Modeling Financial Time Series with Artificial Neural Networks

Financial time series convey the decisions and actions of a population of human actors over time. Econometric and regressive models have been developed in the past decades for analyzing these time series. More recently, biologically inspired artificial neural network models have been shown to overcome some of the main challenges of traditional techniques by better exploiting the non-linear, non-stationary, and oscillatory nature of noisy, chaotic human interactions. This review paper explores the options, benefits, and weaknesses of the various forms of artificial neural networks as compared with regression techniques in the field of financial time series analysis.CELEST, a National Science Foundation Science of Learning Center (SBE-0354378); SyNAPSE program of the Defense Advanced Research Project Agency (HR001109-03-0001

Path tracking control of differential drive mobile robot based on chaotic-billiards optimization algorithm

Mobile robots are typically depending only on robot kinematics control. However, when high-speed motions and highly loaded transfer are considered, it is necessary to analyze dynamics of the robot to limit tracking error. The goal of this paper is to present a new algorithm, chaotic-billiards optimizer (C-BO) to optimize internal controller parameters of a differential-drive mobile robot (DDMR)-based dynamic model. The C-BO algorithm is notable for its ease of implementation, minimal number of design parameters, high convergence speed, and low computing burden. In addition, a comparison between the performance of C-BO and ant colony optimization (ACO) to determine the optimum controller coefficient that provides superior performance and convergence of the path tracking. The ISE criterion is selected as a fitness function in a simulation-based optimization strategy. For the point of accuracy, the velocity-based dynamic compensation controller was successfully integrated with the motion controller proposed in this study for the robot's kinematics. Control structure of the model was tested using MATLAB/Simulink. The results demonstrate that the suggested C-BO, with steady state error performance of 0.6 percent compared to ACO's 0.8 percent, is the optimum alternative for parameter optimizing the controller for precise path tracking. Also, it offers advantages of quick response, high tracking precision, and outstanding anti-interference capability

On learning and the stability of cycles

We study a general equilibrium model where the multiplicity of stationary periodic perfect foresight equilibria is pervasive. We investigate the extent of which agents can learn to coordinate on stationary perfect foresight cycles. The example economy, taken from Grandmont (1985), is an endowment overlapping generations model with fiat money, where consumption in the first and second periods of life are not necessarily gross substitutes. Depending on the value of a preference parameter, the limiting backward (direction of time reversed) perfect foresight dynamics are characterized by steady state, periodic, or chaotic trajectories for real money balances. We relax the perfect foresight assumption and examine how a population of artificial, heterogeneous adaptive agents might learn in such an environment. These artificial agents optimize given their forecasts of future prices, and they use forecast rules that are consistent with steady state or periodic trajectories for prices. The agents' forecast rules are updated by a genetic algorithm. We find that the population of artificial adaptive agents is able to eventually coordinate on steady state and low-order cycles, but not on the higher-order periodic equilibria that exist under the perfect foresight assumption.Business cycles

Hybrid Intelligent Optimization Methods for Engineering Problems

The purpose of optimization is to obtain the best solution under certain conditions. There are numerous optimization methods because different problems need different solution methodologies; therefore, it is difficult to construct patterns. Also mathematical modeling of a natural phenomenon is almost based on differentials. Differential equations are constructed with relative increments among the factors related to yield. Therefore, the gradients of these increments are essential to search the yield space. However, the landscape of yield is not a simple one and mostly multi-modal. Another issue is differentiability. Engineering design problems are usually nonlinear and they sometimes exhibit discontinuous derivatives for the objective and constraint functions. Due to these difficulties, non-gradient-based algorithms have become more popular in recent decades. Genetic algorithms (GA) and particle swarm optimization (PSO) algorithms are popular, non-gradient based algorithms. Both are population-based search algorithms and have multiple points for initiation. A significant difference from a gradient-based method is the nature of the search methodologies. For example, randomness is essential for the search in GA or PSO. Hence, they are also called stochastic optimization methods. These algorithms are simple, robust, and have high fidelity. However, they suffer from similar defects, such as, premature convergence, less accuracy, or large computational time. The premature convergence is sometimes inevitable due to the lack of diversity. As the generations of particles or individuals in the population evolve, they may lose their diversity and become similar to each other. To overcome this issue, we studied the diversity concept in GA and PSO algorithms. Diversity is essential for a healthy search, and mutations are the basic operators to provide the necessary variety within a population. After having a close scrutiny of the diversity concept based on qualification and quantification studies, we improved new mutation strategies and operators to provide beneficial diversity within the population. We called this new approach as multi-frequency vibrational GA or PSO. They were applied to different aeronautical engineering problems in order to study the efficiency of these new approaches. These implementations were: applications to selected benchmark test functions, inverse design of two-dimensional (2D) airfoil in subsonic flow, optimization of 2D airfoil in transonic flow, path planning problems of autonomous unmanned aerial vehicle (UAV) over a 3D terrain environment, 3D radar cross section minimization problem for a 3D air vehicle, and active flow control over a 2D airfoil. As demonstrated by these test cases, we observed that new algorithms outperform the current popular algorithms. The principal role of this multi-frequency approach was to determine which individuals or particles should be mutated, when they should be mutated, and which ones should be merged into the population. The new mutation operators, when combined with a mutation strategy and an artificial intelligent method, such as, neural networks or fuzzy logic process, they provided local and global diversities during the reproduction phases of the generations. Additionally, the new approach also introduced random and controlled diversity. Due to still being population-based techniques, these methods were as robust as the plain GA or PSO algorithms. Based on the results obtained, it was concluded that the variants of the present multi-frequency vibrational GA and PSO were efficient algorithms, since they successfully avoided all local optima within relatively short optimization cycles

Minimum-Fuel Low-Thrust Trajectory Optimization Via a Direct Adaptive Evolutionary Approach

Space missions with low-thrust propulsion systems are of appreciable interest to space agencies because of their practicality due to higher specific impulses. This research proposes a technique to the solution of minimum-fuel non-coplanar orbit transfer problem. A direct adaptive method via Fitness Landscape Analysis (FLA) is coupled with a constrained evolutionary technique to explore the solution space for designing low-thrust orbit transfer trajectories. Taking advantage of the solution for multi-impulse orbit transfer problem, and parameterization of thrust vector, the orbital maneuver is transformed into a constrained continuous optimization problem. A constrained Estimation of Distribution Algorithms (EDA) is utilized to discover optimal transfer trajectories, while maintaining feasibility of the solutions. The low-thrust trajectory optimization problem is characterized via three parameters, referred to as problem identifiers, and the dispersion metric is utilized for analyzing the complexity of the solution domain. Two adaptive operators including the kernel density and outlier detection distance threshold within the framework of the employed EDA are developed, which work based on the landscape feature of the orbit transfer problem. Simulations are proposed to validate the efficacy of the proposed methodology in comparison to the non-adaptive approach. Results indicate that the adaptive approach possesses more feasibility ratio and higher optimality of the obtained solutions.BEAZ Bizkaia, 3/12/DP/2021/00150; SPRI Group, Ekintzaile Program EK-00112-202

Adaptive Estimation of Distribution Algorithms for Low-Thrust Trajectory Optimization

A direct adaptive scheme is presented as an alternative approach for minimum-fuel low-thrust trajectory design in non-coplanar orbit transfers, utilizing fitness landscape analysis (FLA). Spacecraft dynamics is modeled with respect to modified equinoctial elements, considering $J_2$ orbital perturbations. Taking into account the timings of thrust arcs, the discretization nodes for thrust profile, and the solution of multi-impulse orbit transfer, a constrained continuous optimization problem is formed for low-thrust orbital maneuver. An adaptive method within the framework of Estimation of Distribution Algorithms (EDAs) is proposed, which aims at conserving feasibility of the solutions within the search process. Several problem identifiers for low-thrust trajectory optimization are introduced, and the complexity of the solution domain is analyzed by evaluating the landscape feature of the search space via FLA. Two adaptive operators are proposed, which control the search process based on the need for exploration and exploitation of the search domain to achieve optimal transfers. The adaptive operators are implemented in the presented EDA and several perturbed and non-perturbed orbit transfer problems are solved. Results confirm the effectiveness and reliability of the proposed approach in finding optimal low-thrust transfer trajectories.BEAZ Bizkaia, 3/12/DP/2021/00150; SPRI Group, Ekintzaile Program EK-00112-202

hp-HGS strategy for inverse 3D DC resistivity logging measurement simulations

In this paper we present a twin adaptive strategy hp-HGS for solving inverse problems related to 3D DC borehole resistivity measurement simulations. The term "simulation of measurements" is widely used by the geophysical community. A quantity of interest, voltage, is measured at a receiver electrode located in the logging instrument. We use the self-adaptive goal-oriented hp-Finite Element Method (hp-FEM) computer simulations of the process of measurements in deviated wells (when the angle between the borehole and formation layers are < 90 deg). We also employ the hierarchical genetic search (HGS) algorithm to solve the inverse problem. Each individual in the population represents a single configuration of the formation layers. The evaluation of the individual is performed by solving the direct problem by means of the hp-FEM algorithm and by comparison with measured logging curve. We conclude the paper with some discussion on the parallelization of the algorithm. © 2012 Published by Elsevier Ltd

Firefly algorithm for polynomial Bézier surface parameterization

A classical issue in many applied fields is to obtain an approximating surface to a given set of data points. This problem arises in Computer-Aided Design and Manufacturing (CAD/CAM), virtual reality, medical imaging, computer graphics, computer animation, and many others. Very often, the preferred approximating surface is polynomial, usually described in parametric form. This leads to the problem of determining suitable parametric values for the data points, the so-called surface parameterization. In real-world settings, data points are generally irregularly sampled and subjected to measurement noise, leading to a very difficult nonlinear continuous optimization problem, unsolvable with standard optimization techniques. This paper solves the parameterization problem for polynomial Bézier surfaces by applying the firefly algorithm, a powerful nature-inspired metaheuristic algorithm introduced recently to address difficult optimization problems. The method has been successfully applied to some illustrative examples of open and closed surfaces, including shapes with singularities. Our results show that the method performs very well, being able to yield the best approximating surface with a high degree of accuracy