Setup Adjustment for Asymmetric Cost Functions Under Unknown Process Parameters

Label embedding (LE) is an important family of multi-label classification algorithms that digest the label information jointly for better performance. Different real-world applications evaluate performance by different cost functions of interest. Current LE algorithms often aim to optimize one specific cost function, but they can suffer from bad performance with respect to other cost functions. In this paper, we resolve the performance issue by proposing a novel cost-sensitive LE algorithm that takes the cost function of interest into account. The proposed algorithm, cost-sensitive label embedding with multidimensional scaling (CLEMS), approximates the cost information with the distances of the embedded vectors by using the classic multidimensional scaling approach for manifold learning. CLEMS is able to deal with both symmetric and asymmetric cost functions, and effectively makes cost-sensitive decisions by nearest-neighbor decoding within the embedded vectors. We derive theoretical results that justify how CLEMS achieves the desired cost-sensitivity. Furthermore, extensive experimental results demonstrate that CLEMS is significantly better than a wide spectrum of existing LE algorithms and state-of-the-art cost-sensitive algorithms across different cost functions.

By deriving an upper bound of the so-called 'price of anarchy', this paper analyses the efficiency of oligopolistic games in networks with non-separable and asymmetric cost functions, splittable flows and fixed demands. The new bound is determined by the optimal objective function values of some optimisation problems. In particular, for some special cases, the bound turns out to be explicit in the sense that it is representable explicitly by the number of players, and the constants measuring the degree of asymmetry and non-linearity of the cost function. Copyright © 2010 Inderscience Enterprises Ltd.

This study investigates game-based PIMFY models for analyzing the interactions among grant-seeking local governments and the central government. From these models we could find the following. The effective prize dissipation ratio in each local government multiplied by its population is the same in two competing local governments – in the first case, of equal valuation and equal cost functions, and in the second case, of equal valuation and asymmetric cost functions. If the central government uses a policy to strengthen cost advantage in favor of the low cost local government, then economic inefficiency in terms of aggregate outlays will decrease. If there a binding constraint on outlay by local government 1 is assigned by the central government, then at the binding level of outlay, local government 2’s new equilibrium level needs to be calculated and it will be smaller than the equilibrium level without the binding constraint.

The problem of reducing predictive cost is considered in the case when the cost of error function is not symmetric and the optimality criterion is the minimization of the median cost of the error of prediction. Examples are given and comparisons made with the usual solution based on the minimization of the mean cost. In the case of a Gaussian process, the median solution is found to be a simple additive adjustment to the predictive mean, and far easier to compute than the solution based on expected cost.

A modelling approach for solving quite general network equilibrium problems (with fixed trip productions and attractions) intrinsic to the urban transport planning process is presented. The framework can consider a variety of demand models and route choice behaviours within the same implementation, including multiple user classes and combined travel modes that interact on the same physical network. The demand choices are assumed to have a hierarchical structure. When trip distribution is variable, a doubly constrained entropy‐maximizing model is considered at the first level of choice and a hierarchical logit model is used for the remaining demand choices (time of departure, travel mode, transfer point for combined modes, etc.). If trip distribution is considered to be exogenous, the demand choices are modelled as a hierarchical logit. One of the main features of the model is that it considers the effects of congestion on the road network as well as congestion and capacity constraints effects in each public transport service network. The problem is formulated mathematically as a variational inequality, with asymmetric cost functions, and solved following the diagonalization procedure. Each iteration of the aforementioned procedure solves an optimization problem using the Evans algorithm. Sufficient conditions for the existence and uniqueness of the solution to the diagonalized problem are obtained. The main results of a simple example (solved with an academic version of the proposed algorithm) are presented to show the consistency of the equilibrium flows and levels of services obtained using the model. Finally, a real scale implementation of the model is briefly described to show the feasibility of its application.

How to Generate Good Profit Maximization Problems

This paper presents a systematic method for generating optimal helicopter flight trajectories in real time for cockpit display. Helicopter flights in the event of a single engine failure are critical, and display of optimal flight paths on-board is desirable. Due to the large number of states and constraints, however, numerical solutions on a mainframe computer can take a long tune. In this paper, optimal solutions are first obtained off-line using a ground computer. For a given set of initial helicopter states and flight parameters, optimal solutions are fitted by a Fourier series. The coefficients of the Fourier approximations are then interpolated as functions of initial flight states and parameters. The approximate optimal trajectories can be quickly generated on-board using the proposed method. Introduction Engine failure is a major safety issue for all helicopters, especially during takeoff and landing operations. Due to the complexity of the situation and the dependence of safety on many parameters, optimal flight trajectories can provide useful guidance for pilot operation. In particular, on-board display of optimal trajectories is desirable. This paper presents a method for generating optimal flight trajectories in real-tune that can be used for on-board display. Depending on its capability and performance during an engine failure, a transport helicopter can be certified as Category A or Category B. The Federal Aviation Administration (FAA) grants Category B certification to a single or multi-engine helicopter with gross weight less than 20,000 Ib and capable of landing safely in case of one or all engine failures. Category A certification, on the other hand, is granted to multi-engine helicopters with independent engine systems. Category A helicopters must be able to either land safely or continue flight in case of One Engine Inoperation (OEI). This makes Category A helicopters uniquely suited for remote places where emergency landing sites are not available. I Ph.D. Candidate, Center for Control Sciences, Member AIAA * Assistant Professor, Dept. of Aerospace Eng. and Mechanics, Member AIAA + Civil Rotorcraft Group Leader, Rotorcraft and Powered Lift Branch The decision to continue the flight or to land represents an energy management problem. It has been shown''' that this decision depends on initial conditions at the time of failure as well as flight parameters. Due to the numerous initial variables involved in this decision, a method to communicate all this information to the pilot instantaneously, at engine failure, is needed. This method must keep the emergency procedure simple and manageable. In particular, on-board cockpit display of optimal flight trajectories is useful. This requires a reliable real-tune solution of optimal trajectories, on board, with limited time, limited computing power, and limited memory available. If possible, an analytical solution of optimal trajectories is desirable. Unfortunately, this can only be achieved for systems of low order and where the equations of motion and the cost function are simple. Therefore, for a complex system, an open-loop numerical procedure becomes necessary. Research efforts were made to solve optimal control problems in real-time. Schultz et al. used calculus of variation and energy state method to generate optimal trajectories on-board for the National Aerospace Plane (NASP). In his study, the equations of motion of the NASP are less complex than those of the helicopter, and an interval of time of few minutes is allowed. Bryson used neighboring control theory to generate near-optimal solutions that could be used in real-time. This method is elegant but requires a large amount of memory to store the needed perturbation matrices. Also, it is valid on a relatively small neighborhood of the nominal trajectory. Perturbation methods and table lookups are often used if only few parameters are involved. In the current problem, the equations of motion of the helicopter are complex and too many path equality and inequality constraints are present. Also, limitations on tune, computing power, and memory available make all the above methods unsuitable for this problem. This paper proposes a technique of real-time optimal trajectory generation based on approximation and

As short run manufacturing becomes more prevalent, run-to-run components of variation, such as that contributed by set-up error, have greater potential to crucially affect product quality. While efforts should be made to eliminate such between-run variance contributing factors, some will always be present. Here, we assume there is one such factor which we envisage as set-up error that, unless the process is adjusted, remains fixed throughout a run. We develop a single adjustment strategy based on taking a sample of fixed size from the process. If a significant set-up error is indicated, a single compensatory adjustment, equal to the predicted process offset, is executed. The actual procedure depends on process parameters, including adjustment error, run size, and adjustment and sampling costs. The procedure not only specifies the adjustment amount, if any, but the time during the run at which to adjust. The procedure is optimal among all fixed sample size procedures for the chosen cost function. Besides incorporating adjustment and sampling costs, the cost function is based on a 0–1 loss criterion, where the loss is 0 (1) units per item produced if the process offset caused by set-up error is less than or equal to (greater than) a specified amount. Tables are provided, with examples, illustrating the procedure for representative values of process parameters, costs, and run sizes.

Probabilistic retrieval models usually rank documents based on a scalar quantity. However, such models lack any estimate for the uncertainty associated with a document’s rank. Further, such models seldom have an explicit utility (or cost) that is optimized when ranking documents. To address these issues, we take a Bayesian perspective that explicitly considers the uncertainty associated with the estimation of the probability of relevance, and propose an asymmetric cost function for document ranking. Our cost function has the advantage of adjusting the risk in document retrieval via a single parameter for any probabilistic retrieval model. We use the logit model to transform the document posterior distribution with probability space [0,1] into a normal distribution with variable space ( − ∞ , + ∞ ). We apply our risk adjustment approach to a language modelling framework for risk adjustable document ranking. Our experimental results show that our risk-aware model can significantly improve the performance of language models, both with and without background smoothing. When our method is applied to a language model without background smoothing, it can perform as well as the Dirichlet smoothing approach.

The high time needed to reconfigure cloud resources in Network Function Virtualization network environments has led to the proposal of solutions in which a prediction based-resource allocation is performed. All of them are based on traffic or needed resource prediction with the minimization of symmetric loss functions like Mean Squared Error. When inevitable prediction errors are made, the prediction methodologies are not able to differently weigh positive and negative prediction errors that could impact the total network cost. In fact if the predicted traffic is higher than the real one then an over allocation cost, referred to as over-provisioning cost, will be paid by the network operator; conversely, in the opposite case, Quality of Service degradation cost, referred to as under-provisioning cost, will be due to compensate the users because of the resource under allocation. In this paper we propose and investigate a resource allocation strategy based on a Long Short Term Memory algorithm in which the training operation is based on the minimization of an asymmetric cost function that differently weighs the positive and negative prediction errors and the corresponding over-provisioning and under-provisioning costs. In a typical traffic and network scenario, the proposed solution allows for a cost saving by 30% with respect to the case of solution with symmetric cost function.

In this paper, we analyse the performance of the closed-loop Whiplash gradient descent algorithm [1] for L-smooth convex cost functions. Using numerical experiments, we study the algorithm’s performance for convex cost functions, for different condition numbers. We analyse the convergence of the momentum sequence using symplectic integration and introduce the concept of relaxation sequences which analyses the non-classical character of the whiplash method. Under the additional assumption of invexity, we establish a momentum-driven adaptive convergence rate. Furthermore, we introduce an energy method for predicting the convergence rate with convex cost functions for closed-loop inertial gradient dynamics, using an integral anchored energy function and a novel lower bound asymptotic notation, by exploiting the bounded nature of the solutions. Using this, we establish a polynomial convergence rate for the whiplash inertial gradient system, for a family of scalar quadratic cost functions and an exponential rate for a quadratic scalar cost function.

In this paper we are concerned with the problem of sequencing a given set of jobs without preemption on a single machine so as to minimize total cost, where associated with each job is a processing time and a differentiable cost function defined on the completion time of the job. The problem, in general, is NP-complete and, therefore, there is unlikely to be an algorithm to solve the problem in reasonable time, thus a heuristic algorithm is desirable. We present two heuristic algorithms to solve the problem. The first algorithm is based on the differential of the cost functions, and the second algorithm is based on the least square approximation of the cost functions. Computational experiences for the case of quadratic, cubic, and exponential cost functions are presented.

In group decision making (GDM), to facilitate an acceptable consensus among the experts from different fields, time and resources are paid for persuading experts to modify their opinions. Thus, consensus costs are important for the GDM process. Notwithstanding, the unit costs in the common linear cost functions are always fixed, yet experts will generally express more resistance if they have to make more compromises. In this study, we use the quadratic cost functions, the marginal costs of which increase with the opinion changes. Aggregation operators are also considered to expand the applications of the consensus methods. Moreover, this paper further analyzes the minimum cost consensus models under the weighted average (WA) operator and the ordered weighted average (OWA) operators, respectively. Corresponding approaches are developed based on strictly convex quadratic programming and some desirable properties are also provided. Finally, some examples and comparative analyses are furnished to illustrate the validity of the proposed models.

A novel projected two-binary-variable formulation for unit commitment in power systems

Structural sparsity is useful for variable and node selection in distributed networks. In this paper, we propose a distributed algorithm to solve the problem of a quadratic cost function with mixed $\ell_{1,2}$ -norm regularization to promote the group-sparsity of the solution. By introducing virtual pair nodes to each actual node and by decomposing the cost function to each nodes, we obtain a distributed optimization problem on an extended graph model, which is further solved via the PDMM algorithm. Numerical simulation results illustrate the accurate convergence of the proposed algorithm to the centralized solution.