Original Nonlinear Optimization Problem Research Articles

Research on optimization algorithms for localization and capacity determination of chargers considering the spatiotemporal distribution of electric vehicles

The optimized layout of electric vehicle (EV) chargers is not only crucial for users' convenience but also a key element in urban sustainable development, energy transition, and the promotion of new energy vehicles. In order to provide a basis for the problem of localization and capacity determination of chargers and compare the merits of several mainstream algorithms, this paper first establishes an optimization model with the objective of minimizing the total investment cost of all the chargers and the constraint of meeting the charging demands of all electric vehicles. Optimizations were performed using genetic algorithm (GA), surrogate optimization algorithm (SOA), and mixed integer linear programming (MILP) algorithm, respectively. In the case of using MILP, the original nonlinear optimization problem was transformed into a linear problem. In the planning of city-level EV chargers, MILP took 14182.57 s to calculate the minimum cost of 34.62 million yuan. After retaining only 10% of the original data amount, SOA took 87651.34 s to calculate the minimum cost of 3.01 million yuan. The results indicate that GA is prone to falling into local optima and is not suitable for large-scale optimization problems. SOA, on the other hand, requires significant memory consumption, so the issue of memory usage needs to be carefully considered when using it directly. Although MILP is only applicable to linear programming problems, it has the advantages of lower memory usage and higher reliability if the problem can be transformed into a linear one.

Optimal control of discrete‐time nonlinear heterogeneous multi‐agent systems via a distributed DISOPE algorithm

AbstractA distributed offline DISOPE algorithm for optimal state synchronization of leader‐follower systems with nonlinear discrete‐time dynamics is considered, which integrates the model optimization idea and parameter estimation technique together. It can be seen that the convergent solutions of modified linear optimal control problems satisfy the optimality conditions of the original nonlinear optimization problem with non‐LQ performance indices. The heterogeneous agents can cooperate and exchange information via network communication. Based on DISOPE algorithm, a distributed optimal control policy is obtained to assure state synchronization and minimize performance indices in finite time horizon. Finally, a simulation example is provided to illustrate the effectiveness of the distributed DISOPE algorithm.

On some parameter estimation algorithms for the nonlinear exponential autoregressive model

SummaryModeling an exponential autoregressive (ExpAR) time series is the basis of solving the corresponding prediction and control problems. This paper investigates the hierarchical parameter estimation methods for the ExpAR model. By the hierarchical identification principle, the original nonlinear optimization problem is transformed into the combination of a linear and nonlinear optimization problem, and then, we derive a hierarchical least squares and stochastic gradient (LS‐SG) algorithm. Given the difficulty of determining the step‐size in the hierarchical LS‐SG algorithm, an approach is proposed to obtain the optimal step‐size. To improve the parameter estimation accuracy, the multi‐innovation identification theory is employed to develop a hierarchical least squares and multi‐innovation stochastic gradient algorithm for the ExpAR model. Two simulation examples are provided to test the effectiveness of the proposed algorithms.

Efficient hybrid algorithms to solve mixed discrete-continuous optimization problems

PurposeIn real-world cases, it is common to encounter mixed discrete-continuous problems where some or all of the variables may take only discrete values. To solve these non-linear optimization problems, the use of finite element methods is very time-consuming. The purpose of this study is to investigate the efficiency of the proposed hybrid algorithms for the mixed discrete-continuous optimization and compare it with the performance of genetic algorithms (GAs).Design/methodology/approachIn this paper, the enhanced multipoint approximation method (MAM) is used to reduce the original nonlinear optimization problem to a sequence of approximations. Then, the sequential quadratic programing technique is applied to find the continuous solution. Following that, the implementation of discrete capability into the MAM is developed to solve the mixed discrete-continuous optimization problems.FindingsThe efficiency and rate of convergence of the developed hybrid algorithms outperforming GA are examined by six detailed case studies in the ten-bar planar truss problem, and the superiority of the Hooke–Jeeves assisted MAM algorithm over the other two hybrid algorithms and GAs is concluded.Originality/valueThe authors propose three efficient hybrid algorithms, the rounding-off, the coordinate search and the Hooke–Jeeves search-assisted MAMs, to solve nonlinear mixed discrete-continuous optimization problems. Implementations include the development of new procedures for sampling discrete points, the modification of the trust region adaptation strategy and strategies for solving mix optimization problems. To improve the efficiency and effectiveness of metamodel construction, regressors f defined in this paper can have the form in common with the empirical formulation of the problems in many engineering subjects.

From Angular Manifolds to the Integer Lattice: Guaranteed Orientation Estimation With Application to Pose Graph Optimization

Pose graph optimization from relative measurements is challenging because of the angular component of the poses: the variables live on a manifold product with nontrivial topology and the likelihood function is nonconvex and has many local minima. Because of these issues, iterative solvers are not robust to large amounts of noise. This paper describes a global estimation method, called multi-hypothesis orientation-from-lattice estimation in 2-D (MOIE2D), for the estimation of the nodes' orientation in a pose graph. We demonstrate that the original nonlinear optimization problem on the manifold product is equivalent to an unconstrained quadratic optimization problem on the integer lattice. Exploiting this insight, we show that, in general, the maximum likelihood estimate alone cannot be considered a reliable estimator. Therefore, MOIE2D returns a set of point estimates, for which we can derive precise probabilistic guarantees. Experiments show that the method is able to tolerate extreme amounts of noise, far above all noise levels of sensors used in applications. Using MOIE2D's output to bootstrap the initial guess of iterative pose graph optimization methods improves their robustness and makes them avoid local minima even for high levels of noise.

A hybrid nonlinear optimization method for operation of large-scale cascaded hydropower plants

This paper develops a hybrid nonlinear optimization method for solving long-term optimal operation of large-scale cascaded hydropower plants with complex spatial coupling constraints. This method proposes conversion factors relevant to generation and discharge in order to cope with complex nonlinear total generation limitation considered in the optimization problem. Thus, the original nonlinear optimization problem can be broken down into a sequence of standard quadratic programming sub-problems. A combination of progressive optimality algorithm (POA) and quadratic programming (QP) method is employed to optimize the operation of hydropower systems. The results obtained from POA are first chosen as the initial solution of QP, which also decide the feasible decision space. During the solution process, the previous conversion factors are dynamically updated depending on the destroying range of total generation limitation. The boundary values of these constraints are accordingly modified in the new QP model. Solving the QP problem and updating the convention factors are performed alternately until the optimal solution or satisfactory solution for original problem is obtained. The proposed hybrid nonlinear method is applied to scheduling Hongshui River cascaded hydropower plants. The simulation results show that our method can enhance the total power generation in dry season and produce more energy than POA.

Predictive route control for automated baggage handling systems using mixed-integer linear programming

State-of-the-art baggage handling systems transport luggage in an automated way using destination coded vehicles (DCVs). These vehicles transport the bags at high speeds on a network of tracks. In this paper we consider the problem of controlling the route of each DCV in the system. In general this results in a nonlinear, nonconvex, mixed-integer optimization problem, usually very expensive in terms of computational effort. Therefore, we present an alternative approach for reducing the complexity of the computations by simplifying and approximating the nonlinear optimization problem by a mixed-integer linear programming (MILP) problem. The advantage is that for MILP problems solvers are available that allow us to efficiently compute the global optimal solution. The solution of the MILP problem can then be used as a good initial starting point for the original nonlinear optimization problem. We use model predictive control (MPC) for solving the route choice problem. To assess the performance of the proposed (nonlinear and MILP) formulations of the MPC optimization problem, we consider a benchmark case study, the results being compared for several scenarios.

A Narrow Band Method for the Convex Formulation of Discrete Multilabel Problems

We study a narrow band type algorithm to solve a discrete formulation of the convex relaxation of energy functionals with total variation regularization and nonconvex data terms. We prove that this algorithm converges to a local minimum of the original nonlinear optimization problem. We illustrate the algorithm with experiments for disparity computation in stereo and a multilabel segmentation problem, and we check experimentally that the energy of the local minimum is very near to the energy of the global minimum obtained without the narrow band type method.

Predictive Control for Baggage Handling Systems using Mixed Integer Linear Programming

State-of-the-art baggage handling systems transport luggage in an automated way using destination coded vehicles (DCVs). These vehicles transport the bags at high speeds on a network of tracks. In this paper we consider the problem of controlling the route of each DCV in the system. In general this results in a nonlinear, nonconvex, mixed integer optimization problem which is usually very expensive in terms of computational effort. Therefore, we present an alternative approach for reducing the complexity of the computations by simplifying and approximating the nonlinear optimization problem by a mixed integer linear programming (MILP) problem. The advantage is that for MILP problems solvers are available that allow us to efficiently compute the global optimal solution. The solution of the MILP problem can then be used as a good initial starting point for the original nonlinear optimization problem. We use model predictive control (MPC) for solving the route choice problem. We also assess the performance of the proposed (nonlinear and MILP) formulations of the MPC optimization problem using a benchmark case study.

Predictive route choice control of destination coded vehicles with mixed integer linear programming optimization

Abstract State-of-the-art baggage handling systems transport luggage in an automated way using destination coded vehicles (DCVs). These vehicles transport the bags at high speeds on a “mini” railway network. In this paper we consider the problem of controlling the route of each DCV in the system. This is a nonlinear, nonconvex, mixed integer optimization problem. Nonlinear model predictive control (MPC) for mixed integer problems is usually very expensive in terms of computational effort. Therefore, in this paper we present an alternative approach for reducing the complexity of the computations by simplifying and approximating the nonlinear optimization problem by a mixed integer linear programming (MILP) problem. The advantage is that for MILP optimization problems solvers are available to allow us to efficiently compute the global optimal solution. The solution of the MILP problem can then be used as a good initial starting point for the original nonlinear optimization problem. To assess the performance of the proposed formulation of the MPC optimization problem, we consider a benchmark case study, the results being compared for several scenarios.

Optimal output tracking control for bilinear systems

We consider the optimal output tracking control (OOTC) problem for a class of bilinear systems with a quadratic performance index. Using a successive approximation approach (SAA), the original non-linear optimal problem is transformed into a sequence of linear non-homogeneous two-point boundary value (TPBV) problems. An adjoint vector sequence can be obtained from the iterative solution of the sequence of TPBV problems. The OOTC law obtained consists of accurate linear feedback and feedforward terms and a non-linear compensation term which is the limit of the adjoint vector sequence. A reference input observer is constructed to make the approximate OOTC law physically realizable. A numerical simulation is provided to illustrate the effectiveness of the proposed method.

An efficient MP algorithm for structural shape optimization problems

Integral methods -such as the Finite Element Method (FEM) and the Boundary Element Method (BEL1)are frequently used in structural optimization problems to solve systems of partial differential equations. Therefore: one must take into account the large computational requirements of these sophisticated techniques at the time of choosing a suitable Mathematical Programming (MP) algorithm for this kind of problems. Among the currently available M P algorithms, Sequential Linear Programming (SLP) seems t o be one of the most adequate to structural optimization. Basically, SLP consist in constructing succesive linear approximations to the original non linear optimization problem within each step. However, the application of SLP may involve important malfunctions. Thus, the solution to the approximated linear problems can fail to exist, or may lead to a highly unfeasible point of the original non linear problem; also, large oscillations often occur near the optimum, precluding the algorithm to converge. In this paper, we present an improved SLP algorithm with line-search. specially designed for structural optimization problems. In each iteration) an approximated linear problem with aditional side constraints is solved by Linear Programming. The solution to this linear problem defines a search direction. Then, the objective function and the non linear constraints are quadratically approximated in the search direction, and a line-search is performed. The algorithm includes strategies t o avoid stalling in the boundary of the feasible region, and to obtain alternate search directions in the case of incompatible linearized constraints. Techniques developed by the authors for efficient high-order shape sensitivity analysis are referenced. Transactions on the Built Environment vol 52, © 2001 WIT Press, www.witpress.com, ISSN 1743-3509

Routing-Sequence Optimization for Circuit-Switched Networks

A new routing design algorithm is presented for circuit-switched networks with dynamic routing capabilities. It is assumed that, in such networks, a transaction request can be set up by trying a sequence of paths connecting the originating switch and destination switch. The request will be connected through the first path that has an available circuit at the time of the request. The objective of this algorithm is to maximize the network throughput or revenue under a given capacity and load. The algorithm is a heuristic that first solves a simpler linear programming (LP) problem. It then transforms the LP solution into a feasible solution for the original nonlinear optimization problem. The solution is then improved through “route trimming” and “route expansion” processes. By using variants of Karmarkar's method implemented on the AT&T KORBX® system to solve the LP problem, the algorithm can be applied to large networks with potentially hundreds of switches. Furthermore, in many cases the algorithm provides near-optimal routing solutions with objective values that are within 0.5 percent of the optimal solutions.