A Tent Marine Predators Algorithm with Estimation Distribution Algorithm and Gaussian Random Walk for Continuous Optimization Problems

The marine predators algorithm (MPA) is a novel population-based optimization method that has been widely used in real-world optimization applications. However, MPA can easily fall into a local optimum because of the lack of population diversity in the late stage of optimization. To overcome this shortcoming, this paper proposes an MPA variant with a hybrid estimation distribution algorithm (EDA) and a Gaussian random walk strategy, namely, HEGMPA. The initial population is constructed using cubic mapping to enhance the diversity of individuals in the population. Then, EDA is adapted into MPA to modify the evolutionary direction using the population distribution information, thus improving the convergence performance of the algorithm. In addition, a Gaussian random walk strategy with medium solution is used to help the algorithm get rid of stagnation. The proposed algorithm is verified by simulation using the CEC2014 test suite. Simulation results show that the performance of HEGMPA is more competitive than other comparative algorithms, with significant improvements in terms of convergence accuracy and convergence speed.

Optimization Algorithms for Aircraft Preliminary Sizing and Cabin Design

As new aircraft are being designed, optimization of the design parameters becomes necessary to decrease fuel costs and emissions and maximize profits. As opposed to trial-and-error where a design may go through several rounds of testing to improve efficiency, optimization algorithms can save time and effort when implemented properly. Optimization algorithms are of two types: stochastic and deterministic. The stochastic methods used are: Random Monte Carlo, Gaussian Random Walk, and Simulated Annealing. The deterministic method examined is the method of Orthogonal Steepest Descent (OSD). Orthogonal Steepest Descent seems to be the fastest method which is also quite accurate. The next fastest method is Simulated Annealing. The Random Monte Carlo method is less precise by nature, and experiences a greater error and time elapsed because it requires many more iterations to arrive at reasonably small error.

Random Walk of Foraging

The model of vibration driven random walk is adapted to description of foraging performed by simple organisms. Stochastic properties of foraging are described by the Gaussian random number generator, while the attraction of food is represented by a deterministic signal that directs walkers from surroundings to the food. This attraction causes transition from the Gaussian random walk to the Levy flight.

A point-based Bayesian hierarchical model to predict the outcome of tennis matches

A well-established assumption in tennis is that point outcomes on each player’s serve in a match are independent and identically distributed (iid). With this assumption, it is enough to specify the serve probabilities for both players to derive a wide variety of event distributions, such as the expected winner and number of sets, and number of games. However, models using this assumption, which we will refer to as “point-based”, have typically performed worse than other models in the literature at predicting the match winner. This paper presents a point-based Bayesian hierarchical model for predicting the outcome of tennis matches. The model predicts the probability of winning a point on serve given surface, tournament and match date. Each player is given a serve and return skill which is assumed to follow a Gaussian random walk over time. In addition, each player’s skill varies by surface, and tournaments are given tournament-specific intercepts. When evaluated on the ATP’s 2014 season, the model outperforms other point-based models, predicting match outcomes with greater accuracy (68.8% vs. 66.3%) and lower log loss (0.592 vs. 0.641). The results are competitive with approaches modelling the match outcome directly, demonstrating the forecasting potential of the point-based modelling approach.

Some Improvements on a General Particle Filter Based Bayesian Approach for Extracting Bearing Fault Features

In our previous work, a general particle filter based Bayesian method was proposed to derive the graphical relationship between wavelet parameters, including center frequency and bandwidth, and to posteriorly find optimal wavelet parameters so as to extract bearing fault features. In this work, some improvements on the previous Bayesian method are proposed. First, the previous Bayesian method strongly depended on an initial uniform distribution to generate random particles. Here, a random particle represented a potential solution to optimize wavelet parameters. Once the random particles were obtained, the previous Bayesian method could not generate new random particles. To solve this problem, this paper introduces Gaussian random walk to joint posterior probability density functions of wavelet parameters so that new random particles can be generated from Gaussian random walk to improve optimization of wavelet parameters. Besides, Gaussian random walk is automatically initialized by the famous fast kurtogram. Second, the previous work used the random particles generated from the initial uniform distribution to generate measurements. Because the random particles used in the previous work were fixed, the measurements were also fixed. To solve this problem, the first measurement used in this paper is provided by the fast kurtogram, and its linear extrapolations are used to generate monotonically increasing measurements. With the monotonically increasing measurements, optimization of wavelet parameters is further improved. At last, because Gaussian random walk is able to generate new random particles from joint posterior probability density functions of wavelet parameters, the number of the random particles is not necessarily set to a high value that was used in the previous work. Two instance studies were investigated to illustrate how the Gaussian random walk based Bayesian method works. Comparisons with the famous fast kurtogram were conducted to demonstrate that the Gaussian random walk based Bayesian method can better extract bearing fault features.

A stochastic rank ordered logit model for rating multi-competitor games and sports

Many games and sports, including races, involve outcomes in which competitors are rank ordered. In some sports, competitors may play in multiple events over long periods of time, and it is natural to assume that their abilities change over time. We propose a Bayesian state-space framework for rank ordered logit models to rate competitor abilities over time from the results of multi-competitor games. Our approach assumes competitors’ performances follow independent extreme value distributions, with each competitor’s ability evolving over time as a Gaussian random walk. The model accounts for the possibility of ties, an occurrence that is not atypical in races in which some of the competitors may not finish and therefore tie for last place. Inference can be performed through Markov chain Monte Carlo (MCMC) simulation from the posterior distribution. We also develop a filtering algorithm that is an approximation to the full Bayesian computations. The approximate Bayesian filter can be used for updating competitor abilities on an ongoing basis. We demonstrate our approach to measuring abilities of 268 women from the results of women’s Alpine downhill skiing competitions recorded over the period 2002–2013.

Joint Ordering and Pricing Decisions for New Repeat-Purchase Products

This paper studies ordering and pricing problems for new repeat-purchase products. We incorporate the repeat-purchase rate and price effects into the Bass model to characterize the demand pattern. We consider two decision models: (1) two-stage decision model, in which the sales division chooses a price to maximize the gross profit and the purchasing division determines an optimal ordering decision to minimize the total cost under a given demand subsequently, and (2) joint decision model, in which the firm makes ordering and pricing decisions simultaneously to maximize the profit. We combine the generalized Bass model with dynamic lot sizing model to formulate the joint decision model. We apply both models to a specific imported food provided by an online fresh produce retailer in Central China, solve them by Gaussian Random-Walk and Wagner-Whitin based algorithms, and observe three results. First, joint pricing and ordering decisions bring more significant profits than making pricing and ordering decisions sequentially. Second, a great initiative in adoption significantly increases price premium and profit. Finally, the optimal price shows a U-shape (i.e., decreases first and increases later) relationship and the profit increases gradually with the repeat-purchase rate when it is still not very high.