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This paper discusses the computation of matrix chain products of the form M1 X M2 X ... X Mn where Mi's are matrices. The order in which the matrices are computed affects the number of operations. A sufficient condition about the association of the matrices in the optimal order is presented. An O( n) algorithm to find an order of computation which takes less than 25 percent longer than the optimal time Topt is also presented. In most cases, the algorithm yields the optimal order or an order which takes only a few percent longer than Topt (less than I percent on the average). [ABSTRACT FROM AUTHOR]

In this paper, a time-varying distributed convex optimization problem is studied for continuous-time multi-agent systems. The objective is to minimize the sum of local time-varying cost functions, each of which is known to only an individual agent, through local interaction. Here, the optimal point is time varying and creates an optimal trajectory. Control algorithms are designed for the cases of single-integrator and double-integrator dynamics. In both cases, a centralized approach is first introduced to solve the optimization problem. Then, this problem is solved in a distributed manner and a discontinuous algorithm based on the signum function is proposed in each case. In the case of single-integrator (respectively, double-integrator) dynamics, each agent relies only on its own position and the relative positions (respectively, positions and velocities) between itself and its neighbors. A gain adaption scheme is introduced in both algorithms to eliminate certain global information requirement. To relax the restricted assumption imposed on feasible cost functions, an estimator based algorithm using the signum function is proposed, where each agent uses dynamic average tracking as a tool to estimate the centralized control input. As a tradeoff, the estimator-based algorithm necessitates communication between neighbors. Then, in the case of double-integrator dynamics, the proposed algorithms are further extended. Two continuous algorithms based on, respectively, a time-varying and a fixed boundary layer are proposed as continuous approximations of the signum function. To account for interagent collision for physical agents, a distributed convex optimization problem with swarm tracking behavior is introduced for both single-integrator and double-integrator dynamics. It is shown that the center of the agents tracks the optimal trajectory, the connectivity of the agents is maintained, and interagent collision is avoided. [ABSTRACT FROM AUTHOR]

This paper considers the infinite horizon optimal control of logical control networks, including Boolean control networks as a special case. Using the framework of game theory, the optimal control problem is formulated. In the sight of the algebraic form of a logical control network, its cycles can be calculated algebraically. Then the optimal control is revealed over a certain cycle. When the games, using memory \mu>1 (which means the players only consider previous \mu steps' action at each step), are considered, the higher order logical control network is introduced and its algebraic form is also presented, which corresponds to a conventional logical control network (i.e., \mu=1). Then it is proved that the optimization technique developed for conventional logical control networks is also applicable to this \mu-memory case. [ABSTRACT FROM AUTHOR]

Abstract: The goal of designing optimal nearest neighbor classifiers is to maximize classification accuracy while minimizing the sizes of both reference and feature sets. A usual way is to adaptively weight the three objectives as an objective function and then use a single-objective optimization method for achieving this goal. This paper proposes a multi-objective approach to cope with the weight tuning problem for practitioners. A novel intelligent multi-objective evolutionary algorithm IMOEA is utilized to simultaneously edit compact reference and feature sets for nearest neighbor classification. Three comparison studies are designed to evaluate performance of the proposed approach. It is shown empirically that the IMOEA-designed classifiers have high classification accuracy and small sizes of reference and feature sets. Moreover, IMOEA can provide a set of good solutions for practitioners to choose from in a single run. The simulation results indicate that the IMOEA-based approach is an expedient method to design nearest neighbor classifiers, compared with an existing single-objective approach. [Copyright &y& Elsevier]

Differential evolution (DE) was very successful in solving the global continuous optimization problem. It mainly uses the distance and direction information from the current population to guide its further search. Estimation of distribution algorithm (EDA) samples new solutions from a probability model which characterizes the distribution of promising solutions. This paper proposes a combination of DE and EDA (DE/EDA) for the global continuous optimization problem. DE/EDA combines global information extracted by EDA with differential information obtained by DE to create promising solutions. DE/EDA has been compared with the best version of the DE algorithm and an EDA on several commonly utilized test problems. Experimental results demonstrate that DE/EDA outperforms the DE algorithm and the EDA. The effect of the parameters of DE/EDA to its performance is investigated experimentally. [ABSTRACT FROM AUTHOR]