Adam Zielonka

Solution of the inverse heat conduction problem by using the ABC algorithm

In this paper, a numerical method of solving the inverse heat conduction problem based on the respectively new tool for combinational optimization, named the Artificial Bee Colony algorithm (ABC), is presented. In the first step, the direct heat conduction problem, associated to the considered inverse heat conduction problem, is solved by using the finite difference method. In the second step, the proper functional, based on the least squares method, is minimized by using the ABC algorithm, giving the solution of the considered problem. An example illustrating the precision and effectiveness of the method is also shown. The proposed approach is original and promising.

Determination of Optimal Parameters for the Immune Algorithm Used for Solving Inverse Heat Conduction Problems with and without a Phase Change

In this article the inverse heat conduction problem and the inverse Stefan problem with the third kind of boundary condition are solved by applying the immune algorithm. This method has been introduced in recent years and belongs to the group of optimization algorithms inspired by natural processes. In this case the applied algorithm is based on the rules of immune system functioning in vertebrate bodies. It is used for minimizing a functional playing a crucial role in the solution of the problem posed. The algorithm considered is investigated with respect to the parameters which should be chosen in order to provide the most efficient algorithm performance.

Comparison of the Adomian decomposition method and the variational iteration method in solving the moving boundary problem

In this paper, a comparison between two methods: the Adomian decomposition method and the variational iteration method, used for solving the moving boundary problem, is presented. Both of the methods consist in constructing the appropriate iterative or recurrence formulas, on the basis of the equation considered and additional conditions, enabling one to determine the successive elements of a series or sequence approximating the function sought. The precision and speed of convergence of the procedures compared are verified with an example.

A new application of He's variational iteration method for the solution of the one-phase Stefan problem

In this paper, we will use the variational iteration method to find an approximate solution of a one-phase Stefan problem. This problem consists in finding the distribution of temperature in the domain and the position of a moving interface. The problem under consideration is at first approximated with a system of differential equations in a domain with known boundary, and next, the system constructed in this way is solved by the variational iteration method. The validity of the approach is verified by comparing the results obtained with an analytical solution.

Comparison of ABC and ACO algorithms applied for solving the inverse heat conduction problem

In this paper we present the comparison of numerical methods applied for solving the inverse heat conduction problem in which two algorithms of swarm intelligence are used: Artificial Bee Colony algorithm (ABC) and Ant Colony Optimization algorithm (ACO). Both algorithms belong to the group of algorithms inspired by the behavior of swarms of insects and they are applied for minimizing the proper functional representing the crucial part of the method used for solving the inverse heat conduction problems. Methods applying the respective algorithms are compared with regard to their velocity and precision of the received results.

Using the swarm intelligence algorithms in solution of the two-dimensional inverse Stefan problem

In the paper a procedure for solving the two-dimensional inverse Stefan problem is presented. In considered problem the heat transfer coefficient is identified with the aid of known measurements of temperature in selected points of the region as the additional information. Direct Stefan problem is solved by using the alternating phase truncation method. Goal of the paper is to compare two swarm intelligence algorithms-the Ant Colony Optimization algorithm and the Artificial Bee Colony algorithm-applied for minimizing a functional expressing the error of approximate solution.

Using the Artificial Bee Colony Algorithm for Determining the Heat Transfer Coefficient

In this paper we present an application of the Artificial Bee Colony (ABC) algorithm for solving the inverse heat conduction problem, consisting in determining the state function and some of the boundary conditions. The ABC algorithm belongs to the group of swarm intelligence algorithms and is inspired by the technique of searching for the nectar around the hive by the colony of bees. We propose to use this algorithm for minimizing the proper functional, which allows to reconstruct the value of heat transfer coefficient in the successive cooling zones.

Experimental Verification of Selected Artificial Intelligence Algorithms Used for Solving the Inverse Stefan Problem

The article presents a comparative study of three procedures applied for solving the inverse Stefan problem. The investigated problem consists of reconstruction of the unknown boundary condition on the basis of measurement data, and the procedures of solution differ in the way of minimizing the proper functional—in each approach considered, one of three artificial intelligence algorithms (Ant Colony Optimization, Artificial Bee Colony, and Harmony Search) is used. Methods applying the respective algorithms are compared with regard to their velocity and the precision of results.

Application of the Swarm Intelligence Algorithm for Investigating the Inverse Continuous Casting Problem

In the paper a proposal of procedure for solving the inverse problem of continuous casting is presented. The proposed approach consists in applying the swarm intelligence algorithm imitating the behavior of ants for minimizing an appropriate functional which enables to determine the unknown cooling conditions of the process.

Inverse Continuous Casting Problem Solved by Applying the Artificial Bee Colony Algorithm

The paper presents an application of the Artificial Bee Colony algorithm in solving the inverse continuous casting problem consisted in reconstruction of selected parameters characterizing the cooling conditions in crystallizer and in secondary cooling zone. In presented approach we propose to use the bee algorithm for minimization of appropriate functional representing the crucial part of the method.