International Technology Roadmap for Semiconductors 2003の要求清浄度について － シリコンウエハ表面と雰囲気環境に要求される清浄度, 分析方法の現状について －

IEEE transactions on computer-aided design of integrated circuits and systems : a publication of the IEEE Circuits and Systems Society

In this study, we use a new metaheuristic optimization algorithm, called bat algorithm (BA), to solve constraint optimization tasks. BA is verified using several classical benchmark constraint problems. For further validation, BA is applied to three benchmark constraint engineering problems reported in the specialized literature. The performance of the bat algorithm is compared with various existing algorithms. The optimal solutions obtained by BA are found to be better than the best solutions provided by the existing methods. Finally, the unique search features used in BA are analyzed, and their implications for future research are discussed in detail.

Bat algorithm for constrained optimization tasks

This paper presents an overview of the research progress in deterministic global optimization during the last decade (1998---2008). It covers the areas of twice continuously differentiable nonlinear optimization, mixed-integer nonlinear optimization, optimization with differential-algebraic models, semi-infinite programming, optimization with grey box/nonfactorable models, and bilevel nonlinear optimization.

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A review of recent advances in global optimization

In this paper we are concerned with global optimization, which can be defined as the problem of finding points on a bounded subset of Rn in which some real valued functionf assumes its optimal (i.e. maximal or minimal) value. We present a stochastic approach which is based on the simulated annealing algorithm. The approach closely follows the formulation of the simulated annealing algorithm as originally given for discrete optimization problems. The mathematic formulation is extended to continuous optimization problems and we prove asymptotic convergence to the set of global optima. Furthermore, we discuss an implementation of the algorithm and compare its performance with other well known algorithms. The performance evaluation is carried out for a standard set of test functions from the literature. Keywords: global optimization, continuous variables, simulated annealing.

Global optimization and simulated annealing

Partner selection with a due date constraint in virtual enterprises

Modern circuits often contain standard cells of different row heights to meet various design requirements. Higher cells give larger drive strengths at the costs of larger areas and power. Multi-row-height standard cells incur challenging issues to layout designs, especially the mixed-cell-height legalization problem due to the heterogeneous cell structures. Honoring the good cell positions from global placement, we present in this paper a fast and near-optimal algorithm to solve the legalization problem. Fixing the cell ordering from global placement and relaxing the right boundary constraints, we first convert the problem into a linear complementarity problem (LCP). With the converted LCP, we split its matrices to meet the convergence requirement of a modulus-based matrix splitting iteration method (MMSIM), and then apply the MMSIM to solve the LCP. This MMSIM method guarantees the optimality if no cells are placed beyond the right boundary of a chip. Finally, a Tetris-like allocation approach is used to align cells to placement sites on rows and fix the placement of out-of-right-boundary cells, if any. Experimental results show that our proposed algorithm can achieve the best cell displacement and wirelength among all published methods in reasonable runtimes. The MMSIM optimality is theoretically proven and empirically validated. In particular, our formulation provides new generic solutions and research directions for various optimization problems that require solving large-scale quadratic programs efficiently.

Toward Optimal Legalization for Mixed-Cell-Height Circuit Designs

Floorplanning in very large scale integrated-circuit (VLSI) design is the first phase in the process of designing the physical layout of a chip. This makes the floorplanning problem of paramount importance, since it determines the performance, size, yield, and reliability of VLSI chips . From the computational point of view, the VLSI floorplanning is an NP-hard problem. In this paper, we present a hybrid simulated annealing algorithm (HSA) for nonslicing VLSI floorplanning. The HSA uses a new greedy method to construct an initial B*-tree, a new operation on the B*-tree to explore the search space, and a novel bias search strategy to balance global exploration and local exploitation. Experimental results on Microelectronic Center of North Carolina (MCNC) benchmarks show that the HSA can quickly produce optimal or nearly optimal solutions for all the tested problems.

A Hybrid Simulated Annealing Algorithm for Nonslicing VLSI Floorplanning

For circuit designs in advanced technologies, standard-cell libraries consist of cells with different heights; for example, the number of fins determines the height of cells in the FinFET technology. Cells of larger heights give higher drive strengths, but consume larger areas and power. Such mixed cell heights incur new, complicated challenges for layout designs, due mainly to the heterogeneity in cell dimensions and thus their larger solution spaces. There is not much published work on layout designs with mixed-height standard cells. This paper addresses the legalization problem of mixed-height standard cells, which intends to place cells without any overlap and with minimized displacement. We first study the properties of Abacus, generally considered the best legalization method for traditional single-row-height standard cells but criticized not suitable for handling the new challenge, analyze the capability and insufficiencies of Abacus for tackling the new problem, and remedy Abacuss insufficiencies and extend its advantages to develop an effective and efficient algorithm for the addressed problem. For example, dead spaces become a critical issue in mixed-cell-height legalization, which cannot be handled well with an Abacus variant alone. We thus derive a dead-space-aware objective function and an optimization scheme to handle this issue. Experimental results show that our algorithm can achieve the best wirelength among all published methods in reasonable running time, e.g., about 50% smaller wirelength increase than a state-of-the-art work.

An effective legalization algorithm for mixed-cell-height standard cells

The minimum weight-dominating set (MWDS) problem is NP-hard and has a lot of applications in the real world. Several metaheuristic methods have been developed for solving the problem effectively, but suffering from high CPU time on large-scale instances. In this paper, we design an effective hybrid memetic algorithm (HMA) for the MWDS problem. First, the MWDS problem is formulated as a constrained 0–1 programming problem and is converted to an equivalent unconstrained 0–1 problem using an adaptive penalty function. Then, we develop a memetic algorithm for the resulting problem, which contains a greedy randomized adaptive construction procedure, a tabu local search procedure, a crossover operator, a population-updating method, and a path-relinking procedure. These strategies make a good tradeoff between intensification and diversification. A number of experiments were carried out on three types of instances from the literature. Compared with existing algorithms, HMA is able to find high-quality solutions in much less CPU time. Specifically, HMA is at least six times faster than existing algorithms on the tested instances. With increasing instance size, the CPU time required by HMA increases much more slowly than required by existing algorithms.

Wenxing Zhu

Papers

Partner selection with a due date constraint in virtual enterprises

Toward Optimal Legalization for Mixed-Cell-Height Circuit Designs

A Hybrid Simulated Annealing Algorithm for Nonslicing VLSI Floorplanning

An effective legalization algorithm for mixed-cell-height standard cells

An Effective Hybrid Memetic Algorithm for the Minimum Weight Dominating Set Problem