Optimal Design of a Decoupling Network Using Variants of Particle Swarm Optimization Algorithm
01 May 2021-pp 1-5
TL;DR: In this paper, a practical case study is presented, where, in order to design an efficient PDN, the cumulative impedance of the PDN is optimized below the target impedance.
Abstract: This paper discusses a discrete optimization problem of optimal design of Power Delivery Networks (PDN) in VLSI systems. In this paper, a practical case study is presented, where, in order to design an efficient PDN, the cumulative impedance of the PDN is optimized below the target impedance. For this purpose, the decoupling capacitors (from commercially available capacitors) are chosen in such a way that the minimum number of the capacitors are used, and also their optimal locations are identified. The different variants of inertia weight strategies incorporated into particle swarm optimization algorithms are used for this purpose. A comparative analysis of the performance of these algorithms is also presented.
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TL;DR: In this article , a multi-port constrained optimization methodology is presented for the optimal placement of decoupling capacitors in power distribution networks (PDNs) of printed circuit boards (PCBs).
Abstract: A multi-port constrained optimization methodology is presented for the optimal placement of decoupling capacitors in power distribution networks (PDNs) of printed circuit boards (PCBs). The proposed method is based on barrier methods and can simultaneously handle multiple ball grid array (BGA) devices and capacitor ports on practical power/ground plane pairs of polygonal shapes without restriction in the problem geometry. Semi-analytical expressions are developed for the magnitude of device port impedance that is set as the objective function. The placement optimization problem including constraints of planar boundaries and impedance specifications is cast into a matrix expression that meets Karush–Kuhn Tucker (KKT) conditions and solved through Newton–Raphson (N–R) iterations. The convergence of iterations is ensured by guaranteeing the positive definiteness of the system matrix through the Levenberg–Marquardt algorithm. Mutual coupling among multiple ports and discrete components of the problem domain is accounted for via matrix calculus techniques applied to the partial derivatives of optimization variables. The derivatives are evaluated accurately exploiting the semi-analytical relations developed for the distributed planar impedance. The proposed method is tested with several examples, and the results are observed to be in good agreement with those obtained from a numerical electromagnetic (EM) simulator while yielding significant speed-up.
2 citations
TL;DR: In this article , a new hybrid metaheuristic algorithm named Metropolis-based differential particle swarm optimization (MDP) is designed to jointly optimize the multiconstraints and impedance-based hybrid objective function of chiplet-based 2.5D integrated circuit (IC) designs.
Abstract: Interposer and chiplet-based 2.5-D integrated circuit (IC) designs have become a new trend for block-level heterogeneous integration. In this paper, a new hybrid metaheuristic algorithm named Metropolis-based differential particle swarm optimization (MDP) is designed to jointly optimize the multiconstraints and impedance-based hybrid objective function of chiplet-based 2.5-D IC including interposers, chiplets, through-silicon via (TSV) arrays, bumps, and metal-insulator-metal (MIM) capacitors for simultaneous switch noise (SSN) reduction. Combined with the cascaded PDN assembly method, constraints on routing, delay and proximity distance between the entire system and an impedance-oriented function with multiple critical factors, a hybrid objective function with respect to the 2.5-D PDN is obtained. Integrating the advantages of multiple algorithms, a better hybrid MDP algorithm is designed to optimize the proposed key function. This method adopts the Metropolis rule to avoid the waste of the update mechanism for out-of-boundary particles. The placement, orientation of the chiplets, the on-interposer decoupling capacitor and the constraints of the 2.5-D system are co-optimized to find the optimal solution to eliminate the SSN. The overdesign of the system, different target impedance, different objective-oriented circuit optimization schemes and trade-offs in different constraints are also discussed carefully in this paper for 2.5-D ICs.
1 citations
01 Dec 2022
TL;DR: In this paper , a new hybrid metaheuristic algorithm named Metropolis-based differential particle swarm optimization (MDP) is designed to jointly optimize the multiconstraints and impedance-based hybrid objective function of chiplet-based 2.5D integrated circuit (IC) designs.
Abstract: Interposer and chiplet-based 2.5-D integrated circuit (IC) designs have become a new trend for block-level heterogeneous integration. In this paper, a new hybrid metaheuristic algorithm named Metropolis-based differential particle swarm optimization (MDP) is designed to jointly optimize the multiconstraints and impedance-based hybrid objective function of chiplet-based 2.5-D IC including interposers, chiplets, through-silicon via (TSV) arrays, bumps, and metal-insulator-metal (MIM) capacitors for simultaneous switch noise (SSN) reduction. Combined with the cascaded PDN assembly method, constraints on routing, delay and proximity distance between the entire system and an impedance-oriented function with multiple critical factors, a hybrid objective function with respect to the 2.5-D PDN is obtained. Integrating the advantages of multiple algorithms, a better hybrid MDP algorithm is designed to optimize the proposed key function. This method adopts the Metropolis rule to avoid the waste of the update mechanism for out-of-boundary particles. The placement, orientation of the chiplets, the on-interposer decoupling capacitor and the constraints of the 2.5-D system are co-optimized to find the optimal solution to eliminate the SSN. The overdesign of the system, different target impedance, different objective-oriented circuit optimization schemes and trade-offs in different constraints are also discussed carefully in this paper for 2.5-D ICs.
1 citations
DOI•
TL;DR: In this article , a novel approach using the Social-Learning Particle Swarm Optimization (SLPSO) technique along with Adaptive Region Search (ARS) is used to tackle the Large-Scale Optimization Problem (LSOP) of decoupling capacitor placement.
Abstract: Power delivery networks are responsible for supplying clean power to the integrated circuits. Power supply noise plays a critical role in determining the performance of high-speed very large scale integration circuits and systems. In order to maintain power integrity in high-speed systems, decoupling capacitors are used to maintain low impedance of the PDN to eventually minimize power supply noise. However, the discrete optimization problem of selecting decoupling capacitors becomes computationally challenging in the systems having stringent power integrity (PI) requirements. In this work, a novel approach using the Social-Learning Particle Swarm Optimization (SLPSO) technique along with Adaptive Region Search (ARS) is used to tackle the Large-Scale Optimization Problem (LSOP) of decoupling capacitor placement. Region Search (RS) is used to guide particles, followed by ARS to dynamical search for the local best positions and for particles to move faster across the search space while maintaining the diversity of the population. To demonstrate the proposed approach, three practical case studies are presented. The obtained results are compared with current state-of-the-art approaches. The proposed approach drastically reduces computation time and is consistent with better results than other approaches. This consistency of improvement in CPU time in the results of all the examples validates the proposed approach.
DOI•
TL;DR: In this paper , a novel approach using surrogate-assisted swarm intelligence is presented for efficient and fast optimization of power delivery networks (PDNs) in very large scale integration systems are becoming very challenging with the increasing complexity of such systems.
Abstract: The design and optimization of power delivery networks (PDNs) in very large scale integration systems are becoming very challenging with the increasing complexity of such systems. Decoupling capacitors are the key elements used in a PDN to minimize power supply noise and to maintain low impedance of the PDN to avoid system failure. In this article, a novel approach using surrogate-assisted swarm intelligence is presented for efficient and fast optimization of PDNs. For generating the surrogate models, a standard radial basis function network is used. Using the proposed approach, the decoupling capacitors are selected and placed optimally, eventually reducing the cumulative impedance of the PDN below the target impedance. The performance comparison between the conventional and the surrogate-assisted approach is presented. Three case studies are presented on a practical system to demonstrate the competence of the proposed approach. The results obtained by the proposed approach are also compared with the same obtained by the state-of-the-art approaches. For the proposed approach, the runtime is drastically reduced compared to the state-of-the-art approaches for the optimization problem without having any effect on the performance. The consistency of results in all of the case studies confirms the validity of the proposed approach.
References
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TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
Abstract: There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.
41,772 citations
TL;DR: A snapshot of particle swarming from the authors’ perspective, including variations in the algorithm, current and ongoing research, applications and open problems, is included.
Abstract: A concept for the optimization of nonlinear functions using particle swarm methodology is introduced The evolution of several paradigms is outlined, and an implementation of one of the paradigms is discussed Benchmark testing of the paradigm is described, and applications, including nonlinear function optimization and neural network training, are proposed The relationships between particle swarm optimization and both artificial life and genetic algorithms are described
18,439 citations
04 May 1998
TL;DR: A new parameter, called inertia weight, is introduced into the original particle swarm optimizer, which resembles a school of flying birds since it adjusts its flying according to its own flying experience and its companions' flying experience.
Abstract: Evolutionary computation techniques, genetic algorithms, evolutionary strategies and genetic programming are motivated by the evolution of nature. A population of individuals, which encode the problem solutions are manipulated according to the rule of survival of the fittest through "genetic" operations, such as mutation, crossover and reproduction. A best solution is evolved through the generations. In contrast to evolutionary computation techniques, Eberhart and Kennedy developed a different algorithm through simulating social behavior (R.C. Eberhart et al., 1996; R.C. Eberhart and J. Kennedy, 1996; J. Kennedy and R.C. Eberhart, 1995; J. Kennedy, 1997). As in other algorithms, a population of individuals exists. This algorithm is called particle swarm optimization (PSO) since it resembles a school of flying birds. In a particle swarm optimizer, instead of using genetic operators, these individuals are "evolved" by cooperation and competition among the individuals themselves through generations. Each particle adjusts its flying according to its own flying experience and its companions' flying experience. We introduce a new parameter, called inertia weight, into the original particle swarm optimizer. Simulations have been done to illustrate the significant and effective impact of this new parameter on the particle swarm optimizer.
9,373 citations
TL;DR: A detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far are presented.
Abstract: Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE.
4,321 citations
27 May 2001
TL;DR: Developments in the particle swarm algorithm since its origin in 1995 are reviewed and brief discussions of constriction factors, inertia weights, and tracking dynamic systems are included.
Abstract: This paper focuses on the engineering and computer science aspects of developments, applications, and resources related to particle swarm optimization. Developments in the particle swarm algorithm since its origin in 1995 are reviewed. Included are brief discussions of constriction factors, inertia weights, and tracking dynamic systems. Applications, both those already developed, and promising future application areas, are reviewed. Finally, resources related to particle swarm optimization are listed, including books, Web sites, and software. A particle swarm optimization bibliography is at the end of the paper.
4,041 citations