Nonlinear Cost Research Articles

Robust Portfolio Optimization in an Illiquid Market in Discrete-Time

We present a robust dynamic programming approach to the general portfolio selection problem in the presence of transaction costs and trading limits. We formulate the problem as a dynamic infinite game against nature and obtain the corresponding Bellman-Isaacs equation. Under several additional assumptions, we get an alternative form of the equation, which is more feasible for a numerical solution. The framework covers a wide range of control problems, such as the estimation of the portfolio liquidation value, or portfolio selection in an adverse market. The results can be used in the presence of model errors, non-linear transaction costs and a price impact.

A Multiscale Alignment Method for Ensemble Filtering with Displacement Errors

AbstractHigh-resolution models nowadays simulate phenomena across many scales and pose challenges to the design of efficient data assimilation methods that reduce errors at all scales. Smaller-scale features experience rapid nonlinear error growth that gives rise to displacement errors, which cause suboptimal ensemble filter performance. Previous studies have started exploring methods that can reduce displacement errors. In this study, a multiscale alignment (MSA) method is proposed for ensemble filtering. The MSA method iteratively processes the model state from the largest to the smallest scales. At each scale, an ensemble filter is applied to update the state with observations, and the analysis increments are utilized to derive displacement vectors for each member that align the ensemble at smaller scales before the next iteration. The nonlinearity in smaller-scale priors is reduced by removing larger-scale displacement errors. Because the displacement vectors are derived from analysis increments in the state space rather than the nonlinear observation-space cost function formulated in previous studies, this method provides a less costly and more robust way to solve for the displacement vectors. Observing system simulation experiments using a two-layer quasigeostrophic model were conducted to provide a proof of concept of the MSA method. Results show that the MSA method significantly improves the accuracy of posteriors compared to the existing ensemble filter methods with or without multiscale localization. Advantage of the MSA method are more evident when the ensemble size is relatively small and the cycling period is comparable to the average eddy turnover time of the dynamical system.

Estimation of interquartile range in stratified sampling under non-linear cost function

Using stratified random sampling scheme, we discuss three estimators in estimating the finite population interquartile range (IQR) by using the known values of the 1st and 3rd quartiles of the auxiliary variable. Expressions for bias and MSE are derived up to first order of approximation. We propose an allocation procedure where a non-linear cost function is considered to minimize the mean square error (MSE) of the estimators for a specified cost. We use the real data set to compare the performances of estimators under proportional allocation and proposed allocation.

On the Use of Electromagnetic Inversion for Metasurface Design

We show that the use of the electromagnetic inverse source framework offers great flexibility in the design of metasurfaces. In particular, this approach is advantageous for antenna design applications where the goal is often to satisfy a set of performance criteria such as half power beamwidths and null directions, rather than satisfying a fully-known complex field. In addition, the inverse source formulation allows the metasurface and the region over which the desired field specifications are provided to be of arbitrary shape. Some of the main challenges in solving this inverse source problem, such as formulating and optimizing a nonlinear cost functional, are addressed. Lastly, some two-dimensional (2D) and three-dimensional (3D) simulated examples are presented to demonstrate the method, followed by a discussion of the method's current limitations.

Decentralized Economic Operation Control for Hybrid AC/DC Microgrid

A hybrid ac/dc microgrid, which consists of alternating current (ac) subgrid(s) and direct current (dc) subgrid(s), can efficiently integrate ac and dc loads, distributed generators (DGs) with minimum conversion stages. The ac and dc subgrids are connected by the bidirectional power converter (BPC) to realize power interaction between them. This paper proposes a decentralized economic operation control for the hybrid ac/dc microgrid, which aims to realize economic power sharing among all DGs and economic power interaction between subgrids. For the DGs, the nonlinear droop controls based on ac frequency-incremental cost and dc voltage-incremental cost are proposed, which can equalize DGs' incremental costs autonomously, and hence decrease the subgrids' generation costs with the equal incremental cost principle. For the BPC, the economic power interaction control is proposed to optimize the power interaction between the two subgrids and further decrease the total generation cost (TGC). In addition, the economic operation is categorized into different modes according to the load conditions. The hybrid microgrid with nonlinear incremental cost droops is modeled, and the overall stability analysis is conducted to ensure stable operation in all load conditions and modes. The performance of the proposed control is verified by the real-time hardware-in-loop (HIL) test.

A Model for Optimizing Railway Alignment Considering Bridge Costs, Tunnel Costs, and Transition Curves

Owing to wide-ranging searches (there are various alignments between two points) as well as complex and nonlinear cost functions and a variety of geometric constraints, the problem of optimal railway alignment is classified as a complex problem. Thus, choosing an alignment between two points is usually done based on a limited number of alignments designed by experts. In recent years, the study of railway alignment optimization has shown the importance of optimization and the introduction of various algorithms and their usefulness in solving different problems. It is expected that applying meta-heuristic optimization algorithms such as methods based on swarm intelligence can lead to better alignments. In this study, we tried to modify models based on previous studies in order to design and develop a model based on a single framework to provide three-dimensional optimization of alignments applicable in the real world. To obtain this, the particle swarm algorithm is used and a geographic information system is incorporated as a means of search in three-dimensional space. In particular, the cost function used in previous studies considering the costs related to structures (bridges and tunnels) are improved regarding hydraulic structure alignments. Furthermore, the transition curve of horizontal alignment and slope restrictions of curves are considered in this project by using the penalty function in order to obtain the most practical results possible. Finally, this study examines three problems for which the results are acceptable in cases of railway alignment geometry and its application in the real world.

The development and numerical verification of a compromised real time optimal control algorithm for hybrid electric vehicle

Hybrid electric vehicles (HEV) have been recognized as a viable technology to significantly improve the fuel economy of on-road vehicles operated in urban areas featuring frequent stop-and-go operation. The optimization of the HEV control strategy is a dynamic optimal problem involving a nonlinear cost function and several nonlinear constraints. To take advantage of the global optimality of dynamic programming (DP) and the real-time capability of the equivalent consumption minimization strategy (ECMS) in optimizing the HEV operation strategy, a model that combines ECMS with DP is proposed in this paper, which is defined as ECMSwDP. Using this approach, the optimal equivalent factor λ for ECMS is derived using DP under various driving conditions and the different grades of synthetic driving cycle. The fuel economy simulated using the ECMSwDP control strategy is comparable to the optimal solution derived using DP. The potential of the real-time control strategy developed using ECMSwDP to improve fuel economy is demonstrated using a transit hybrid electric bus as an example.

A Theoretical Framework on Reliability Optimization for Improving System Operational Availability

Purpose: We seek to identify an optimization model from among reliability optimization models to overcome the trade-off between a high level of availability and high cost.BRMethods: Using sensitivity analysis, we identify the main factors affecting operational availability and investigated the cost of each factor for achieving the target operational availability. We then minimized the total cost incurred for achieving the target operational availability by using an optimization model. Here, we also present an alternative optimization model in which the operational availability is maximized subject to a budget limitation.BRResults: We show that an optimal investment can be achieved by using special cost functions such as linear and convex functions. It is challenging to attain optimality with more general nonlinear cost functions.BRConclusion: We not only present an efficient approach to assessing the cost-efficiency for a high level of readiness of a system, but also provide insights into the manner of setting an appropriate target availability and identifying the factors to invest in for achieving the target availability.

Improved NSAF Algorithms with Variable Control Parameter Against Impulsive Noises

Some improved normalized subband adaptive filter algorithms derived from nonlinear cost functions, such as the logarithmic function and the arctangent function, have shown splendid robustness against the impulsive noises. However, due to the usage of the constant control parameter in their cost functions, these algorithms need to make a balance between the steady-state error and the convergence rate, especially when the unknown impulse response changes suddenly. For settling this trade-off issue, a way of obtaining the variable control parameter (VCP) recursively is constructed by an exponential function in this paper. In the contexts of system identification and acoustic echo cancellation, simulation results testified the improved performance of these proposed VCP algorithms in terms of the convergence rate, steady-state error, and tracking capability.

Energy-aware predictive control for electrified bus networks

For an urban bus network to operate efficiently, conflicting objectives have to be considered: providing sufficient service quality while keeping energy consumption low. The paper focuses on energy efficient operation of bus lines, where bus stops are densely placed, and buses operate frequently with possibility of bunching. The proposed decentralized, bus fleet control solution aims to combine four conflicting goals incorporated into a multi-objective, nonlinear cost function. The multi-objective optimization is solved under a receding horizon model predictive framework. The four conflicting objectives are as follows. One is ensuring periodicity of headways by watching leading and following vehicles i.e. eliminating bus bunching. Equal headways are only a necessary condition for keeping a static, predefined, periodic timetable. The second objective is timetable tracking. A conflicting objective to the former is minimizing passenger waiting time. When more than the expected passengers are waiting for the bus it is desirable to haste the vehicle in order to prevent bunching. The final objective is energy efficiency. To this end, an energy consumption model is formulated considering battery electric vehicles with recuperation during braking. Different weighting strategies are compared and evaluated through realistic scenarios, realized in a validated microscopic traffic simulation environment. Simulation results suggest 3–8% network level energy saving compared to bus holding control while maintaining punctuality and periodicity of buses.

Regional gradient optimal control problem governed by a distributed bilinear systems

This paper gives an extension of previous work on gradient optimal control of distributed parabolic systems to the case of distributed bilinear systems which are a type of nonlinear systems. We introduce the notion of flux optimal control of distributed bilinear systems. The idea is trying to achieve a neighborhood of the gradient state of the considered system by minimizing a nonlinear quadratic cost. Using optimization techniques, a method showing how to reach a desired flux at a final time, only on internal subregion of the system domain will be proposed. The proposed simulation illustrates the theoretical approach by commanding the heat bilinear equation flux to a desired profile.

Deep Reactive Policies for Planning in Stochastic Nonlinear Domains

Recent advances in applying deep learning to planning have shown that Deep Reactive Policies (DRPs) can be powerful for fast decision-making in complex environments. However, an important limitation of current DRP-based approaches is either the need of optimal planners to be used as ground truth in a supervised learning setting or the sample complexity of high-variance policy gradient estimators, which are particularly troublesome in continuous state-action domains. In order to overcome those limitations, we introduce a framework for training DRPs in continuous stochastic spaces via gradient-based policy search. The general approach is to explicitly encode a parametric policy as a deep neural network, and to formulate the probabilistic planning problem as an optimization task in a stochastic computation graph by exploiting the re-parameterization of the transition probability densities; the optimization is then solved by leveraging gradient descent algorithms that are able to handle non-convex objective functions. We benchmark our approach against stochastic planning domains exhibiting arbitrary differentiable nonlinear transition and cost functions (e.g., Reservoir Control, HVAC and Navigation). Results show that DRPs with more than 125,000 continuous action parameters can be optimized by our approach for problems with 30 state fluents and 30 action fluents on inexpensive hardware under 6 minutes. Also, we observed a speedup of 5 orders of magnitude in the average inference time per decision step of DRPs when compared to other state-of-the-art online gradient-based planners when the same level of solution quality is required.

Development of Sustainable Recycling Investment Framework Considering Uncertain Demand and Nonlinear Recycling Cost

This paper presents a more active and efficient recycling investment strategy that considers the balances among the current production constraints, manufacturing profits, and recycling investments for a sustainable circular economy as compared to the current methods. While existing production planning has numerous uncertainties and nonlinear characteristics, the circular economy-based production planning constitutes more complex uncertainties and nonlinear characteristics that result from an uncertain return rate, demand uncertainties, and nonlinear return on investment costs. This paper suggests a stochastic nonlinear programming model-based active recycling investment framework so as to generate a more effective process plan to handle these characteristics. In the proposed framework, recycling investment strategies are quantitatively analyzed when considering uncertain demand and unclear production conditions. In addition, the effective solving techniques for the circular economy based production framework are obtained while using Monte-Carlo based sample average approximation and memetic algorithm. To prove the effectiveness of the proposed framework, it is implemented for a given system and the numerical analyses that were conducted for the various sustainable manufacturing scenarios.

Uncovering Specific-Shape Graph Anomalies in Attributed Graphs

As networks are ubiquitous in the modern era, point anomalies have been changed to graph anomalies in terms of anomaly shapes. However, the specific-shape priors about anomalous subgraphs of interest are seldom considered by the traditional approaches when detecting the subgraphs in attributed graphs (e.g., computer networks, Bitcoin networks, and etc.). This paper proposes a nonlinear approach to specific-shape graph anomaly detection. The nonlinear approach focuses on optimizing a broad class of nonlinear cost functions via specific-shape constraints in attributed graphs. Our approach can be used to many different graph anomaly settings. The traditional approaches can only support linear cost functions (e.g., an aggregation function for the summation of node weights). However, our approach can employ more powerful nonlinear cost functions, and enjoys a rigorous theoretical guarantee on the near-optimal solution with the geometrical convergence rate.

Risky Supplier Encroachment and Reliability Investment Spillover

The common wisdom is that a retailer will get hurt when its wholesale supplier encroaches on the retailer’s territory by selling directly to the same end market. Motivated by practices in variety of industries that supplier with random supply loss maintain dual channel structure, this study demonstrates that a retailer may benefit from supplier encroachment. The encroachment incentivizes the supplier to invest more in improving its supply reliability, and this investment can spill to and benefit the retailer. Although the encroachment always decreases the contribution margin the retailer obtained, the spillover effect increases the retailer’s profit as long as the competition caused by encroachment is not extremely fierce. Eventually, Pareto gains arise in the supply chain. To check the robustness of the spillover effect, we extend the main model with considering selling cost, supplier’s positive production cost, nonlinear investment cost, bargain power, and decentralized encroachment, respectively. In these extensions, the retailer still could benefit from the encroachment, which means the spillover effect is robust.

Magnetometer-free Realtime Inertial Motion Tracking by Exploitation of Kinematic Constraints in 2-DoF Joints.

Inertial Measurement Units (IMUs) are used to track the motion of kinematic chains in a wide variety of robotic and biomedical applications. However, inertial motion tracking is severely limited by the fact that magnetic fields are inhomogeneous in indoor environments and near electronic devices. Methods that use only accelerations and angular rates for orientation estimation yield no absolute heading information and suffer from heading drift. To overcome this limitation, we propose a novel method that exploits an orientation-based kinematic constraint in joints with two degrees of freedom (DoF), such as cardan joints, saddle joints, the human wrists, elbow or ankles. The method determines the relative heading of the joint segments in real time by minimization of a nonlinear cost function. A filter for singularity treatment ensures accurate tracking during motion phases for which the cost function minimum is ambiguous. We experimentally validate the method in metacarpophalangeal (MCP) joints between the palm and the fingers. Accurate relative orientation tracking is achieved continuously despite several singular motion phases and even though the heading components of the 6D orientations drift by more than 360 degrees within ten minutes. The proposed method overcomes a major limitation of inertial motion tracking and thereby facilitates the use of this technology in robotic and biomechanical applications.

MPC relevant identification method for Hammerstein and Wiener models

This work focuses on obtaining models that may produce a better performance of Model Predictive Controllers - MPC. Several papers published in the last 25 years have proposed methods based on the minimization of multi-step ahead prediction functions. These methods have been called MPC Relevant Identification (MRI). Most of the papers focused on obtaining linear models. In the last 5 years, some methods have been proposed to obtain nonlinear models based on the minimization of the same cost function. These papers were based on the direct minimization of the nonlinear cost function to produce models with NARMAX structure. However, simplified MPC schemes may be obtained using models with Wiener and Hammerstein structures. This paper presents some new theoretical results which allow the development of MRI identification algorithms for models with Wiener and Hammerstein structures, without the need to perform the minimization of the nonlinear cost function. The statistical properties of the models identified by the algorithm proposed are evaluated using Monte Carlo simulations and the prediction capability of the algorithm is evaluated using didactic plants. Results reveal a good multi-step ahead prediction capability.

Robust ellipsoid fitting method based on optimization of a novel nonlinear cost function in navigation systems

Low-cost sensors based on micro-electro-mechanical systems (MEMS) are typically used for attitude determination in navigation systems especially magnetometer which is used for heading determination. The measured value of the MEMS magnetometer is subjected to different kinds of error such as random noise, constant bias, non-orthogonality, scale factor deviation and more importantly hard iron and soft iron effects. Therefore, in order to reach more accurate measurement, high-precision calibration is needed. One of the most common methods for calibrating MEMS magnetic sensors is least squares ellipsoid fitting. But, the common least squares ellipsoid fitting method can be inefficient for real-time applications in the presence of colored noise and outliers. In this paper, a modified ellipsoid fitting method is proposed in which a nonlinear optimization is developed to minimize a novel cost function. In the cost function of the proposed robust method, the effect of outliers and noise is considered and the standard deviation of the data is kept minimum. Finally, the efficiency of the new algorithms is demonstrated through the experimental results.

Assigning Priorities (or Not) in Service Systems with Nonlinear Waiting Costs

For queueing systems with multiple customer types differing in service time distributions and costs for waiting, it is known that giving priority to one type over others minimizes the long-run average waiting costs when waiting is penalized linearly in time. However, when waiting costs are nonlinear, which is typically a more reasonable depiction of reality, it is not clear whether policies that ignore the type information such as the first-come-first-serve policy (FCFS) should be replaced with type-based priority policies. To shed some light on to this problem, we study a single-server queueing system with two types of customers under static queueing policies that use information on customers’ types and order of arrival. Our main theorem ranks the type-based priority policies and FCFS according to their long-run average waiting costs under nonlinear cost functions. We then apply this result to polynomial cost functions and generate insights into when prioritization is advantageous. For example, we find that when customers are similar in terms of their service time distributions, then the parameter region where FCFS is more preferable over type-based priority policies under quadratic costs increases with traffic intensity. We also conduct a numerical study to compare the best static policy with a well-known dynamic policy that requires information on the current waiting times of customers. We find that the best static policy performs comparably with (sometimes even better than) this dynamic policy except when the traffic is heavy and it is not clear which type should receive priority.

A genetic algorithm with local search for solving single-source single-sink nonlinear non-convex minimum cost flow problems

Network models are widely used for solving difficult real-world problems. The minimum cost flow problem (MCFP) is one of the fundamental network optimisation problems with many practical applications. The difficulty of MCFP depends heavily on the shape of its cost function. A common approach to tackle MCFPs is to relax the non-convex, mixed-integer, nonlinear programme (MINLP) by introducing linearity or convexity to its cost function as an approximation to the original problem. However, this sort of simplification is often unable to sufficiently capture the characteristics of the original problem. How to handle MCFPs with non-convex and nonlinear cost functions is one of the most challenging issues. Considering that mathematical approaches (or solvers) are often sensitive to the shape of the cost function of non-convex MINLPs, this paper proposes a hybrid genetic algorithm with local search (namely GALS) for solving single-source single-sink nonlinear non-convex MCFPs. Our experimental results demonstrate that GALS offers highly competitive performances as compared to those of the mathematical solvers and a standard genetic algorithm.