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In this paper, it is proved that for any Boolean function of n variables, there are infinitely many functions, each of which is its concave continuation to the n-dimensional unit cube. For an arbitrary Boolean function of n variables, a concave function is constructed, which is the minimum among all its concave continuations to the n-dimensional unit cube. It is proven that this concave function on the n-dimensional unit cube is continuous and unique. Thanks to the results obtained, in particular, it has been constructively proved that the problem of solving a system of Boolean equations can be reduced to the problem of numerical maximization of a target function, any local maximum of which in the desired domain is a global maximum, and, thus, the problem of local maxima for such problems is completely solved.

Aimed at the short-term extreme value prediction of ship motion, a sliding window method based on motion spectrum information is proposed to extract feature data, based on which, a series prediction model of convolutional neural networks (CNN) and long short-term memory (LSTM) is built. The CNN module aims at the local correlation characteristics of the input data, and the LSTM module aims at the time dimension characteristics of the data. The simulation test results of S175 ship show that the model has a good prediction effect on the motion extremum information in the next 1 and 2 cycles, and the evaluation indexes are significantly better than those of LSTM and gate recurrent unit (GRU) models, which has an important application value.

Copyright of Journal of Shanghai Jiao Tong University (1006-2467) is the property of Journal of Shanghai Jiao Tong University Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Coverage path planning (CPP) is the foundation of multiple robotic applications. The efficiency of CPP is affected by the local extremum, which describes a situation with the robot surrounded by obstacles and explored areas, even if unexplored areas remain in the environment. Most online CPP methods reactively deal with the local extremum after the mobile robot is trapped within it. However, repeated coverage is generated since the path of escaping the local extremum revisits the covered areas. This paper presents an online spiral coverage framework with proactive prevention of extremum (SP2E) to address the CPP problem in an unknown environment. Unlike other CPP methods, the SP2E approach prevents the local extremum through a cut vertex detection algorithm and a direction adaptation algorithm. The cut vertex detection algorithm predicts the local extremum by detecting cut vertexes, and the direction adaptation algorithm prevents it by adjusting the spiral path’s direction. The SP2E approach was validated by simulations and real-world experiments, and its performance was compared with other CPP algorithms. The results of simulations and real-world experiments demonstrate that the SP2E approach provides the minimum coverage time and computation time while avoiding the local extremum. [ABSTRACT FROM AUTHOR]

The particle swarm optimization (PSO) algorithm has certain disadvantages; for instance, the convergence viscosity of the algorithm is reduced in the post evolution phase, the optimization search efficiency is also reduced, the algorithm is easy to be inserted with a local extremum during the calculation of a complex problem of a high-dimensional multiple extremum, and the convergence thereof is low. To compensate for the PSO disadvantage, we propose a particle swarm optimization of the comprehensive improvement strategy, which is a simple particle swarm optimization with a dynamic adaptive hybridization of the extremum disturbance and the ecds-PSO algorithm. This new comprehensively improved particle swarm algorithm discards the particle velocity and reduces the PSO from the second-order to a first-order difference equation. The evolutionary process is controlled by the particle position variables only. The hybridization operation of increasing the extremum disturbance and introducing a genetic algorithm can accelerate the particles to overstep the local extremum. The mathematical derivation and the plurality of a comparative experiment provide the following information: the improved particle swarm optimization is a simple and effective optimization algorithm that can enhance the algorithm accuracy, the convergence viscosity and the ability of avoiding the local extremum, and effectively reduce the calculation complexity. [ABSTRACT FROM AUTHOR]

The well-known lower bound for the maximum number of prime implicants of a Boolean function (the length of the reduced DNF) differs by times from the upper bound and is asymptotically attained at a symmetric belt function with belt width . To study the properties of connected Boolean functions with many prime implicants, we introduce the notion of a locally extremal function in a certain neighborhood in terms of the number of prime implicants. Some estimates are obtained for the change in the number of prime implicants as the values of the belt function range over a -neighborhood. We prove that the belt function for which the belt width and the number of the lower layer of unit vertices are asymptotically equal to is locally extremal in some neighborhood for and not locally extremal if . A similar statement is true for the functions that have prime implicants of different ranks. The local extremality property is preserved after applying some transformation to the Boolean function that preserves the distance between the vertices of the unit cube. [ABSTRACT FROM AUTHOR]

Recently, the study of the near and far space with the help of small spacecraft has become more important. In this regard, we can definitely talk about the whole industry of small space technology, the problems of its creation, application, launch and operation. Today we have a large arsenal of carrier rockets of various classes, numerous conversion rocket technologies has been accumulated, allowing, directly or indirectly, to ensure not only the delivery of small space technology to working orbits, but also to perform control and other functions for basic spacecraft of various purposes. This paper addresses the problem of the relative motion of small spacecraft, taking into account their layout on the launch platform and separation parameters. As a solution, an algorithm is proposed for finding the optimal layout of devices on the platform and modeling their separation and subsequent movement. The choice of perturbing factors that are used in the simulation of orbital motion is substantiated. The results of the layout and graphics of the relative position of the launch platform and the small spacecraft, the relative position of the two separated vehicles at a given time interval are given. The modeling of the movement of the separated apparatus near the international space station is presented.

The unified 1st-order sufficient condition was proposed for existence of the local extremums of n-variable functions, in a case more general than classical unconstrained optimization ones. The difficulty of no such 1st-order sufficient condition in optimization theories was solved. Moreover, the 1st-order sufficient condition for 1-variable functions was proved to be a special case of the results. The work can eliminate the shortages of the 2nd-order sufficient conditions for existence of local extremums of classical multivariate functions, and the result is both necessary and sufficient under the assumption of quasiconvexity or quasiconcavity. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic self-adapting and simple particle swarm optimization algorithm with the disturbed extremum and crossover is proposed in order to improve the problem of particle swarm optimization in dealing with high-dimensional multi-extremum problem which is easy to fall into the local extremum and the accuracy of search and speed of the rapid decline problem in the late evolution. The dynamic self-adapting inertia weight and simplified speed equation strategy reduce the computational difficulty of the algorithm and improve the problem of slow convergence and low precision of the evolutionary algorithm due to the particle divergence caused by the velocity term; Extreme value perturbation and hybridization strategies are used to adjust the global extremes and individual positions of the particles to ensure the diversity and vigor of the particles in the late evolutionary period, and improve the ability of the particles to get rid of the local extremes. Three sets of computational experiments are carried out to compare and evaluate the search speed, convergence accuracy and population diversity of the improved algorithm, the results show that the improved algorithm has obtained a very good optimization effect and improved the practicability of the particle swarm optimization algorithm. It shows that the improved algorithm has improved the search speed, precision and population diversity of the optimization algorithm which improves the practicability of the particle swarm algorithm and achieves the expected effect. [ABSTRACT FROM AUTHOR]

The molecular kinetic theory optimization algorithm has the disadvantages of poor optimization accuracy and ease of being stuck into local extremum. A new molecular kinetic theory optimization algorithm with two populations is proposed. In this algorithm, the whole population is divided into two sub-groups: the elite subgroup and the ordinary subgroup. The ordinary subgroup uses the search strategy of traditional molecular kinetic theory optimization algorithm to do a wide range search. Through cooperation ,the elite subgroup does a refinement search to improve the convergence accuracy of the algorithm. Information exchange among sub-groups is completed through individual migration. Two subgroups complete the search process by cooperation. Test results show that the improved algorithm significantly improves the convergence speed, accuracy and stability. [ABSTRACT FROM AUTHOR]

Copyright of Basic Sciences Journal of Textile Universities / Fangzhi Gaoxiao Jichu Kexue Xuebao is the property of Basic Sciences Journal of Textile Universities and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Maximal information coefficient (MIC) is an indicator to explore the correlation between pairwise variables in large data sets, and the accuracy of MIC has an impact on the measure of dependence for each pair. To improve the equitability in an acceptable run-time, in this paper, an intelligent MIC (iMIC) is proposed for optimizing the partition on the y-axis to approximate the MIC with good accuracy. It is an iterative algorithm on quadratic optimization to generate a better characteristic matrix. During the process, the iMIC can quickly find out the local optimal value while using a lower number of iterations. It produces results that are close to the true MIC values by searching just n times, rather than n 2 computations required for the previous method. In the compared experiments of 169 indexes about 202 countries from World Health Organization (WHO) data set, the proposed algorithm offers a better solution coupled with a reasonable run-time for MIC, and good performance search for the extreme values in fewer iterations. The iMIC develops the equitability keeping the satisfied accuracy with fast computational speed, potentially benefitting the relationship exploration in big data. [ABSTRACT FROM AUTHOR]

The power output curves of solar photovoltaic (PV) system have multiple peaks under partially shaded condition. As the same as traditional MPPT (Maximum Power Point Tracking) search methods, bat algorithm often makes optimized results fall into local extremum. So an improved bat algorithm is proposed. Chaos search strategy is introduced in initial arrangement to improve the uniformity and ergodicity of population. Adapting weight is introduced to balance the global searching ability and the local searching ability. Dynamic contraction regain decreases the search range more effectively. Compared with the original algorithm, the rapidity and accuracy of algorithm have been improved. The simulation shows that improved bat algorithm can find the globally optimal point fast, with high precision, under the partially shaded condition. [ABSTRACT FROM AUTHOR]