A one-layer recurrent neural network with a discontinuous hard-limiting activation function for quadratic programming.

In this paper, a one-layer recurrent neural network with a discontinuous hard-limiting activation function is proposed for quadratic programming. This neural network is capable of solving a large class of quadratic programming problems. The state variables of the neural network are proven to be globally stable and the output variables are proven to be convergent to optimal solutions as long as the objective function is strictly convex on a set defined by the equality constraints. In addition, a sequential quadratic programming approach based on the proposed recurrent neural network is developed for general nonlinear programming. Simulation results on numerical examples and support vector machine (SVM) learning show the effectiveness and performance of the neural network.     

The Hopfield-Tank neural network applied to the mobile agent planning problem

Mobile agent planning (MAP) is increasingly viewed as an important technique of information retrieval systems to provide location aware services of minimum cost in mobile computing environment. Although Hopfield-Tank neural network has been proposed for solving the traveling salesperson problem, little attention has been paid to the time constraints on resource validity for optimizing the cost of the mobile agent. Consequently, we modify Hopfield-Tank neural network and design a new energy function to not only cope with the dynamic temporal features of the computing environment, in particular the server performance and network latency when scheduling mobile agents, but also satisfy the location-based constraints such as the starting and end node of the routing sequence must be the home site of the traveling mobile agent. In addition, the energy function is reformulated into a Lyapunov function to guarantee the convergent stable state and existence of the valid solution. Moreover, the objective function is derived to estimate the completion time of the valid solutions and predict the optimal routing path. Simulations study was conducted to evaluate the proposed model and algorithm for different time variables and various coefficient values of the energy function. The experimental results quantitatively demonstrate the computational power and speed of the proposed model by producing solutions that are very close to the minimum costs of the location-based and time-constrained distributed MAP problem rapidly. The spatio-temporal technique proposed in this work is an innovative approach in providing knowledge applicable to improving the effectiveness of solving optimization problems.     

Sequential approximate multi-objective optimization using radial basis function network

In industrial design optimization, objectives and constraints are generally given as implicit form of the design variables, and are evaluated through computationally intensive numerical simulation. Under this situation, response surface methodology is one of helpful approaches to design optimization. One of these approaches, known as sequential approximate optimization (SAO), has gained its popularity in recent years. In SAO, the sampling strategy for obtaining a highly accurate global minimum remains a critical issue. In this paper, we propose a new sampling strategy using sequential approximate multi-objective optimization (SAMOO) in radial basis function (RBF) network. To identify a part of the pareto-optimal solutions with a small number of function evaluations, our proposed sampling strategy consists of three phases: (1) a pareto-optimal solution of the response surfaces is taken as a new sampling point; (2) new points are added in and around the unexplored region; and (3) other parts of the pareto-optimal solutions are identified using a new function called the pareto-fitness function. The optimal solution of this pareto-fitness function is then taken as a new sampling point. The upshot of this approach is that phases (2) and (3) add sampling points without solving the multi-objective optimization problem. The detailed procedure to construct the pareto-fitness function with the RBF network is described. Through numerical examples, the validity of the proposed sampling strategy is discussed.     

A Train Dispatching Model Under a Stochastic Environment: Stable Train Routing Constraints and Reformulation

After major capacity breakdown(s) on a railway network, train dispatchers need to generate appropriate dispatching plans to recover the impacted train schedule from perturbations and minimize the expected total train delay time under stochastic scenarios. In this paper, we propose a cumulative flow variables-based integer programming model for dispatching trains under a stochastic environment on a general railway network. Stable Train Routing (STR) constraints are introduced to ensure that trains traverse on the same route across different capacity breakdown scenarios, which are further reformulated to equivalent linear inequality constraints. Track occupancy and safety headways are modelled as side constraints which are dualized through a proposed Lagrangian relaxation solution framework. The original complex train dispatching problem is then decomposed to a set of single-train and single-scenario optimization subproblems. For each subproblem, a standard label correcting algorithm is embedded for finding the time dependent least cost path on a space-time network. The resulting dual solutions can be transformed to feasible solutions through priority rules. Numerical experiments are conducted to demonstrate the efficiency and effectiveness of the proposed solution approach.     

Computer aided optimization of natural gas pipe networks using genetic algorithm

This study is concerned to determine the optimum pipe size for networks used in natural gas applications. The genetic algorithm has been used in optimizing network parameters. The topology of the network is predefined. The study deals with the discrete nature of decision variables, namely, pipe diameters, as they are usually available in market in standard sizes. Hard constraints and soft constraints are considered. An imposed penalty factor is introduced to allow solutions that violate soft constraints to remain in the population during the solution progress guiding the algorithm convergence to a minimum network cost.In a case study, engineers with average experience of 6 years in the design office of a gas company performed the design of a gas network problem using their experience and judgment. The adopted method by engineers depends on a trial and error, time consuming, procedure. Their results are compared with the results obtained from the developed genetic algorithm optimization technique.The developed optimization technique has provided a distinctive reduction in the total cost of pipe networks over the existing heuristic approach which is based on human experience and judgment. A saving up to 12.1% has been achieved using the present analysis, in the special case studied.     

Constrained multi-variable generalized predictive control using a dual neural network

Multi-variable generalized predictive control algorithm has obtained great success in process industries. However, it suffers from a high computational cost because the multi-stage optimization approach in the algorithm is time-consuming when constraints of the control system are considered. In this paper, a dual neural network is employed to deal with the multi-stage optimization problem, and bounded constraints on the input and output signals of the control system are taken into account. The dual neural network has many favorable features such as simple structure, rapid execution, and easy implementation. Therefore, the computation efficiency, in comparison with the consecutive executions of numerical algorithms on digital computers, is increased dramatically. In addition, the dual network model can yield the exact optimum values of future control signals while many other neural networks only obtain the approximate optimal solutions. Hence the multi-variable generalized predictive control algorithm based on the dual neural network is suitable for industrial applications with the real-time computation requirement. Simulation examples are given to demonstrate the efficiency of the proposed approach.     

Linear and quadratic programming neural network analysis

Neural networks for linear and quadratic programming are analyzed. The network proposed by M.P. Kennedy and L.O. Chua (IEEE Trans. Circuits Syst., vol.35, pp.554-562, May 1988) is justified from the viewpoint of optimization theory and the technique is extended to solve optimization problems, such as the least-squares problem. For quadratic programming, the network converges either to an equilibrium or to an exact solution, depending on whether the problem has constraints or not. The results also suggest an analytical approach to solve the linear system Bx =b without calculating the matrix inverse. The results are directly applicable to optimization problems with C(2) convex objective functions and linear constraints. The dynamics and applicability of the networks are demonstrated by simulation. The distance between the equilibria of the networks and the problem solutions can be controlled by the appropriate choice of a network parameter.     

Neural network for quadratic optimization with bound constraints

A recurrent neural network is presented which performs quadratic optimization subject to bound constraints on each of the optimization variables. The network is shown to be globally convergent, and conditions on the quadratic problem and the network parameters are established under which exponential asymptotic stability is achieved. Through suitable choice of the network parameters, the system of differential equations governing the network activations is preconditioned in order to reduce its sensitivity to noise and to roundoff errors. The optimization method employed by the neural network is shown to fall into the general class of gradient methods for constrained nonlinear optimization and, in contrast with penalty function methods, is guaranteed to yield only feasible solutions.     

Multi-fingered robot hand optimal task force distribution: Neural inverse kinematics approach

Grasping and manipulation force distribution optimization of multi-fingered robotic hands can be formulated as a problem for minimizing an objective function subject to form-closure constraints, kinematics, and balance constraints of external force. In this paper we present a novel neural network for dexterous hand-grasping inverse kinematics mapping used in force optimization. The proposed optimization is shown to be globally convergent to the optimal grasping force. The approach followed here is to let an artificial neural network (ANN) learn the nonlinear inverse kinematics functional relating the hand joint positions and displacements to object displacement. This is done by considering the inverse hand Jacobian, in addition to the interaction between hand fingers and the object. The proposed neural-network approach has the advantages that the complexity for implementation is reduced, and the solution accuracy is increased, by avoiding the linearization of quadratic friction constraints. Simulation results show that the proposed neural network can achieve optimal grasping force.     

Time-varying two-phase optimization and its application toneural-network learning

In this paper, a time-varying two-phase (TVTP) optimization neural network is proposed based on the two-phase neural network and the time-varying programming neural network. The proposed TVTP algorithm gives exact feasible solutions with a finite penalty parameter when the problem is a constrained time-varying optimization. It can be applied to system identification and control where it has some constraints on weights in the learning of the neural network. To demonstrate its effectiveness and applicability, the proposed algorithm is applied to the learning of a neo-fuzzy neuron model.     

相关积分结合鲁棒预测控制求解实时优化问题及应用

针对现有传统相关积分优化算法在求解实时优化时存在的问题,如考虑实时约束不足、算法参数较为单 一且参数难以凑试等,提出一种将鲁棒预测控制与相关积分相结合的实时优化算法,采用传统相关积分优化算法计算优化目标函数和调优变量的梯度,将调优变量实时梯度作为表征系统是否还有优化裕度的中间变量,利用基于多胞体模型的鲁棒预测控制方法对调优变量增量进行实时求解,并将调优变量的增量作为调优变量的设定值. 所提出改进算法继承了传统相关积分优化的优点,同时也提升了原有算法的约束处理能力,保证了其优化解的实时可行性.仿真研究以及二甲苯加热炉热效率实时优化的工业应用测试结果验证了所提出方法的可行性和有效性.     

Design of Marx generators as a structured eigenvalue assignment

We consider the design problem for a Marx generator electrical network, a pulsed power generator. We show that the components design can be conveniently cast as a structured real eigenvalue assignment with significantly lower dimension than the state size of the Marx circuit. Then we present two possible approaches to determine its solutions. A first symbolic approach consists in the use of Gröbner basis representations, which allows us to compute all the (finitely many) solutions. A second approach is based on convexification of a nonconvex optimization problem with polynomial constraints. We also comment on the conjecture that for any number of stages the problem has finitely many solutions, which is a necessary assumption for the proposed methods to converge. We regard the proof of this conjecture as an interesting challenge of general interest in the real algebraic geometry field.     

A parameter free Continuous Ant Colony Optimization Algorithm for the optimal design of storm sewer networks: Constrained and unconstrained approach

This paper describes the application of the newly introduced Continuous Ant Colony Optimization Algorithm (CACOA) to optimal design of sewer networks. Two alternative approaches to implement the algorithm is presented and applied to a storm sewer network in which the nodal elevations of the network are considered as the decision variables of the optimization problem. In the first and unconstrained approach, a Gaussian probability density function is used to represent the pheromone concentration over the allowable range of each decision variable. The pheromone concentration function is used by each ant to randomly sample the nodal elevations of the trial networks. This method, however, will lead to solutions which may be infeasible regarding some or all of the constraints of the problem and in particular the minimum slope constraint. In the second and constrained approach, known value of the elevation at downstream node of a pipe is used to define new bounds on the elevation of the upstream node satisfying the explicit constraints on the pipe slopes. Two alternative formulations of the constrained algorithm are used to solve a test example and the results are presented and compared with those of unconstrained approach. The methods are shown to be very effective in locating the optimal solution and efficient in terms of the convergence characteristics of the resulting algorithms. The proposed algorithms are also found to be relatively insensitive to the initial colony and size of the colony used compared to the original algorithm.     

An extrapolation approach for the solution of singular optima

In this paper, an efficient extrapolation approach for the solutions of singular problems in structural topology optimization subjected to stress constraints is presented. On the basis of the ε-relaxed formulation recently proposed by the authors, the sensitivities of the active design variables and the Lagrange multipliers associated with the active constraints with respect to the relaxation parameter at the current optimum of the relaxed problem are derived. Through the use of these sensitivities, a singular optimum can be obtained by employing the extrapolation technique at a relatively large value of ε, thus great computation efforts associated with the continuation approach for the solution of singular optimum can be saved. Several numerical examples illustrate the effectiveness of the proposed approach. Received February 15, 1999     

Neurocomputing strategies in structural design — decomposition based optimization

The present paper introduces a scheme utilizing neurocomputing strategies for a decomposition approach to large scale optimization problems. In this scheme the modelling capabilities of a backpropagation neural network are employed to detect weak couplings in a system and to effectively decompose it into smaller, more tractable subsystems. When such partitioning of a design space is possible (decomposable systems), independent optimization in each subsystem is performed with a penalty term added to an objective function to eliminate constraint violations in all other subsystems. Dependencies among subsystems are represented in terms of global design variables, and since only partial information is needed, a neural network is used to map relations between global variables and all system constraints. A featuresensitive network (a variant of ahierarchical vector quantization technique, referred to as the HVQ network) is used for this purpose as it offers easy training, approximations of an arbitrary accuracy, and processing of incomplete input vectors. The approach is illustrated with applications to minimum weight sizing of truss structures with multiple design constraints.     

The influence of joint angle constraints on the optimum design of a planar robot manipulator following a complicated prescribed path

The application of a general optimization methodology, previously proposed by the authors, is extended here to the design of a three link revolute-joint planar manipulator performing a complicated prescribed task. In particular the end effector follows a “figure-of-eight” path. The minimization of average torque required for execution of the task is addressed and the optimization is carried out with the link lengths and base coordinates taken as the five design variables. In addition to simple physical bounds placed on the variables, the maximum deliverable torques of the driving motors represent further constraints on the system. Joint angle constraints, which are severe for this problem, are also imposed. This results in a challenging optimization problem. Two different approaches are used in the application of torque and joint angle constraints. The complications arising from lock-up and nonassembly are handled by specially devised procedures. The optimization is carried out via a penalty function formulation of the constrained problem to which Snyman's unconstrained trajectory optimization algorithm is applied in a special way. Without joint angle constraints feasible designs with low objective function values are obtained. With the imposition of joint angle constraints the method yields good, but compromised, solutions.     

An evolutionary Bayesian belief network methodology for optimum management of groundwater contamination

An integrated methodology, based on Bayesian belief network (BBN) and evolutionary multi-objective optimization (EMO), is proposed for combining available evidence to help water managers evaluate implications, including costs and benefits of alternative actions, and suggest best decision pathways under uncertainty. A Bayesian belief network is a probabilistic graphical model that represents a set of variables and their probabilistic relationships, which also captures historical information about these dependencies. In complex applications where the task of defining the network could be difficult, the proposed methodology can be used in validation of the network structure and the parameters of the probabilistic relationship. Furthermore, in decision problems where it is difficult to choose appropriate combinations of interventions, the states of key variables under the full range of management options cannot be analyzed using a Bayesian belief network alone as a decision support tool. The proposed optimization method is used to deal with complexity in learning about actions and probabilities and also to perform inference. The optimization algorithm generates the state variable values which are fed into the Bayesian belief network. It is possible then to calculate the probabilities for all nodes in the network (belief propagation). Once the probabilities of all the linked nodes have been updated, the objective function values are returned to the optimization tool and the process is repeated. The proposed integrated methodology can help in dealing with uncertainties in decision making pertaining to human behavior. It also eliminates the shortcoming of Bayesian belief networks in introducing boundary constraints on probability of state values of the variables. The effectiveness of the proposed methodology is examined in optimum management of groundwater contamination risks for a well field capture zone outside Copenhagen city.     

Integrated layout and topology optimization design of multi-frame and multi-component fuselage structure systems

The purpose of this paper is to present an extended integrated layout and topology optimization method dealing with the multi-frame and multi-component fuselage structure systems design. Considering an aircraft or aerospace fuselage system including main structure, numbers of frames and featured components located on the frames, a simultaneous optimization procedure is proposed here including geometrical design variables of components and frames as well as topological design variables of main structure and frame structures. The multi-point constraints (MPC) scheme is used to simulate the rivets or bolts connecting the components, frames and structures. The finite circle method (FCM) is implemented to avoid the overlaps among different components and frames. Furthermore, to deal with the difficulties of large numbers of non-overlapping constraints, a penalty method is used here to compose the global strain energy and non-overlapping constraints into a single objective function. To guarantee the fuselage system’s balance, the constraint on the system centroid is also introduced into the optimization. Different numerical examples are tested and the optimized solutions have demonstrated the validity and effectiveness of the proposed formulation.     

Optimization of a nonlinear area traffic control system with elastic demand

An area traffic control network system is considered in this paper. Optimal signal settings can be determined while trip rates and network flow are in equilibrium. This problem can be formulated as a nonlinear mathematical program with equilibrium constraints. For the objective function, the system performance can be defined as a function of signal setting variables. For the constraint set, a user equilibrium traffic assignment with elastic demand obeying Wardrop’s first principle is formulated as a variational inequality problem. Due to the nonlinearity and non-differentiability of the perturbed solutions in equilibrium constraints, a non-smooth approach is investigated in this paper. Numerical tests are performed using a variety of example road networks to quantify the effectiveness and robustness of the proposed method.     

Using variable reduction strategy to accelerate evolutionary optimization

In this study, we introduce a novel approach of variable reduction and integrate it into evolutionary algorithms in order to reduce the complexity of optimization problems. We develop reduction processes of variable reduction for derivative unconstrained optimization problems (DUOPs) and constrained optimization problems (COPs) with equality constraints and active inequality constraints. Variable reduction uses the problem domain knowledge implied when investigating optimal conditions existing in optimization problems. For DUOPs, equations involving derivatives are considered while for COPs, we discuss equations expressing the equality constraints. From the relationships formed in this way, we obtain relationships among the variables that have to be satisfied by optimal solutions. According to such relationships, we can utilize some variables (referred to as core variables) to express some other variables (referred to as reduced variables). We show that the essence of variable reduction is to produce a minimum collection of core variables and a maximum number of reduced variables based on a system of equations. We summarize some application-oriented situations of variable reduction and stress several important issues related to the further application and development of variable reduction. Essentially, variable reduction can reduce the number of variables and eliminate equality constraints, thus reducing the dimensionality of the solution space and improving the efficiency of evolutionary algorithms. The approach can be applied to unconstrained, constrained, continuous and discrete optimization problems only if there are explicit variable relationships to be satisfied in the optimal conditions. We test variable reduction on real-world and synthesized DUOPs and COPs. Experimental results and comparative studies point at the effectiveness of variable reduction.