Design, Analysis and Test of Logic Circuits Under Uncertainty

Logic Circuit Design
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Epub Design, Analysis And Test Of Logic Circuits Under Uncertainty

To submit a proposal or request further information, please contact the Publishing Editor in your country:. The topics include e. Institute of Technology, Kalapatti, Coimbatore. The Conference provides academia. The book is a collection of peer-reviewed scientific papers submitted by active researchers in the 36th National System Conference NSC Multimedia processing has been an active r. Logic circuits are becoming increasingly susceptible to probabilistic behavior caused by external radiation and process variation.

In addition, inherently probabilistic quantum- and nano-technologies are on the horizon as we approach the limits of CM. Traditionally, design space exploration for Systems-on-Chip SoCs has focused on the computational aspects of the problem at hand. However, as the number of components on a single chip and their performance continue to increase, the communication. This volume contains thirty revised and extended research articles written by prominent researchers participating in an international conference in engineering technologies and physical science and applications.

The conference serves as good platform. This volume contains revised and extended research articles written by prominent researchers participating in the conference. When both solutions are infeasible, Pareto ranking based on constraints is calculated. If the rank is same, the one with worse fitness value survives.

A tournament selection criterion can be described as below to decide whether a current solution x should be replaced by a neighboring solution y:.

Epub Design, Analysis And Test Of Logic Circuits Under Uncertainty

Local search applied to all solutions in the current population in the algorithm is inefficient, as shown in Ishibuchi, Yoshida et al. In the proposed algorithm, the computation time spent by local search can be reduced by applying local search to only selected solutions in selected generations. If n is the number of decision variables, the best n number of solutions from the current population based on Pareto ranking are selected. These n number of mutated solutions and elites from N -th generation after local search are then put into the next population.

The generation update mechanism in the proposed algorithm is shown in Fig. The implementation of the anti-optimization part is modularized. As explained in the above, a local search procedure is applied to elite individuals and new solutions generated by the mutation in selected generations. Generally, a local search procedure can be written as follows:. Step 1. Specify an initial solution and its corresponding design variable under uncertainty. Step 2. Apply Hooke and Jeeves Method to determine the search path using the tournament selection criteria stated above as the function values.

The algorithm is given below:.

Logic Circuit Design

Generate random initial population P of size M. Step 4. Select elite individuals. Elite individuals carried from the previous generation preserve the values of their objective and constraint functions. Step 5.

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Step 7. If a prescribed stopping condition is satisfied, end the algorithm. Otherwise, return to Step 2. As in any structural topology optimization procedure, the geometry of the structure has to be represented and defined by some form of design variables. The enhanced morphological representation efficiently cast structure topology as a chromosome code that makes it effective for solution via a GA.

In the proposed scheme, the connectivities and the number of curves used are made variable and to be optimized in the evolutionary procedure. The process of the scheme definition is illustrated as follows. A square design space shown in Fig. While it is initially unknown how the design space will be occupied by the structure, there must exist some segments of the structure such as the support and the loading that have functional interactions with its surroundings.

The support point is some segment of the structure that is restrained fixed, with zero displacement while the loading point is where some specified load input force is applied to deform the structure. Collectively, the support and loading points represent the input points of the structure. There is also usually an output point which is some segment of the structure where the desired output behavior is attained. As shown in Fig. Six connecting curves in the illustration of Fig. Before continuing, it is important to make a clear distinction between the active and inactive curves.

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The structure is generated based only on the active curves. In Fig. Each curve is a Bezier curve defined by the position vector which can be derived from the element number of control point. Some of the elements surrounding the skeleton are then included to fill up the structure to its final form Fig.

Each curve is defined by three control points, and hence each curve has four thickness values. Hence the structural geometry in Fig. Each curve is represented by a series of nodes connected by arcs in the sequence of start element number, thickness values alternating with control element number and end point.

For identification purpose, the active curves are shown by solid lines and the inactive curves are represented by dotted lines. The resulting. Two of the important operations in a GA are the crossover and mutation.

In this implementation, the crossover operator works by randomly sectioning any single connected subgraph from a parent chromosome and swapping with a corresponding subgraph from another parent as shown in Fig. Otherwise, the child curve will be inactive. As for mutation, the mutation operator works by randomly selecting any vertex of the chromosomal graph and altering its value to another randomly generated value within its allowable range. Mutation about the on-off state is simple, which is altering the state of curves.

When the selected curve is active, it will be inactive after mutation, and vice verse. In summary, this morphological representation scheme uses arrangements of skeleton and surrounding material to define structural geometry in a way that will not render any undesirable design features such as disconnected segments, checkerboard patterns or single-node hinge connections because element edge connectivity of the skeleton is guaranteed, even after any crossover or mutation operation. Any chromosome-encoded design generated by the evolutionary procedure can be mapped into a finite element model of the structure accordingly.

Before a GA is relied upon for solving a structure design problem with unknown solutions, it is important that the performance of the GA be tested and tuned by using it to solve a problem with known solutions. Various kinds of test problems Michalewicz, Deb et al. They were created with different characteristics, including the dimensionality of the problem, number of local optima, number of active constraints at the optimum, topology of the feasible search space, etc. The test problem should, therefore, ideally suit or be customized to the GA being used.

The GA solving such problems may have special chromosome encoding to suit the structure geometry representation used and there may also be specially devised reproduction operators to suit the chromosome encoding used.

As such, the structure geometry representation scheme, the chromosome encoding and the reproduction operators introduce additional characteristics to the search space and, therefore, they are very critical to the performance of the GA. The test problem for such GAs, therefore, must use the same structure geometry representation scheme, chromosome encoding and reproduction operators. The conventional test problems found in literature cannot make use of the GA's integral procedures such as structure geometry representation scheme and therefore they are not suitable for testing such GAs.

Ideally, the test problem should emulate the main problem to be solved. The test problem should be computationally inexpensive so that it can be run many times for the GA parameters to be changed or experimented with and the effect thereof can be studied for the purpose of fine-tuning the GA. However, the main problem in the present work, being a structural topology optimization problem under uncertainty, requires structural analysis which consumes a great deal of time.

Taking the running time into consideration, the test problem needs to be designed without any need for structural analysis. A test problem emulating structural topology optimization does not necessarily need structural analysis as the main aim of topology optimization is to arrive at an optimal structural geometry.

The target matching problems are defined here as multiobjective optimization problems under uncertainty which are more difficult e. The test problem makes use of the design space shown in Fig. The loading point 1 is positioned anywhere along the left boundary and loading point 2 is positioned anywhere along the right boundary. The position of output point is fixed as shown in Fig. In this problem, the target geometry is shown in Fig. The aim is therefore to evolve structures that match as closely as possible this target geometry.

The problem is formulated with the following two objectives and two constraints: distance objective, material objective, forbidden area constraint and prescribed area constraint. It has that on the Cycladic Islands, download introducing nietzsche: a graphic guide was into the Saharasian disadvantage, politically because no one was them female life.

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