Janez Grad

A computer implementation of the Push-and-Pull algorithm and its computational comparison with LP simplex method

The simplex algorithm requires artificial variables for solving linear programs, which lack primal feasibility at the origin point. We present a new general-purpose solution algorithm, called Push-and-Pull, which obviates the use of artificial variables. The algorithm consists of preliminaries for setting up the initialization followed by two main phases. The Push Phase develops a basic variable set (BVS) which may or may not be feasible. Unlike simplex and dual simplex, this approach starts with an incomplete BVS initially, and then variables are brought into the basis one by one. If the BVS is complete, but the optimality condition is not satisfied, then Push Phase pushes until this condition is satisfied, using the rules similar to the ordinary simplex. Since the proposed strategic solution process pushes towards an optimal solution, it may generate an infeasible BVS. The Pull Phase pulls the solution back to feasibility using pivoting rules similar to the dual simplex method. All phases use the usual Gauss pivoting row operation and it is shown to terminate successfully or indicates unboundedness or infeasibility of the problem. A computer implementation, which enables the user to run either Push-and-Pull or ordinary simplex algorithms, is provided. The fully coded version of the algorithm is available from the authors upon request. A comparison analysis to test the efficiency of Push-and-Pull algorithm comparing to ordinary simplex is accomplished. Illustrative numerical examples are also presented.

An algorithm for simplex tableau reduction: the push-to-pull solution strategy

The simplex algorithm requires artificial variables for solving linear programs, which lack primal feasibility at the origin point. We present a new general-purpose solution algorithm, called push-to-pull, which obviates the use of artificial variables. The algorithm consists of preliminaries for setting up the initialization followed by two main phases. The push phase develops a basic variable set (BVS) which may or may not be feasible. Unlike simplex and dual simplex, this approach starts with an incomplete BVS initially, and then variables are brought into the basis one by one. If the BVS is complete, but the optimality condition is not satisfied, then push phase pushes until this condition is satisfied, using the rules similar to the ordinary simplex. Since the proposed strategic solution process pushes towards an optimal solution, it may generate an infeasible BVS. The pull phase pulls the solution back to feasibility using pivoting rules similar to the dual simplex method. All phases use the usual Gauss pivoting row operation and it is shown to terminate successfully or indicates unboundedness or infeasibility of the problem. A computer implementation, which further reduces the size of simplex tableau to the dimensions of the original decision variables, is provided. This enhances considerably the storage space, and the computational complexity of the proposed solution algorithm. Illustrative numerical examples are also presented.

Predicting species identity of bumblebees through analysis of flight buzzing sounds

Abstract We present a study of buzzing sounds of several common species of bumblebees, with the focus on automatic classification of bumblebee species and types. Such classification is useful for bumblebee monitoring, which is important in view of evaluating the quality of their living environment and protecting the biodiversity of these important pollinators. We analysed natural buzzing frequencies for queens and workers of 12 species. In addition, we analysed changes in buzzing of Bombus hypnorum worker for different types of behaviour. We developed a bumblebee classification application using machine learning algorithms. We extracted audio features from sound recordings using a large feature library. We used the best features to train a classification model, with Random Forest proving to be the best training algorithm on the testing set of samples. The web and mobile application also allows expert users to upload new recordings that can be later used to improve the classification model and expand it to include more species.