuristics
1.8 Motivations and contributions of the thesis
ful selection of design parameters. As integrated circuit technology scales down to nanometer regime, designers need to embrace new EDA paradigms while design- ing a robust, complex analog/RF system. For analyzing tradeoffs among various design specifications in the presence of process variability during circuit design, it is necessary to observe variations in the performance specifications which can be mapped into a multi-dimensional objective space (Pareto space), spanned by competing objective functions (performance specifications) produced under de- sign constraints. Analyzing multiple objective functions (two design specifica- tions) simultaneously requires complete exploration of design space, and increase in number of design variables increases size of this space. Further, with addi- tion of design constraints to the design metric, the analysis becomes cumbersome.
Therefore, it is necessary to have an efficient design methodology to capture the performance of circuit followed by an efficient constraint handling strategy.
– Our objective is to develop an efficient optimization framework for analog/RF circuit design. The optimization framework should be able to handle multiple de- sign specifications, a number of design parameters and several design constraints, simultaneously to analyze tradeoffs among circuit parameters.
– Here, we present the application of both single objective and multiobjective op- timization frameworks based on MRFD method (MRFD and MOMRFD, respec- tively) to design several analog/RF circuits. The single objective framework based on MRFD method discussed in previous section is extended to the application of optimizing analog/RF circuits. Apart from RFD based optimizer, a hierarchical mutation based multiobjective genetic algorithm (hNSGA-II) and an improved multiobjective framework based on hybrid of brain storm optimization algorithm and RFD scheme (IMBSO) are also developed to optimize various analog/RF cir- cuits. The proposed algorithms are employed to design various performance speci- fications of a two-stage operational amplifier, a folded cascode amplifier and a low
noise amplifier circuit, and it is observed that both MOMRFD and IMBSO demon- strate competitive solutions (in terms of convergence and diversity) in achieving suitable Pareto optimal solutions for different circuit designs.
• IR drop minimization in memristive crossbar array (MCA)
– With increase in density of integration of memristors and size of crossbar array, IR drop along the memristive network also increases. As we know that there are many factors that contribute towards IR drop across MCAs. The first set of factors arises from technology scaling, increased circuit complexity and high-density de- signs. Because of smaller feature sizes (up to micro and nanometer) inside MCAs, instances of large IR drops across the crossbar become significant at lower sup- ply voltages. The natural response to minimize IR drop is to locate the affected regions across the crossbar network and to redesign the entire network through planning and careful refinement using suitable optimization techniques.
– Here, we model the issue of IR drop as a single objective minimization problem subject to constraints representing various factors and analyze the optimization problem using MRFD method. To demonstrate the improvement in reduction of IR drop across MCA, experiments have been performed on MCA benchmarks for efficient evaluation of optimal IR drop. It is observed that MRFD shows compet- itive performance among the metaheuristics in mitigating the reliability issues in MCAs.