Nonlinear Cost Function Research Articles

Efficient nonlinear inversion for atmospheric sounding and other applications

Retrieving atmospheric and/or surface state variables using remote observations typically involves minimizing a nonlinear cost function in measurement space. Many methods exist for minimizing nonlinear functions, but the applicability of one method over another has a large dependence on the degree of nonlinearity of the cost function and the initial guess error. We present a minimization method, called DRAD, that is applicable to highly nonlinear cost functions and to problems where little a priori information about the retrieved variables is available. To illustrate the method, water vapor and temperature profiles are retrieved using simulated Atmospheric Infrared Sounder observations. We focus on the efficiency of DRAD for retrievals generated for a wide range of initial guess errors. For a comparison, we also generate retrievals using the Levenberg-Marquardt method.

The use of relative priorities in optimizing the performance of a queueing system

Relative priorities in an n-class queueing system can reduce server and customer costs. This property is demonstrated in a single server Markovian model where the goal is to minimize a non-linear cost function of class expected waiting times. Special attention is given to minimizing server’s costs when the expected waiting time of each class is restricted.

Rank-Cluster-and-Prune: An algorithm for generating clusters in complex set partitioning problems

Clustering problems are often difficult to solve due to nonlinear cost functions and complicating constraints. Set partitioning formulations can help overcome these challenges, but at the cost of a very large number of variables. Therefore, techniques such as delayed column generation must be used to solve these large integer programs. The underlying pricing problem can suffer from the same challenges (non-linear cost, complicating constraints) as the original problem, however, making a mathematical programming approach intractable. Motivated by a real-world problem in printed circuit board (PCB) manufacturing, we develop a search-based algorithm (Rank-Cluster-and-Prune) as an alternative, present computational results for the PCB problem to demonstrate the tractability of our approach, and identify a broader class of clustering problems for which this approach can be used. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009

A Fuzzy Robust Nonlinear Programming Model for Stream Water Quality Management

An interval-parameter fuzzy robust nonlinear programming (IFRNP) approach was developed for stream water quality management under uncertainty. The interval and fuzzy robust programming methods were incorporated within a general framework to address uncertainties associated with the nonlinear objective and the left- and right-hand sides of the constraints. A piecewise linearization approach was developed to deal with the nonlinear cost function. IFRNP could explicitly address complexities of various system uncertainties, where parameters were represented as both interval numbers and fuzzy membership functions. Furthermore, the dual uncertain information associated with the lower and upper bounds of each interval parameter could be effectively tackled through the concept of fuzzy boundary interval. The proposed IFRNP method was applied to a case of water quality management in the Guoyang section of the Guo River in Anhui province, China. A number of cost-effective schemes for water quality management were generated, and allowable wastewater discharge amounts were recommended. The results indicated that IFRNP was applicable to water quality management problems, where high nonlinearities and dual uncertainties exist.

A Preliminary Application of the Differential Evolution Algorithm to Calculate the CNOP

A projected skill is adopted by use of the differential evolution (DE) algorithm to calculate a conditional nonlinear optimal perturbation (CNOP). The CNOP is the maximal value of a constrained optimization problem with a constraint condition, such as a ball constraint. The success of the DE algorithm lies in its ability to handle a non—differentiable and nonlinear cost function. In this study, the DE algorithm and the traditional optimization algorithms used to obtain the CNOPs are compared by analyzing a theoretical grassland ecosystem model and a dynamic global vegetation model. This study shows that the CNOPs generated by the DE algorithm are similar to those by the sequential quadratic programming (SQP) algorithm and the spectral projected gradients (SPG2) algorithm. If the cost function is non—differentiable, the CNOPs could also be caught with the DE algorithm. The numerical results suggest the DE algorithm can be employed to calculate the CNOP, especially when the cost function is nons—differentiable.

A New Improved Hybrid Meta-Heuristics Method for Unit Commitment with Nonlinear Fuel Cost Function

A New Improved Hybrid Meta-Heuristics Method for Unit Commitment with Nonlinear Fuel Cost Function

A note on time/cost tradeoff curve generation for project scheduling with multi-mode resource availability costs

In this note we combine two known algorithms and show how they can be used in order to generate tradeoff curves between time and cost for deterministic project scheduling problems with multiple modes and resource availability costs. The approach can handle linear and non-linear non-decreasing cost functions and it is based on the exact algorithm presented in Demeulemeester (1995) for the resource availability cost problem without multiple modes. As the problem is NP-hard, the method is computationally viable to solve only problems of a moderate size. The performance of the combined algorithm is compared to solutions generated by GAMS/CPLEX.

Active Coordination of Thermal Household Appliances for Load Management Purposes

In this paper, a coordination approach for thermostat-controlled household appliances is developed. Under consideration are heating and cooling devices such as refrigerators, freezers, water boilers and heat pumps, which are usually characterized by an intermittent (duty cycle) operation. Without influence from the outside, an internal hysteresis switching controller toggles the “on/off” state of a device when its temperature boundary is reached. In order to realize the approach proposed here, the devices are connected to a central control entity by two-way communication. The coordination consists of a step-wise heuristic solution of a binary optimization problem, which serves to select a number of devices in each time step that are subject to compulsory switching, i.e. toggling the “on/off” state. It allows a large group of devices to track a setpoint trajectory with its aggregated power consumption, acting like a distributed virtual energy storage, while the individual temperature bounds of the appliances are not violated. This behavior can be used for grid-control purposes, such as the provision of active power reserves. It will be shown that the group of appliances can be characterized by an approximate aggregated dynamical model consisting of a first-order differential equation together with an approximate aggregated nonlinear cost function penalizing the control actions. The developed methodology is evaluated in a numerical simulation with a small appliance cluster corresponding to a residential housing area.

A Novel Coding Scheme for Practical Economic Dispatch by Modified Particle Swarm Approach

This paper proposes a new approach and coding scheme for solving economic dispatch problems in power systems through simulated annealing like particle swarm optimization (SA-PSO). This novel coding scheme could effectively prevent obtaining infeasible solutions through the application of stochastic search methods, thereby dramatically improving search efficiency and solution quality. Many nonlinear characteristics of power generators, and their operational constraints, such as generation limitations, ramp rate limits, prohibited operating zones, transmission loss, and nonlinear cost functions, were all considered for practical operation. The effectiveness and feasibility of the proposed method were demonstrated by four system case studies and compared with previous literature in terms of solution quality and computational efficiency. The experiment showed encouraging results, suggesting that the proposed approach was capable of efficiently determining higher quality solutions addressing economic dispatch problems.

A novel string structure for economic dispatch problems with practical constraints

The novel string structure for solving the economic dispatch problems through genetic algorithm (GA) is presented. The proposed string scheme can effectively prevent getting infeasible solution when evolutionary computation methods are preceded. Therefore, it can increase the searching efficiency and also solution quality dramatically. Many nonlinear characteristics of the power generators and practical constraints, such as generation limitation, ramp rate limits, prohibited operating zone, transmission loss and nonlinear cost functions are all considered for realistic operation. The effectiveness and feasibility of the proposed method are demonstrated by three real systems, and compared with the literatures method in terms of the solution quality and computation efficiency. The experimental shows encouraging results that the proposed approach was indeed capable of obtaining higher quality and efficiency solutions in economic dispatch problems.

A novel modeling approach for express package carrier planning

AbstractExpress package carrier networks have large numbers of heavily‐interconnected and tightly‐constrained resources, making the planning process difficult. A decision made in one area of the network can impact virtually any other area as well. Mathematical programming therefore seems like a logical approach to solving such problems, taking into account all of these interactions. The tight time windows and nonlinear cost functions of these systems, however, often make traditional approaches such as multicommodity flow formulations intractable. This is due to both the large number of constraints and the weakness of the linear programming (LP) relaxations arising in these formulations. To overcome these obstacles, we propose a model in which variables represent combinations of loads and their corresponding routings, rather than assigning individual loads to individual arcs in the network. In doing so, we incorporate much of the problem complexity implicitly within the variable definition, rather than explicitly within the constraints. This approach enables us to linearize the cost structure, strengthen the LP relaxation of the formulation, and drastically reduce the number of constraints. In addition, it greatly facilitates the inclusion of other stages of the (typically decomposed) planning process. We show how the use of templates, in place of traditional delayed column generation, allows us to identify promising candidate variables, ensuring high‐quality solutions in reasonable run times while also enabling the inclusion of additional operational considerations that would be difficult if not impossible to capture in a traditional approach. Computational results are presented using data from a major international package carrier. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008

On the price of anarchy for non-atomic congestion games under asymmetric cost maps and elastic demands

We derive several bounds for the price of anarchy of the noncooperative congestion games with elastic demands and asymmetric linear or nonlinear cost functions. The bounds established depend on a constant from the cost functions as well as the ratio between user benefit and social surplus at Nash equilibrium. The results can be viewed a generalization of that of Chau and Sim [C.K. Chau, K.M. Sim, The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands, Operations Research Letters 31 (2003) 327–334] for the symmetric case, or a generalization of Perakis [G. Perakis, The price of anarchy when costs are nonseparable and asymmetric, Lecture Notes in Computer Science 3064 (2004) 46–58] to the elastic demand.

An Efficient Multiple Data Sources Selection Algorithm in Data-Sharing Environments

PDF HTML阅读 XML下载 导出引用 引用提醒 一种有效的数据共享环境多数据源选择算法 DOI: 作者: 作者单位: 作者简介: 通讯作者: 中图分类号: 基金项目: An Efficient Multiple Data Sources Selection Algorithm in Data-Sharing Environments Author: Affiliation: Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:针对数据共享环境多数据源选择MDSS(multiple data sources selection)问题,基于Pareto最优理论提出了MDSSA(MDSS algorithm)算法.该算法借助崭新的基于法线测量的非线性路径代价方程计算出到每个数据源的最优路径集合,进而通过代价对比确定实施数据访问的最佳数据源及路径,极大地缩小了搜索空间,在搜索到有效路径的同时,确保了算法的响应时间.大量仿真实验表明,MDSSA算法是有效的. Abstract:The problem of multiple data sources selection (MDSS) in DSE (data-sharing environments) is addressed and the algorithm MDSSA (MDSS algorithm) is presented. MDSSA introduces the concept of Pareto optimization which reduces the search space greatly. By means of a novel normal-measure based nonlinear cost function, MDSSA computes approximate Pareto optimal paths to each data source first, and then gives the optimal data source and its corresponding path by comparing the cost of all candidate paths, resulting in finding more effective paths and much shorter response time. Extensive simulations show the efficiency of the algorithm. 参考文献 相似文献 引证文献

SU-GG-T-39: Optimized Planning of a High Dose Rate Prostate Brachytherapy Treatment Using Constrained Nonlinear Programming

Purpose: To describe an efficient prostate HDR optimization strategy using constrained nonlinear programming. Method and Materials: Calculation points, contours and source positions were exported from a clinical prostate HDR implant case to a PC running MatLab. A matrix Dij is computed for the dose rate to each calculation point i from each dwell position j. The dose d = Dij*t for dwell time t was calculated using the TG-43 formalism. Both the prostate and urethra are planned for a uniform dose d0 with equal weights. The MatLab optimization toolbox is used to compute the minimum of an arbitrary nonlinear cost function subject to linear inequality constraint Dij*t ⩾ d0 with t values between any lower and upper bound. We investigated the effects of performing an unbounded optimization and setting negative dwell times to zero; linear (n=1) versus quadratic (n=2) cost function with positive dwell times; and lowering the upper bound. These methods were compared to manual optimization performed by an expert user. Results: Utilizing a quadratic cost function, nearly perfect target coverage is obtained with acceptable urethral dose when negative dwell times are allowed. Setting negative dwell times to zero seriously compromises dose homogeneity. The effect of applying a linear cost function as well as that of lowering the upper dwell time bound is to significantly increase the hot spots. A quadratic cost function with positive dwell times and upper dwell time limit of nine times the mean provided a clinically optimal treatment plan. Compared to manual plans, optimized plans had superior target coverage, lower inhomogeneity and were calculated in minutes instead of hours. Conclusion: Constrained nonlinear programming is an effective tool to optimize prostate HDR treatment planning. A relatively high upper dwell time limit with a quadratic cost function yielded the best clinical results.

The toll effect on price of anarchy when costs are nonlinear and asymmetric

We examine the efficiency of the optimal tolls by establishing the bound for the price of anarchy when the levied tolls are also considered as a part of the cost functions. For linear and nonlinear asymmetric cost functions, we prove that the price of anarchy of the system with tolls is lower than that without tolls. Furthermore, we show that the total disutility caused to the users by the tolls is bounded by a multiple of the original optimal system cost.

Using Model Reduction Methods within Incremental Four-Dimensional Variational Data Assimilation

Abstract Incremental four-dimensional variational data assimilation is the method of choice in many operational atmosphere and ocean data assimilation systems. It allows the four-dimensional variational data assimilation (4DVAR) to be implemented in a computationally efficient way by replacing the minimization of the full nonlinear 4DVAR cost function with the minimization of a series of simplified cost functions. In practice, these simplified functions are usually derived from a spatial or spectral truncation of the full system being approximated. In this paper, a new method is proposed for deriving the simplified problems in incremental 4DVAR, based on model reduction techniques developed in the field of control theory. It is shown how these techniques can be combined with incremental 4DVAR to give an assimilation method that retains more of the dynamical information of the full system. Numerical experiments using a shallow-water model illustrate the superior performance of model reduction to standard truncation techniques.

Optimal probability density function control for NARMAX stochastic systems

This paper presents a new control strategy for a class of non-Gaussian stochastic systems so that the output probability density function (PDF) of the system can be made to follow a desired PDF. The system considered is represented by an Nonlinear AutoRegressive and Moving Average with eXogenous (NARMAX) inputs with input channel time-delay and non-Gaussian noise. A multi-step-ahead nonlinear cumulative cost function is used to improve tracking performance. For this purpose, a relationship between the PDFs of all the inputs and the PDFs of multiple-step-ahead output is formulated by constructing an auxiliary multivariate mapping. By minimizing this performance function, a new explicit predictive controller design algorithm is established with less conservatism than some previous results. Furthermore, an improved approach is developed to guarantee the local stability of the closed-loop system by tuning the weighting parameters recursively. Simulations are given to demonstrate the effectiveness of the proposed control algorithm and desired results have been obtained.

Hydrothermal self-scheduling problem in a day-ahead electricity market

This paper addresses the self-scheduling problem of determining the unit commitment status for power generation companies before submitting the hourly bids in a day-ahead market. The hydrothermal model is formulated as a deterministic optimization problem where expected profit is maximized using the 0/1 mixed-integer linear programming technique. This approach allows precise modelling of non-convex variable cost functions and non-linear start-up cost functions of thermal units, non-concave power-discharge characteristics of hydro units, ramp rate limits of thermal units and minimum up and down time constraints for both hydro and thermal units. Model incorporates long-term bilateral contracts with contracted power and price patterns, as well as forecasted market hourly prices for day-ahead auction. Solution is achieved using the homogeneous interior point method for linear programming as state of the art technique, with a branch and bound optimizer for integer programming. The effectiveness of the proposed model in optimizing the generation schedule is demonstrated through the case studies and their analysis.

An integer programming approach to generating airline crew pairings

The ability to generate crew pairings quickly is essential to solving the airline crew scheduling problem. Although techniques for doing so are well-established, they are also highly customized and require significant implementation efforts. This greatly impedes researchers studying important problems such as robust planning, integrated planning, and automated recovery, all of which also require the generating of crew pairings. As an alternative, we present an integer programming (IP) approach to generating crew pairings, which can be solved via traditional methods such as branch-and-bound using off-the-shelf commercial solvers. This greatly facilitates the prototyping and testing of new research ideas. In addition, we suggest that our modeling approach, which uses both connection variables and marker variables to capture the non-linear cost function and constraints of the crew scheduling problem, can be applicable in other scheduling contexts as well. Computational results using data from a major US hub-and-spoke carrier demonstrate the performance of our approach.

ON INITIALIZATION OF ML DOA COST FUNCTION FOR UCA

Maximum likelihood (ML) direction-of-arrival (DOA) estimation is essentially an optimization of multivariable nonlinear cost function. Since the final estimate is highly dependent on the initial estimate, an initialization is critical in nonlinear optimization. Alternating Projection (AP) initialization has been proposed as computationally efficient method for the initialization of the ML DOA cost function. In this paper, we propose a multi-dimensional (M-D) search scheme of uniform exhaustive search and improved exhaustive search. Improved exhaustive search is used to reduce the computational load of uniform exhaustive search. In the improved exhaustive search algorithm, the two-step procedure is applied to reduce the computational load of the uniform exhaustive search initialization scheme. In numerical results, it is shown that the performance of the proposed scheme is better than that of AP initialization.