A swarm-exploring neurodynamic network (SENN) based on a two-timescale model is proposed in this study for solving nonconvex nonlinear programming problems. First, by using a convergent-differential neural network (CD...
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A swarm-exploring neurodynamic network (SENN) based on a two-timescale model is proposed in this study for solving nonconvex nonlinear programming problems. First, by using a convergent-differential neural network (CDNN) as a local quadratic programming (QP) solver and combining it with a two-timescale model design method, a two-timescale convergent-differential (TTCD) model is exploited, and its stability is analyzed and described in detail. Second, swarm exploration neurodynamics are incorporated into the TTCD model to obtain an SENN with global search capabilities. Finally, the feasibility of the proposed SENN is demonstrated via simulation, and the superiority of the SENN is exhibited through a comparison with existing collaborative neurodynamics methods. The advantage of the SENN is that it only needs a single recurrent neural network (RNN) interact, while the compared collaborative neurodynamic approach (CNA) involves multiple RNN runs.
In continuous variable, smooth, nonconvex nonlinear programming, we analyze the complexity of checking whether We construct a special class of indefinite quadratic programs, with simple constraints and integer data, a...
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In continuous variable, smooth, nonconvex nonlinear programming, we analyze the complexity of checking whether We construct a special class of indefinite quadratic programs, with simple constraints and integer data, and show that checking (a) or (b) on this class is NP-complete. As a corollary, we show that checking whether a given integer square matrix is not copositive, is NP-complete.
In this note we specify a necessary and sufficient condition for global optimality in concave quadratic minimization problems. Using this condition, it follows that, from the perspective of worst-case complexity of co...
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In this note we specify a necessary and sufficient condition for global optimality in concave quadratic minimization problems. Using this condition, it follows that, from the perspective of worst-case complexity of concave quadratic problems, the difference between local and global optimality conditions is not as large as in general. As an essential ingredient, we here use the epsilon-subdifferential calculus via an approach of Hiriart-Urruty and Lemarechal (1990).
Interior-point methods are among the most efficient approaches for solving large-scale nonlinearprogramming problems. At the core of these methods, highly ill-conditioned symmetric saddle-point problems have to be so...
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Interior-point methods are among the most efficient approaches for solving large-scale nonlinearprogramming problems. At the core of these methods, highly ill-conditioned symmetric saddle-point problems have to be solved. We present combinatorial methods to preprocess these matrices in order to establish more favorable numerical properties for the subsequent factorization. Our approach is based on symmetric weighted matchings and is used in a sparse direct LDLT factorization method where the pivoting is restricted to static supernode data structures. In addition, we will dynamically expand the supernode data structure in cases where additional fill-in helps to select better numerical pivot elements. This technique can be seen as an alternative to the more traditional threshold pivoting techniques. We demonstrate the competitiveness of this approach within an interior-point method on a large set of test problems from the CUTE and COPS sets, as well as large optimal control problems based on partial differential equations. The largest nonlinear optimization problem solved has more than 12 million variables and 6 million constraints.
With the growing urban population and its rapid growth of mobility needs, metro systems often suffer from congestion in peak hours in many mega-cities over the world. This incurs severe travel delays for commuters and...
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With the growing urban population and its rapid growth of mobility needs, metro systems often suffer from congestion in peak hours in many mega-cities over the world. This incurs severe travel delays for commuters and safety risks for metro operators. Hence, passenger flow management and control becomes an essential way to reduce station congestion during high-peak hours. This paper investigates the passenger flow control problem with the objective of increasing the number of boarding passengers. Considering the scenario that the destination of each passenger entering the station is unknown, a flow control problem with dynamic and station-based constraints is proposed to dynamically determine the number of passengers boarding each train at each station. Compared with existing flow control strategies, this model can improve the equity for boarding passengers of different OD pairs. The station-based flow control problem is formulated as a complicated nonlinearnonconvex quadratic programming model. To solve the intractable nonlinearprogramming model, we reformulate it into the dynamic programming formation and develop two efficient heuristic algorithms to solve it. We carry out two sets of numerical experiments, including the small-scale case with synthetic data and the real-world case with the operation data of Beijing metro system, to evaluate the performance of our model and algorithms. Several performance indicators, e.g. average waiting time and Gini coefficient, are presented to verify the efficiency and fairness of proposed model. The numerical results applied to Beijing urban subway network indicate that our approach can reduce the passengers' waiting time and the line-level Gini coefficient by 5.21% and 23.52% compared with the benchmark flow control strategy with maximum loading and station-based constraints.
Trim loss is one of the most common problem arising in process industries. Its mathematical model is a nonconvex mixed integer nonlinearprogramming problem subject to several constraints. In this paper we consider fo...
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ISBN:
(纸本)9781424450534
Trim loss is one of the most common problem arising in process industries. Its mathematical model is a nonconvex mixed integer nonlinearprogramming problem subject to several constraints. In this paper we consider four hypothetical cases, taken from literature [1] and propose an efficient approach based on Particle Swarm Optimization namely ILXPSO for solving trim loss problem. The numerical results when compared with the results available in literature [1] show the efficiency and robustness of the proposed algorithm.
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