In the 1950s, Markowitz proposed to combine different investment instruments to design a portfolio that either maximizes the expected return under constraints on volatility (risk) or minimizes the risk under given expected return. Markowitz’s formulas are still widely used in financial practice. However, these formulas assume that we know the exact values of expected return and variance for each instrument, and that we know the exact covariance of every two instruments. In practice, we only know these values with some uncertainty. Often, we only know the lower and upper bounds on these values – i.e., in other words, we only know the intervals that contain these values. In this paper, we show how to select an optimal portfolio under such interval uncertainty.
It is known that the problems of optimal design are NP-hard – meaning that, in general, a feasible algorithm can only produce close-to-optimal designs. The more computations we perform, the better design we can produce. In this paper, we theoretically derive quantitative formulas describing how the design qualities improves with the increasing computational abilities. We then empirically confirm the resulting theoretical formula by applying it to the problem of aircraft fuel efficiency.
The optimal number of doctors and appointment interval for an outpatient appointment system in a class of individual block/fixed interval are determined using an adaptive-penalty Genetic Algorithm. The length of service time for doctor consultation, the time required for the laboratory tests, and the time deviating from the appointment time are modelled by random variables. No-show patients are also included in the system. Using the adaptive penalty scheme, optimization constraints are automatically and numerically handled. The solution methodology is readily applicable to other appointment systems. The study has a significant implication from the viewpoint of economic and risk management of health care service.
This study uses technical indicator data to propose a new data-driven approach called nonparametric path identification to investigate the differences in the determinants, mechanism, and impact of the Sino-US stock markets. First, MA_5 is relevant to NASDAQ, whereas MA_10 is relevant to SSEC, which indicates that the trend of NASDAQ is more stable than that of SSEC. Second, different nonlinear mechanisms exist in the two stock markets, such that MA_10 and SAR have a nonlinear correlation to SSEC and NASDAQ, respectively. This finding indicates that the volatility reversion of NASDAQ is faster than SSEC. In addition, the relationship of middle Bollinger Bands (mavg) with SSEC is linear, whereas that with NASDAQ is nonlinear. Third, the most significant impact on SSEC is from CMF, whereas that on NASDAQ is from Average Directional Index (ADX). This result indicates the existence of more speculative behavior in SSEC than in NASDAQ.
This paper conducts a risk assessment of strategic emerging industries’ technical standards alliances. First, we study the ecological properties and operational cycles of technical standards alliances based on the ecological system. Following the rule by which identification precedes assessment, we apply factor analysis to identify the key risk factors in the ecological system of such alliances. We then construct a fuzzy synthetic assessment model and conduct an empirical analysis on the energy saving and environmental protection industries in China. Taking the unique research perspective of the ecological system and using interdisciplinary research methods, this study establishes itself as a theoretical model to be used as a guideline in practice. The result is expected to provide a useful reference for furthering technological innovation in China’s strategic emerging industries.
To prevent car accidents, it should be possible for pedestrians and other drivers to detect oncoming vehicles. Many car accidents are caused because persons are not aware of approaching traffic, and this applies especially to visual awareness. The daytime running light (DRL) and the third braking light (TBL) were developed to significantly increase the visibility of vehicles, and their effectiveness has been verified through numerous studies. Usage of light-emitting diode (LED) lighting technology has also become popular in auto-lighting systems because of its advantages of energy efficiency, long life, and stylish appearance. However, LED lighting technology is very different from conventional incandescent or high-intensity discharge (HID) lighting technology. In this paper, we determine the effectiveness of LEDs as DRLs and TBLs. We measure human attention levels by observing brainwaves and performing eye-tracking experiments that shows the relationship between the theory of attention, brainwaves, and eye tracking. The results obtained show that it is feasible to evaluate automotive exterior lighting using the attention levels of subjects.
This paper applied possibilistic approaches to a portfolio selection model. We considered a return rate as fuzzy variables. Based on the concept of possibilistic moments of fuzzy numbers, fuzzy stock returns and market risks are quantified by possibilistic mean and lower possibilistic semivariance, respectively. The non-dominated sorting genetic algorithm II (NSGA-II) was used to obtain the pareto optimal investment strategies for the integrated oil and gas company stocks.
Clustering, a highly useful unsupervised classification, has been applied in many fields. When, for example, we use clustering to classify a set of objects, it generally ignores any uncertainty included in objects. This is because uncertainty is difficult to deal with and model. It is desirable, however, to handle individual objects as is so that we may classify objects more precisely. In this paper, we propose new clustering algorithms that handle objects having uncertainty by introducing penalty vectors. We show the theoretical relationship between our proposal and conventional algorithms verifying the effectiveness of our proposed algorithms through numerical examples.
The rough clustering algorithm we proposed based on the optimization of objective function (RCM) has a problem because conventional rough clustering algorithm results do not ensure that solutions are optimal. To solve this problem, we propose rough clustering algorithms based on optimization of an objective function with fuzzy-set representation. This yields more flexible results than RCM. We verify algorithm effectiveness through numerical examples.
The tangential force that occurs between railway wheels and rails and the force is very important because it greatly affects the brake performance. However,tangential force, which fluctuates due to factors such as weather and rail conditions, is difficult to actually measure. We consider how to estimate tangential force based on observed in railway operation. First, we try using a dynamical model to improve the input accuracy in estimating tangential force. Second, we propose a way to estimate tangential force by using fuzzy inference with modified input. Third, we show through numerical experiments that our proposed method works appropriately and effectively.
Verifying a rational response is the most crucial step in searching for an optimal solution in bilevel linear programming. Such verification is even difficult in a model with ambiguous objective function of the follower who reacts rationally to a leader’s decision. In our model, we assume that the ambiguous coefficient vector of follower lies in a convex polytope and we formulate bilevel linear programming with the ambiguous objective function of the follower as a special three-level programming problem. We use the k-th best method that sequentially enumerates a solution and examine whether it is the best of all possible reactions. The optimality test process over possible reactions in lower-level problems usually encounters degenerate bases that become obstacles to verifying the optimality of an enumerated solution efficiently. To accelerate optimality verification, we propose search strategies and the evaluation of basic possible reactions adjacent to a degenerate basic solution. We introduce these methods in both local and global optimality testing, confirming the effectiveness of our proposed methods in numerical experiments.
Sequential cluster extraction algorithms are useful clustering methods that extract clusters one by one without the number of clusters having to be determined in advance. Typical examples of these algorithms are sequential hard c-means (SHCM) and possibilistic clustering (PCM) based algorithms. Two types of L1-regularized possibilistic clustering are proposed to induce crisp and possibilistic allocation rules and to construct a novel sequential cluster extraction algorithm. The relationship between the proposed method and SHCM is also discussed. The effectiveness of the proposed method is verified through numerical examples. Results show that the entropy-based method yields better results for the Rand Index and the number of extracted clusters.
In this study, a maximizing model of Bezdek-like spherical fuzzy c-means clustering is proposed, which is based on the regularization of the maximizing model of spherical hard c-means. Such a maximizing model was unclear in Bezdek-like method, whereas other types of methods have been investigated well both in minimizing and maximizing model. Using theoretical analysis and numerical experiments, the classification rule of the proposed method is shown. Using numerical examples, the proposed method is shown to be valid for document clustering, because documents are represented as spherical data via term document-inverse document frequency weighting and normalization processing.
In this paper, we consider a multi-dimension uncertain linear quadratic (LQ) optimal control with cross term. With the aid of the equation of optimality of a general multi-dimension uncertain optimal control, we present a necessary and sufficient condition for the existence of optimal linear feedback optimal control which is associated with a Riccati differential equation. Moreover, some properties of the solution for the Riccati differential equation are discussed. Furthermore, the uniqueness of the feedback optimal control for the uncertain linear quadratic optimal control with cross term is proved. Finally, as an application, an example is presented to illustrate the theory obtained.
One of the widely used methods to gauge risk is the Security Risk Factor Table (SRFT) model. While this model has been empirically successful, its use is limited by the fact that its formulas do not have a theoretical explanation – and thus, there is no guarantee that these formulas will work in other situations as well. In this paper, we provide a theoretical explanation for the SFRT formulas.
Recently, many studies have been conducted on Multi-Objective Genetic Algorithm (MOGA), in which Genetic Algorithms are applied to Multi-objective Optimization Problems (MOPs). Among various applications, MOGA is also applied to engineering design problems, which require not only high-performance Pareto solutions to be obtained, but also an analysis of the obtained Pareto solutions and extraction of design knowledge about the problem itself. In order to analyze the Pareto solutions obtained by MOGA, it is necessary to consider the objective space and the design variable space. The aim of this study is to extract and analyze solutions of relevant interest to designers. In this paper, we propose three solutions to analyze and extract design knowledge from MOGA. (1) We define “Non-Correspondence in Spread” between the objective space and the design variable space. (2) We try to extract the Non-Correspondence area in Spread using the index defined in this paper. (3) We apply the defined index to genetic search to obtain Pareto solutions that have different design variables and similar fitness values. This paper applies the above index to the trajectory design optimization problem and extracts Non-Correspondence area in Spread from the obtained Pareto solutions. This paper also shows that robust Pareto solutions can be obtained using genetic search using the defined index.
Gaussian Process Dynamical Models (GPDMs) constitute a nonlinear dimensionality reduction technique that provides a probabilistic representation of time series data in terms of Gaussian process priors. In this paper, we report a method based on GPDMs to visualize the states of time-series data. Conventional GPDMs are unsupervised, and therefore, even when the labels of data are available, it is not possible to use this information. To overcome the problem, we propose a supervised GPDM (S-GPDM) that utilizes both the data and their corresponding labels. We demonstrate experimentally that the S-GPDM can locate related motion data closer together than conventional GPDMs.
Nowadays the root finding problem for nonlinear system equations is still one of the difficult problems in computational sciences. Many attempts using deterministic and meta-heuristic methods have been done with their advantages and disadvantages, but many of them have fail to converge to all possible roots. In this paper, a novel method of locating and finding all of the real roots from the system of nonlinear equations is proposed mainly using the spiral dynamics inspired optimization by Tamura and Yasuda . The method is improved by the usage of the Sobol sequence of points for generating initial candidates of roots which are uniformly distributed than of pseudo-random generated points. Using clustering technique, the method localizes all potential roots so the optimization is conducted in those points simultaneously. A set of problems as the benchmarks from the literature is given. Having only a single run for each problem, the proposed method has successfully found all possible roots within a bounded domain.