三种常见现代优化算法的比较

现代最优化算法比较常见的有遗传算法、蚁群算法、粒子群算法、鱼群算法和模拟退火算法。这些算法主要是解决优化问题中的难解问题。文章主要是对遗传算法、粒子群算法和模拟退火算法三个算法的优化性能进行比较。首先介绍了三个算法的基本思想,以此可以了解三种算法有着自身的特点和优势,而后用这三种算法对典型函数进行计算,并对优化结果比较分析,提出了今后研究的方向。     

A note on computing equilibria in economies with activity analysis models of production

Equilibria in economies without production can be approximated by computing fixed points of continuous functions. With production present, the functions are usually replaced by set-valued mappings and fixed-point algorithms converge slowly. Here we propose continuous functions whose fixed points are equilibria in economies whose production is modelled by a finite list of activities. The penalty is that a least-distance program must be solved at each iteraction. The approach generalizes to allow ad valorem taxes on production. Finally, analogous arguments apply to the computation of an invariant optimal vector of capital stocks.     

An algorithm for the generalized transportation problem

This paper describes a new computational technique for solving spatial economic equilibrium problems which are generalizations of the classic transportation problem. This technique makes use of a type of algorithm which has been developed in recent years to compute Kakutani fixed points and solve related problems. Existing algorithms for the generalized transportation problem employ quadratic programming, and therefore require that demand and supply functions be linear. By contrast, the algorithm of this paper can handle demand and supply relationships which are nonlinear or even semi-continuous. It can also handle non-constant transport costs and various other complications. The technique is capable of yielding highly accurate solutions, and appears to be computationally efficient on problems of reasonable size.     

一个基于无迹卡尔曼滤波的传热反问题求解方法

准确估计材料的物性参数、初始条件、边界条件等对于热能工程领域具有重要意义。导热反问题(Inverse HeatConduction Problems,IHCP)提供了一种获取上述参数的有效途径,IHCP的成功应用在一定程度上取决于反演算法的效率。文章提出一种同时考虑被反演对象演化信息和测量信息的反演模型,原始IHCP问题被转化为一个状态-空间问题,无迹卡尔曼滤波(Unscented Kalman Filter,UKF)方法被发展用于求解该反演模型。数值模拟结果表明,该算法能够改善反演精度,而且,该算法的执行并不要求计算目标函数的梯度信息、雅克比矩阵和黑森矩阵,有效地降低了计算的复杂性与代价,从而为求解IHCP问题提供了一个有效途径。     

Riesz estimators

We consider properties of estimators that can be written as vector lattice (Riesz space) operations. Using techniques widely used in economic theory and functional analysis, we study the approximation properties of these estimators paying special attention to additive models. We also provide two algorithms RIESZVAR(i-ii) for the consistent parametric estimation of continuous multivariate piecewise linear functions.     

Estimating cell frequencies under inequality constraints based on the Kullback–Leibler information

This article considers the problem of estimating the cell frequencies in a contingency table under inequality constraints. Algorithms are proposed for cell frequency estimation via minimizing the Kullback–Leibler distance subject to inequality constraints. The proposed algorithms are shown to be simple, easy to be used, fast, and reliable. Theorems are derived to guarantee the convergence of the algorithms. Applications and extensions of the algorithms are provided for more general problems than contingency table. The R programs that implement the proposed algorithms are presented in Appendix B.     

Differentiated oligopolistic markets with concave cost functions via Ky Fan inequalities

A Nash–Cournot model for oligopolistic markets with concave cost functions and a differentiated commodity is analyzed. Equilibrium states are characterized through Ky Fan inequalities. Relying on the minimization of a suitable merit function, a general algorithmic scheme for solving them is provided. Two concrete algorithms are therefore designed that converge under suitable convexity and monotonicity assumptions. The results of some numerical tests on randomly generated markets are also reported.     

Assessing the relationships between Nationalism, Ethnocentrism, and Individualism in Flanders using Bergstrom's approximate discrete model

Although Nationalism, Ethnocentrism, and Individualism in Flanders have been the subject of several studies before, a longitudinal analysis has not been performed on all three concepts simultaneously nor have their relationships and the direction of their relationships been studied in continuous time. In this study we performed a continuous-time state-space analysis on panel data collected from 1274 subjects, in the years 1991, 1995 and 1999. The LISREL program is used for estimating the approximate discrete model (ADM), and for comparison, also the exact discrete model (EDM) is estimated by means of the Mx program. Details of continuous time modeling, especially the EDM and ADM, are dealt with. Individualism and Ethnocentrism turn out to be connected in a moderately strong feedback relationship with the effect from Individualism towards Ethnocentrism somewhat stronger than that in the opposite direction. Both Individualism and Ethnocentrism have small effects on Nationalism. The autoregression functions, cross-lagged effect functions, and mean predictions are shown.     

Optimal locations and flow allocations for aggregation hubs in supply chain networks of perishable products

Establishment of aggregation hubs in a supply chain network (SCN) is typically a facility location-allocation (FLA) decision, which is known to be a NP-hard optimization problem. Considering the flow of heterogeneous perishable products, like fresh produce, with different spoilage rates, further increases the complexity of such a problem. This is due to the effect of transportation time and conditions, services provided in the hub, and hub proximity to supply sources, on the quality and quantity of products eventually reaching the demand destinations, and hence on the location-allocation decision. In this paper, this problem is formulated as a mixed integer linear programming (MILP) model that considers a number of problem characteristics simultaneously for the first time, to minimize the transportation, spoilage, processing, and capacity-based hub establishment costs. Due to its complexity, two hybrid algorithms that combine a meta-heuristic with a perishability-modified transportation algorithm, are proposed to solve the problem. The algorithms are based on binary particle swarm optimization (BPSO) and simulated annealing (SA). Taguchi analysis is used to tune the significant parameters of both algorithms considering different problem sizes. Computational analysis is further conducted to evaluate and compare the performances of the algorithms using randomly generated test instances and exact solutions obtained using CPLEX. Results show that while both algorithms are capable of obtaining optimum solutions for most instances, the hybrid BPSO slightly outperforms the hybrid SA in terms of consistency and solution time.     

Parametric Inference for Diffusion Processes Observed at Discrete Points in Time: a Survey

This paper is a survey of estimation techniques for stationary and ergodic diffusion processes observed at discrete points in time. The reader is introduced to the following techniques: (i) estimating functions with special emphasis on martingale estimating functions and so-called simple estimating functions; (ii) analytical and numerical approximations of the likelihood function which can in principle be made arbitrarily accurate; (iii) Bayesian analysis and MCMC methods; and (iv) indirect inference and EMM which both introduce auxiliary (but wrong) models and correct for the implied bias by simulation.     

A polyhedral approximation approach to concave numerical dynamic programming

This paper introduces a numerical method for solving concave continuous state dynamic programming problems which is based on a pair of polyhedral approximations of concave functions. The method is globally convergent and produces computable upper and lower bounds on the value function which can in theory be made arbitrarily tight. This is true regardless of the pattern of binding constraints, the smoothness of model primitives, and the dimensionality and rectangularity of the state space. We illustrate the method's performance using an optimal firm management problem subject to credit constraints and partial investment irreversibilities.     

On solving bias‐corrected non‐linear estimation equations with an application to the dynamic linear model

In a seminal paper, Mak, Journal of the Royal Statistical Society B, 55, 1993, 945, derived an efficient algorithm for solving non‐linear unbiased estimation equations. In this paper, we show that when Mak's algorithm is applied to biased estimation equations, it results in the estimates that would come from solving a bias‐corrected estimation equation, making it a consistent estimator if regularity conditions hold. In addition, the properties that Mak established for his algorithm also apply in the case of biased estimation equations but for estimates from the bias‐corrected equations. The marginal likelihood estimator is obtained when the approach is applied to both maximum likelihood and least squares estimation of the covariance matrix parameters in the general linear regression model. The new approach results in two new estimators when applied to the profile and marginal likelihood functions for estimating the lagged dependent variable coefficient in the dynamic linear regression model. Monte Carlo simulation results show the new approach leads to a better estimator when applied to the standard profile likelihood. It is therefore recommended for situations in which standard estimators are known to be biased.     

Structural estimation of jump-diffusion processes in macroeconomics

This paper shows how to solve and estimate a continuous-time dynamic stochastic general equilibrium (DSGE) model with jumps. It also shows that a continuous-time formulation can make it simpler (relative to its discrete-time version) to compute and estimate the deep parameters using the likelihood function when non-linearities and/or non-normalities are considered. We illustrate our approach by solving and estimating the stochastic AK and the neoclassical growth models. Our Monte Carlo experiments demonstrate that non-normalities can be detected for this class of models. Moreover, we provide strong empirical evidence for jumps in aggregate US data.     

Estimation of Engel Curves from Survey Data with Zero Expenditures*

The objective of this article is to propose a Bayesian method for estimating a system of Engel functions using survey data that include zero expenditures. We deal explicitly with the problem of zero expenditures in the model and estimate a system of Engel functions that satisfy the adding‐up condition. Furthermore, using Markov chain Monte Carlo method, we estimate unobservable parameters, including consumption of commodities, total consumption and equivalence scale, and use their posterior distributions to calculate inequality measures and total consumption elasticities.     

A characterization of the existenceof optimal dominant strategy mechanisms

This paper provides two theorems which characterize the domains of valuation functions for which there exist Pareto efficient and truth dominant strategy mechanisms (balanced Groves mechanisms). Theorem 1 characterizes the existence of balanced Groves mechanisms for a general class of valuation functions. Theorem 2 provides new balance-permitting domains of valuation functions by reducing the problem of solving partial differential equations to the problem of solving a polynomial function. It shows that a balanced Groves mechanism exists if and only if each valuation function in the family under consideration can be obtained by solving a polynomial function with order less than , where n is the number of individuals. Received: 5 January 1997 / Accepted: 25 May 1999     

A general framework for approximate sampling with an application to generating points on the boundary of bounded convex regions

We consider the problem of generating a sample of points according to some given probability distribution over some region. We give a general framework for constructing approximate sampling algorithms based on the theory of Markov chains. In particular, we show how it can be proven that a Markov chain has a limiting distribution. We apply these results to prove convergence for a class of so-called Shake-and-Bake algorithms, which can be used to approximate any absolutely continuous distribution over the boundary of a full-dimensional convex body.     

A new look at static spatial price equilibrium models

In this paper we propose a new view and more general formulations of static single commodity spatial equilibrium models, that lead to simpler and more efficient algorithms than those previously employed for solving models of this type. The proposed formulations incorporate general transportation networks and may be extended to allow for multiple commodities. Solution algorithms are suggested for the problem with multiple commodities, when there exists an equivalent optimization problem. We show that the multiple commodity problem may be cast in the form of a variational inequality, when there does not exist an equivalent optimization problem and propose algorithms to solve this version of the problem as well.     

Automatic Editing for Business Surveys: An Assessment of Selected Algorithms

Statistical offices are responsible for publishing accurate statistical information about many different aspects of society. This task is complicated considerably by the fact that data collected by statistical offices generally contain errors. These errors have to be corrected before reliable statistical information can be published. This correction process is referred to as statistical data editing. Traditionally, data editing was mainly an interactive activity with the aim to correct all data in every detail. For that reason the data editing process was both expensive and time-consuming. To improve the efficiency of the editing process it can be partly automated. One often divides the statistical data editing process into the error localisation step and the imputation step. In this article we restrict ourselves to discussing the former step, and provide an assessment, based on personal experience, of several selected algorithms for automatically solving the error localisation problem for numerical (continuous) data. Our article can be seen as an extension of the overview article by Liepins, Garfinkel & Kunnathur (1982). All algorithms we discuss are based on the (generalised) Fellegi–Holt paradigm that says that the data of a record should be made to satisfy all edits by changing the fewest possible (weighted) number of fields. The error localisation problem may have several optimal solutions for a record. In contrast to what is common in the literature, most of the algorithms we describe aim to find all optimal solutions rather than just one. As numerical data mostly occur in business surveys, the described algorithms are mainly suitable for business surveys and less so for social surveys. For four algorithms we compare the computing times on six realistic data sets as well as their complexity.     

On the continuity of representations of effectivity functions

An effectivity function assigns to each coalition of individuals in a society a family of subsets of alternatives such that the coalition can force the outcome of society’s choice to be a member of each of the subsets separately. A representation of an effectivity function is a game form with the same power structure as that specified by the effectivity function. In the present paper we investigate the continuity properties of the outcome functions of such representation. It is shown that while it is not in general possible to find continuous representations, there are important subfamilies of effectivity functions for which continuous representations exist. Moreover, it is found that in the study of continuous representations one may practically restrict attention to effectivity functions on the Cantor set. Here it is found that general effectivity functions have representations with lower or upper semicontinuous outcome function.