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.
1.9 Organization of the thesis
optimize various analog/RF amplifier circuits. Further, a preliminary review on op- timization techniques to minimize the IR drop in memristive crossbar arrays is also presented. The strengths and weaknesses of different optimization techniques are dis- cussed. A background on proposed optimization techniques is also provided. Finally, a summary of this review is presented.
• Chapter 3: In this chapter, two different metaheuristics based on random walk method and river formation dynamics (RFD) method are presented to analyze large scale power distribution networks on GPU. The speedup and accuracy of the proposed works are compared with different solution techniques in order to demonstrate efficiency and us- ability of proposed methods.
• Chapter 4: In this chapter, various challenges in designing a large power distribution network are outlined. A single objective optimization framework is developed based on RFD method to design large scale power distribution networks. Further, the single objective framework is modified by incorporating various factors to RFD scheme. The performance improvement in the proposed single objective framework is demonstrated by minimizing IR drop and area for large scale power distribution networks.
• Chapter 5: In this chapter, single objective optimization of various analog/RF circuits is presented using RFD and MRFD. Further, to analyze tradeoff among various design specifications, a multiobjective framework based on RFD is also presented, i.e., MOM- RFD. Apart from MOMRFD, a hierarchical mutation based multiobjective genetic al- gorithm (hNSGA-II) and an improved multiobjective framework based on hybrid of brain storm optimization algorithm and RFD scheme (IMBSO) are also presented to design a two-stage operational amplifier, a folded cascode amplifier and a low noise amplifier.
• Chapter 6: In this chapter, optimization of IR drop across memristor crossbar arrays (MCAs) is discussed. The issue of IR drop across MCA is translated into a single
objective minimization problem subjected to constraints representing factors and the optimization problem is solved using MRFD method. The results are compared with other peer algorithms to showcase effectiveness of MRFD method.
• Chapter 7: In this chapter, a summary of the work presented in the thesis is discussed.
Finally, a highlight to the main contributions of the work and directions for future re- search are discussed.
2
Methods for Performance Analysis and Design Optimization of VLSI Circuits : A Review
Contents
2.1 VLSI power distribution network analysis . . . 22 2.2 Power distribution network design . . . 23 2.3 Optimization of analog/RF circuits . . . 24 2.4 IR drop minimization of memristor crossbar arrays . . . 25 2.5 Peer metaheuristics . . . 26 2.6 Background on Proposed Metaheuristics . . . 31 2.7 An insight into metaheuristics performance measures . . . 37 2.8 Summary . . . 39
This chapter presents a review regarding the research work being carried out in problems from four different domains that we have discussed in chapter 1. In section 2.1, a brief review on different methodologies being proposed to perform power distribution network analysis (mostly IR drop analysis) are discussed. This is followed by an overview of different op- timization techniques used to design a power distribution network in section 2.2. As the scientific community has proposed many techniques for the automation of the analog/RF cir- cuit sizing, those approaches are briefly surveyed in section 2.3 focusing on the optimization techniques. Section 2.4 outlines the optimization methods presented to minimize IR drop issue in MCA.
With the availability of computing resources, there has been a significant growth of inter- est in metaheuristic domain. As metaheuristics provide acceptable solutions in a reasonable amount of time for solving complex problems in science and engineering, the usage of the family of such approximate optimization techniques has gained a lot of popularity in the past two decades. Among such optimization techniques, few algorithms are found to be most promising and successful techniques (peer algorithms), such as genetic algorithm (GA), dif- ferential evolution (DE), particle swarm optimization (PSO), etc. Section 2.5 outlines these peer algorithms and their variants. In section 2.6, the working aspect of a few metaheuristics are discussed. These metaheuristics are used to design variants of metaheuristics in the pro- posed research work for solving the problems in four different domains. Finally, an important aspect common to all the metaheuristics, i.e., performance evaluation, is presented along with a brief description on basic answer to the selection of any metaheuristic for a certain problem.
2.1 VLSI power distribution network analysis
Many algorithmic techniques have been proposed in the past to address issues related to reliability and design space of power distribution networks. These proposed methods tend to incorporate direct solvers, iterative solvers and heuristics based methods to perform very large industry-scale power distribution network analysis. The use of direct solvers, such as LU de-