Nonlinear Cost Research Articles

An Optimal Two Stage Identification Algorithm for Discrete Hammerstein Time Delay Systems

This paper deals with the problem of identification of Hammerstein time delay systems. In fact, we propose a Hierarchical optimization based approach allowing to estimate simultaneously the time delay, the linear dynamic parameters and the nonlinear static parameters of such systems. This approach consists, firstly, in decomposing a complex nonlinear cost function into two simple cost functions and secondly, in using the gradient method to minimize each function (HH-G). The convexity condition to authorize the use of the rounding property is also developed and the convergence analysis of the proposed algorithm indicates that the parameter estimation errors converge to zero under persistent excitation conditions and the estimated time delay converge to a finite value. The simulation results are presented to illustrate the effectiveness of the proposed method.

A Self-Calibration Method of Zooming Camera

In this article we proposed a novel approach to self- calibrate a camera with variable focal length. We show that the estimation of camera’s intrinsic parameters is possible from only two points of an unknown planar scene. The projection of these points by using the projection matrices in two images only permit us to obtain a system of equations according to the camera’s intrinsic parameters . From this system we formulated a nonlinear cost function which its minimization allows us to estimate the camera’s intrinsic parameters in each view. The results on synthetic and real data justify the robustness of our method in term of reliability and convergence.

Economic Load Dispatch Using Linear Programming

This paper presents an optimum solution of the economic dispatch (ED) problem without considering transmission losses using linear programming (LP). In the ED problem, several on-line units (generators) are available, and it is needed to determine the power to produce by each unit in order to meet the required load at minimum total cost. To apply LP, the nonlinear cost functions of all generators are approximated by linear piecewise functions. To examine the effectiveness of this linearization method, a comprehensive set of benchmark test problems is used consisting of 3, 6, 18, 20, 38, and 40 generators. Using this set, LP solutions of linearized ED problems are compared with several other techniques available in the literature. The LP technique with piecewise linearization shows an overall competitive advantage in terms of total cost, solution time, and load satisfaction accuracy. The impact of varying the width of the linearized pieces (segments) is also discussed. All the computational analysis is performed using MATLAB software environment.

A heterogeneous reliable location model with risk pooling under supply disruptions

This paper investigates a facility location model that considers the disruptions of facilities and the cost savings from the inventory risk-pooling effect and economies of scale. Facilities may have heterogeneous disruption probabilities. When a facility fails, its customers may be reassigned to other surviving ones to hedge against lost-sales costs. We first develop both an exact and an approximate expression for the nonlinear inventory cost, and then formulate the problem as a nonlinear integer programming model. The objective is to minimize the expected total cost across all possible facility failure scenarios. To solve this problem, we design two methods, an exact approach using special ordered sets of type two (SOS2) and a heuristic based on Lagrangian relaxation. We test the model and algorithms on data sets with up to 150 nodes. Computational results show that the proposed algorithms can solve the problem efficiently in reasonable time. Managerial insights on the optimal facility deployment, customer assignments and inventory control strategies are also drawn.

Dynamic joint pricing and production policy for perishable products

AbstractA joint dynamic pricing and production problem for perishable products without shortages is considered. The demand rate is price‐dependent and time‐varying. This paper constructs an optimal control model to maximize the total profit under a general nonlinear production cost function. The feature of the optimal joint dynamic pricing and production policy is analyzed by solving the corresponding optimal control problem on the basis of improved Pontryagin's maximum principle. Then, an effective algorithm is designed to obtain the optimal joint policy. The case of the joint static optimal policy is also investigated and compared with the dynamic one. Finally, numerical examples are presented to illustrate the effectiveness of the proposed methods, and some managerial implications are provided for the management of perishable items.

Variable bin size selection for periestimulus time histograms (PSTH) with minimum mean square error criteria

To date the most common method for extracting neuronal responses is by constructing PSTHs that are time locked to task events. Many parameters of interests such as response magnitude, onset and duration are then calculated from the constructed PSTHs. However the precision of PSTH response estimate critically depends on the choice of bin sizes. This dependence demands objective criteria for bin size selection. A seminal study by Shimazaki and Shinomoto [1] derived an optimal cost function for choosing a fixed bin size for a time varying Poisson process. It is easy to see that using a one-size-fit-all recipe for bin sizes will invariably overestimate and underestimate rate changes for fast and slow fluctuations respectively. Here we extend previous results by calculating the cost function that minimizes mean square error for variable bin sizes with the same assumptions used previously for time varying Poisson processes Cost(N,Δ )=1n2T∑i=1N2ki-(ki-Δik ¯)2Δi. To minimize this nonlinear and nonconvex cost function, we utilize an array of methods some of which are widely used for nonlinear optimization, namely: Active set, Simultaneous perturbation stochastic approximation (SPSA), Genetic Algorithm and an approximate heuristic algorithm. Average performance of each algorithm on a typical simulated neuronal firing is calculated using 50 iterations. All methods resulted in a lower cost function compared to fixed bin size as expected. Plotting the final cost vs the algorithm run time shows that the method of 'Active set' overall has the best cost reduction while still being reasonably fast compared to the fixed bin size approach (Figure ​(Figure1)1) . Further investigation of the properties of this cost function and developing computationally efficient methods for its minimization will be the basis of future work. Figure 1 Comparing the costs and time efforts of the algorithms.

Design of Polarization-Insensitive Demultiplexing Lattice Filters in SOI

In this paper, we propose a novel optimization technique that make use of nonlinear cost functions to design polarization-insensitive wavelength division demultiplexing (DEMUX) lattice filters in silicon-on-insulator (SOI) waveguides. These waveguides are characterized by large effective index and group index birefringences that are fully taken into account in the simulations. The optimization takes advantage of the periodicity of spectral responses of the various elements building a lattice filter. In performing the design, we consider design sensitivity to parameter variations and propose solutions that are compatible with CMOS processes using a waveguide thickness of 220 nm. The design can nonetheless be generalized to other waveguide dimensions and filter topologies for the realization of more complex integrated photonic circuits. Finally, we illustrate the approach by designing and simulating four channel demultiplexers with 200 and 800 GHz channel spacing in both the O- and C-band. Compared to the conventional polarization diversity scheme, this polarization-insensitive design methodology may reduce the total footprint and power consumption by up to 50%, and is therefore of great interest for short reach data communication applications.

A multi-period location model with transportation economies-of-scale and perishable inventory

In this paper, we propose a multi-period location model with transportation economies-of-scale that distributes a single perishable product. The problem involves a single supplier, a layer of potential facility locations, and a layer of retailers. Each facility is assumed to practice cross-docking and each retailer faces a constant demand rate in each planning period. A Zero-Inventory-Ordering (ZIO) inventory policy is assumed to be adopted at each retailer. The demand at each retailer must be satisfied by the end of the planning horizon, although backlogging is allowed in the intermediate periods. The decisions to be made comprise the location of facilities, the allocation of retailers to the open facilities with single-sourcing, and the logistics shipping plan over time for the open facilities and the retailers allocated to them. The goal is to minimize the total cost that includes (1) the fixed setup cost for locating facilities, (2) the inbound cost at the open facilities, (3) the transportation cost from the facilities to the retailers (which is assumed to be an economies-of-scale function), and (4) the inventory cost at the retailers. We first formulate the problem as a mixed integer nonlinear programming model. By effectively utilizing the structural properties of the cost functions and combining with the ZIO, we show how to linearize the nonlinear cost components. The results of a set of numerical experiments performed on randomly generated medium-sized problem instances are reported.

A rescheduling and cost allocation mechanism for delayed arrivals

We propose a solution to the problem of rescheduling a sequence of arrivals that are subject to a delay event at a common destination. Such situations include jobs arriving at a single production facility, aircraft whose landings are postponed, and ships that are inbound to a dock or lightering facility. Each arrival faces a nonlinear cost due to the delay, but the delay costs can be mitigated by allowing the arrivals to be reordered. We optimize the reordering process by designing a Vickrey–Clarke–Groves (VCG) mechanism to construct a payoff matrix describing the amounts necessary to move the currently assigned arrival slots either earlier or later. Using this payoff matrix, we compute the optimal reordering of the arrivals by utilizing the well-known solution to the assignment problem, which maximizes the benefit in a computationally efficient fashion. The VCG mechanism is strategyproof, that is, no arrival has an incentive to misreport the value of moving up or down in the sequence. We also show that participating in the centralized process is to no arrival׳s disadvantage. Because VCG procedures in general are subject to budget deficits, we provide alternative mechanisms to overcome this difficulty. Finally, we carry out computational experiments demonstrating that the VCG mechanism can be implemented for realistically-sized problem sets and that the cost savings are significant.

Consensus modeling with nonlinear utility and cost constraints: A case study

In complex group decision making (GDM), reaching a consensus needs both the adequate communication and exchange between the individual decision makers (DMs) and the input of a moderator, who may take various effective actions, such as providing financial compensation (collectively referred to as “consensus cost”), to convince the DMs to gradually modify their opinions and to reach a final consensus. This study constructs new consensus models that aim to maximize the GDM utility under the premise of limited consensus cost and nonlinear utility/preference constraints for both the individual DMs and the moderator. The objective function (the utility level of the entire GDM) derived from the proposed models can be seen as a measurement of the group consensus degree. Moreover, using the pollutant reduction negotiations between the government and manufacturing enterprises as a case background, we construct a group reduction consensus model based on nonlinear preference constraints and limited consensus cost and economically interpret the model parameters. Results show that different preference combinations of the DM and moderator will affect the optimal consensus values. Additionally, the moderator’s preference structure influences the final GDM results to some extent. The modeling mechanism used in this paper will be reference for solving real-life consensus GDM problems.

Cost–benefit analysis of corrugated blast walls

Blast walls are generally used to reduce explosion consequences as a form of passive mitigation for offshore installations. Currently, three main types of blast wall are used; flat, stiffened panel and corrugated. Given its particular geometric characteristics, corrugated blast walls are better energy-absorbing systems than other types of blast wall. Thus, corrugated blast walls are often installed in offshore installations to protect against hydrocarbon explosions. However, limited information is available on the influence of parameters of corrugated blast walls such as breadth, height, angle and thickness on lateral deflection, as well as cost. Hence, optimised parameters that consider the comparison between damage (deformation) and cost must be determined for corrugated blast walls. The aim of this study is to investigate the effects of design parameters on the nonlinear structural characteristics and cost of corrugated blast walls in association with cost-benefit analysis. A dynamic finite element analysis was performed by analysis system/Livermore software-dynamics (ANSYS/LS-DYNA) by varying wall thickness, breadth, height and angle of corrugation. Design guidance is offered with an example of how to determine the parameters of a blast wall.

Inventory models with nonlinear shortage costs and stochastic lead times; applications of shape properties of randomly stopped counting processes

AbstractIn this article, we study generalizations of some of the inventory models with nonlinear costs considered by Rosling in (Oper. Res. 50 (2002) 797–809). In particular, we extend the study of both the periodic review and the compound renewal demand processes from a constant lead time to a random lead time. We find that the quasiconvexity properties of the cost function (and therefore the existence of optimal (s, S) policies), holds true when the lead time has suitable log‐concavity properties. The results are derived by structural properties of renewal delayed processes stopped at an independent random time and by the study of log‐concavity properties of compound distributions. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 345–356, 2015

Nash equilibrium payoffs for stochastic differential games with jumps and coupled nonlinear cost functionals

In this paper, we investigate Nash equilibrium payoffs for two-player nonzero-sum stochastic differential games with coupled nonlinear cost functionals. We obtain an existence theorem and a characterization theorem for Nash equilibrium payoffs. The novelty of this paper is to study Nash equilibrium payoffs for coupled cost functionals.

Design of automated negotiation mechanisms for decentralized heterogeneous machine scheduling

We consider a hard decentralized scheduling problem with heterogeneous machines and competing job sets that belong to different self-interested stakeholders (agents). The determination of a beneficial solution, i.e., a respective contract in terms of a common schedule, is particularly difficult due to information asymmetry and self-interested behavior of the involved agents. The agents intend to minimize their individual costs that consist of tardiness cost and their share of the machine operating cost. The aim of this study is to find socially beneficial outcomes by means of negotiation mechanisms that comply with decentralized information and conflicting interests. For this purpose, we present an automated negotiation protocol, which is inspired by metaheuristics, along with a set of optional building blocks. In the protocol, new solutions are iteratively generated, as mutations of a single provisional contract, and proposed to the agents, while feasible rules with quotas restrict the acceptance decisions of the agents. The computational experiments show that the protocol—without central information and subject to strategic behavior—can achieve high quality solutions which are very close to results from centralized multi-criteria procedures. Particular building block configurations yield improved outcomes. Concluding, the considered scheduling problem enhances standard scheduling models by incorporating multiple stakeholders, nonlinear cost functions, and machine operating cost, whereas the presented negotiation approach contributes to the methodology and practice of collaborative decision making.

Nonlinear costs of reproduction in a long‐lived plant

Summary A trade‐off between current reproduction and future performance is a key component of life‐history theory, but the shape of this trade‐off for any specific fitness component remains elusive. We induced three to five levels of reproductive effort (RE) by manipulating fruit set of a long‐lived orchid in two populations that differed in the length of the growing season and local climate and examined survival, size and fecundity the following year. Natural fruit set was 72% higher in the long‐season population, but was not associated with a significant survival cost in any population. Survival decreased linearly with experimentally increased RE in the short‐season population. In both populations, natural RE incurred growth and fecundity costs, and growth costs increased nonlinearly with diminishing costs at high RE. Fecundity costs increased linearly with RE in the long‐season population, but nonlinearly with diminishing costs at high RE in the other. The results demonstrate that the shape of the cost function may be nonlinear with context‐dependent intercept, slope and curvature. They are consistent with the prediction that survival costs appear only when RE exceeds natural levels, while growth and fecundity costs are evident at natural RE. Synthesis. We suggest that studies inducing multiple levels of RE are required to understand life‐history trade‐offs and their context dependence. This kind of information is fundamental for an understanding of the link between environmental heterogeneity, adaptive differentiation and life‐history evolution.

Dynamics of a Bertrand duopoly with differentiated products and nonlinear costs: Analysis, comparisons and new evidences

This paper studies mathematical properties and dynamics of a duopoly with price competition and horizontal product differentiation by introducing quadratic production costs (decreasing returns to scale), thus extending the model with linear costs (constant returns to scale) of Fanti et al. [11]. The economy is described by a two-dimensional non-invertible discrete time dynamic system. The paper first determines fixed points and other invariant sets, showing that synchronized dynamics can occur. Then, stability properties are compared in the cases of quadratic costs and linear costs by considering the degree of product differentiation and the speed of adjustment of prices as key parameters. It is also shown that synchronization takes place if products tend to be relatively complements and stressed similarities and differences between models with quadratic and linear costs. Finally, the paper focuses on the phenomenon of multistability thus underlying new evidences in comparison with the model with linear costs.

Information Sharing in a Supply Chain with a Common Retailer

We study the problem of information sharing in a supply chain with two competing manufacturers selling substitutable products through a common retailer. Our analysis shows that the retailer’s incentive to share information strongly depends on nonlinear production cost, competition intensity, and whether the retailer can offer a contract to charge a payment for the information. Without information contracting, the retailer has an incentive to share information for free when production economy is large but has no incentive to do so when there is production diseconomy. With information contracting, the retailer has an incentive to share information when either production diseconomy/economy is large or competition is intense. We characterize the conditions under which the retailer shares information with none, one, or both of the manufacturers. We also show that the retailer prefers to sell information sequentially rather than concurrently to the manufacturers, whereas the manufacturers’ preferences are reversed.This paper was accepted by Yossi Aviv, operations management.

Notes on alpha stream optimization

In this paper, we discuss investment allocation to multiple alpha streams that are traded on the same execution platform. This includes when trades are crossed internally, resulting in turnover reduction. We discuss approaches to alpha weight optimization, in which profit and loss is maximized subject to bounds on volatility (or the Sharpe ratio). The presence of negative alpha weights, which are allowed when alpha streams are traded on the same execution platform, complicates the optimization problem. By using a factor-model approach to the alpha covariance matrix, the original optimization problem can be viewed as a one-dimensional root-searching problem plus an optimization problem that requires a finite number of iterations. We discuss this approach without costs, with linear costs and with nonlinear costs in a certain approximation. This makes the allocation problem tractable without forgoing nonlinear portfolio capacity bound effects.

Nash Equilibrium Payoffs for Stochastic Differential Games with two Reflecting Barriers

In this paper we study Nash equilibrium payoffs for nonzero-sum stochastic differential games with two reflecting barriers. We obtain an existence and a characterization of Nash equilibrium payoffs for nonzero-sum stochastic differential games with nonlinear cost functionals defined by doubly controlled reflected backward stochastic differential equations with two reflecting barriers.

Nash Equilibrium Payoffs for Stochastic Differential Games with two Reflecting Barriers

In this paper we study Nash equilibrium payoffs for nonzero-sum stochastic differential games with two reflecting barriers. We obtain an existence and a characterization of Nash equilibrium payoffs for nonzero-sum stochastic differential games with nonlinear cost functionals defined by doubly controlled reflected backward stochastic differential equations with two reflecting barriers.