In this paper, we propose a novel gate sizing approach for circuit optimization in the presence of scarce information about the distributions of the process variations. The proposed methodology relies upon the concepts of utility theory and risk minimization for multimetric optimization of delay, dynamic power, leakage power, and crosstalk noise, via gate sizing. A deterministic linear equivalent model from a fundamentally stochastic design optimization problem, ensuring high levels of expected utility and significant speedup in the optimization process for large circuits is derived in this work. Experimental results indicate that the proposed algorithm is efficient in terms of optimization results with multifold speedup in execution times compared to the traditional approaches.

Data and object clustering techniques are used in a wide variety of scientific applications such as biology, pattern recognition, information systems, etc. Traditionally, clustering methods have focused on optimizing a single metric, however, several multidisciplinary applications such as robot team deployment, ad hoc networks, facility location, etc., require the simultaneous examination of multiple metrics during clustering. In this paper, we propose a novel approach for spatial data clustering based on the concepts of microeconomic theory, which can simultaneously optimize both the compaction and the equipartitioning objectives. The algorithm models a multistep, normal form game consisting of randomly initialized clusters as players that compete for the allocation of data objects from resource locations. A Nash-equilibrium-based methodology is used to derive solutions that are socially fair for all the players. After each step, the clusters are updated using the KMeans algorithm, and the process is repeated until the stopping criteria are satisfied. Extensive simulations were performed on several real data sets as well as artificially synthesized data sets to evaluate the efficacy of the algorithm. Experimental results indicate that the proposed algorithm yields significantly better results as compared to the traditional algorithms. Further, the proposed algorithm yields a high value of fairness, a metric that indicates the quality of the solution in terms of simultaneous optimization of the objectives. Also, the sensitivity of the various design parameters on the performance of our algorithm is analyzed and reported.

The aggressive scaling of technology has not only accentuated the effects of intradie parametric variations in devices, but it has also impacted the effects of optimizing a certain performance metric on the optimality of other metrics. Thus, there is a need for optimization methods that can perform the simultaneous optimization of multiple metrics considering the effects of process variations. In this article, a novel variation-aware gate sizing framework has been developed that can perform simultaneous optimization of multiple performance metrics. In this framework, the relationships between the optimization metrics (like dynamic power, leakage power, and crosstalk noise) are modeled as a function of the gate sizes in the objective function. The delay values obtained from unconstrained delay optimization and the noise margins derived from coupling capacitance information form the constraints for the multimetric optimization problem. As an abstract framework, it is independent of the type of mathematical programming approach as well as the metrics chosen to be optimized. The framework has been implemented using a mathematical programming approach and has been tested on ITC'99 benchmarks for different combinations of multimetric and single-metric optimizations of delay, dynamic power, leakage power, and crosstalk noise. The results indicate that the framework identifies good solution points, and is efficient for postlayout optimization via gate sizing.

Technology scaling has not only magnified the effects of device process variations, but it has also precipitated the need for simultaneous optimization of several performance metrics. In this paper, we propose a novel gate sizing approach for multi-metric optimization of delay, power, and crosstalk noise. The algorithm is based on the concepts of mathematical programming, and models the process variation uncertainty considering spatial correlations. The approach identifies leakage power, dynamic power, and crosstalk noise as the objectives, and the optimized gate delays are kept as constraints. Initially, the deterministic upper and lower bounds of the objectives are identified, and during the final step, a crisp non-linear programming problem is formulated using these boundary values. The problem is solved using KNITRO, an interior-point based optimization solver. The proposed model maximizes the variation resistance, thus providing higher yield. ITC'99 benchmarks were used to test the proposed approach, and the results indicate that our algorithm identifies the solution points that are closest to the nominal bounds, while maintaining high timing yield.

Application of clustering approaches in cross-disciplinary domains has necessitated the identification of new methods capable of simultaneous examination of multiple conflicting metrics during optimization. In this work, we propose a novel multi-objective clustering approach based on the concepts of microeconomic theory. In a multi-step, normal form game theoretic setup, each randomly initialized cluster is categorized as either a player or a resource in the game. The players in the game compete against each other for allocation of resources, and try to maximize their own utilities. The utility for a strategy of a player is a function of the clustering objectives. A Nash equilibrium based methodology is used to identify a solution that is socially fair. The algorithm is tested on real as well as artificially synthesized spatial data sets to evaluate the efficacy of the algorithm, and the quantitative measure of the quality of clusters in terms of fairness.

In this research, we propose a novel approach for simultaneous optimization of power, crosstalk noise and delay via gate sizing, in the presence of scarce information about the distribution of the variations. The methodology uses the concepts of utility theory and risk minimization to identify a deterministic equivalent model of the stochastic problem, ensuring high levels of expected utilities of constraints, and significant speedup in the optimization process for large circuits. A comparative study with an existing gate sizing methodology shows that our method is multi-fold faster as well as comparable in terms of the optimization.

The aggregation of robots into teams is necessitated due to the limited power and communication capabilities in emergency environments. The formation of robot teams significantly enhances the performance and efficiency of search and rescue missions in such environments. As opposed to the classical partitioning application domains, the robot aggregation requires multiple confticting objectives to be optimized. We propose a novel microeconomic methodology for simultaneous multi-objective partitioning of robots. The method utilizes the strengths of K-Means algorithm, game theoretic modeling, and Nash equilibrium methodology for fast and socially fair partitioning. In this work, partitions are created on the basis of compaction and equipartitioning objectives to identify decentralized robot teams with each robot in a team closest to its communication gateway, as well as each team equally represented in terms of strength. Rigorous simulations were performed to evaluate the performance of the method, and the results indicate that the proposed method performs significantly better than the K-Means methodology, and identifies good solution points.

The optimal allocation of resources to emergency locations in the event of multiple crises in an urban environment is an intricate problem, especially when the available resources are limited. In such a scenario, it is important to allocate emergency response units in a fair manner based on the criticality of the crisis events and their requests. In this research, a crisis management tool is developed which incorporates a resource allocation algorithm. The problem is formulated as a game-theoretic framework in which the crisis events are modeled as the players, the emergency response centers as the resource locations with emergency units to be scheduled, and the possible allocations as strategies. The payoff is modeled as a function of the criticality of the event and the anticipated response times. The game is played assuming a specific region within a certain locality of the crisis events to derive an optimal allocation. If a solution is not feasible, the perimeter of the locality in consideration is increased and the game is repeated until convergence. Experimental results are presented to illustrate the efficacy of the proposed methodology and metrics are derived to quantify the fairness of the solution. A regression analysis is performed to establish the statistical significance of the results.

Resource management is a well studied field. Existence of multiple emergencies in a locality, in a time overlapped manner, demands an optimal allocation of required resources to the emergencies. This is an intricate problem if the availability of resources is limited. Involvement of human lives in such situations poses a very important constraint of social fairness on the optimality criteria of allocation. Hence, these situations necessitate an allocation methodology that could allocate the requested resources to the emergencies such that even a lower criticality emergency is serviced in a socially optimal manner. In this research, an emergency management tool is developed that models the problem as a game theoretic framework in which the crisis events are modeled as the players, the emergency response centers as the resource locations with the possible emergency unit allocations as strategies. The pay-off is modeled as a function of the criticality of the event and the anticipated response times. A single step, non-cooperative, normal form game is formulated and a Nash equilibrium based solution methodology is implemented to provide fair allocation of resources to the emergencies. Experimental results are presented to illustrate the efficacy of the proposed methodology and metrics are derived to quantify the fairness of the solution. A regression analysis is performed to establish the statistical significance of the results.