Erkki Laitinen

Radio coverage optimization with genetic algorithms

Cellular network operators are dealing with complex problems when planning the network operation. In order to automate the planning process, the development of simulation and optimization tools are under research. In this paper genetic algorithms with three different approaches are studied in order to optimize the base station sites. This research shows that a proper approach in developing the individual structure and fitness function has crucial importance in solving practical base station siting problems with genetic algorithms.

Optimisation problems for control of distributed resources

We consider a two-level optimisation problem of resource allocation in communication networks, which is based on profit maximisation of the network subject to capacity constraints. The cost function of the upper level problem involves a sum of non-differentiable functions whose values are computed algorithmically. The corresponding solution methods utilise duality theory and decomposition technique for optimisation problems.

Asynchronous domain decomposition methods for continuous casting problem

Two asynchronous domain decomposition methods (which appear to be a two-stage Schwarz alternating algorithms) to solve the finite difference schemes approximating dynamic continuous casting problem are theoretically and numerically studied. Fully implicit and semi-implicit (implicit for the diffusion operator while explicit for the nonlinear convective term) finite difference schemes are considered. Unique solvability of the finite difference schemes as well as a monotone dependence of the solution on the right-hand side (the so-called comparison theorem) are proved. Geometric rate of convergence for the iterative methods is investigated, the comparison theorem being the main tool of this study. Numerical results are included and analyzed.

Iterative Solution Methods for Large-Scale Constrained Saddle-Point Problems

Iterative solution methods for a class of finite-dimensional constrained saddle point problems are developed. These problems arise if variational inequalities and minimization problems are solved with the help of mixed finite element statements involving primal and dual variables. In the paper, we suggest several new approaches to the construction of saddle point problems and present convergence results for the iteration methods. Numerical results confirm the theoretical analysis.

Explicit algorithms to solve a class of state constrained parabolic optimal control problems

Abstract We consider an optimal control problem of a system governed by a linear parabolic equation with the following features: control is distributed, observation is either distributed or final, there are constraints on the state function and on its time derivative. Iterative solution methods are proposed and investigated for the finite difference approximations of these optimal control problems. Due to explicit in time approximation of the state equation and the appropriate choice of the preconditioners in the iterative methods, the implementation of all constructed methods is carried out by explicit formulae. Computational experiments confirm the theoretical results.

Iterative methods and parallel solution of the dam problem

Abstract A free boundary problem of fluid flow in the porous medium is considered. A finite difference scheme is constructed and written in the form of the inclusion for the sum of several multi-valued operators. The study of this mesh scheme and iterative algorithms of its numerical solution is performed. Solution of the mesh problem by Gauss–Seidel and by Schwarz alternating methods was executed. The numerical results are reported which confirm the theoretical results.

Easily implementable iterative methods for variational inequalities with nonlinear diffusion–convection operator and constraints to the gradient of solution

Abstract New iterative solution methods are proposed for the finite element approximation of a class of variational inequalities with nonlinear diffusion-convection operator and constraints to the gradient of solution. Implementation of every iteration of these methods reduces to the solution of a system of linear equations and a set of two-dimensional minimization problems. Convergence is proved by the application of a general result on the convergence of the iterative methods for a nonlinear constrained saddle point problem.

Optimization of GoS of cellular network

The network should operate as effectively as possible with a good GoS. This is possible only with a very accurate network planning process. In this paper we consider network planning and more precisely the steps of coverage and capacity planning. We show that the optimization of these steps is possible simultaneously and quite in an automatic way.

Application of the conditional gradient method to resource allocation in wireless networks

We propose a new two-level iterative method for solution of a general problem of optimal allocation of a homogeneous resource (bandwidth) in a wireless communication network. It is divided into service zones (clusters) and the network manager can buy external volumes of this resource. This approach leads to a convex optimization problem, which is solved with a dual Lagrangian method, where calculation of the cost function value decomposes into a system of independent zonal optimization problems. Each of them is treated as a market equilibrium problem. This optimization problem is solved with conditional gradient method for different information exchange schemes for participants. Besides, we suggest several ways to adjust the basic problemto the case of moving nodes. We give some results of numerical experiments on the proposed method which confirm its preference over the previous ones.

Ant stigmergy on the grid: optimizing the cooling process in continuous steel casting

The paper presents a new distributed metaheuristic algorithm in an optimal control problem related to the cooling process in the continuous casting of steel. The optimization task is to tune 18 coolant flows in the caster secondary cooling system to achieve the target surface temperatures along the slab. Sequential search algorithms are proved inefficient for this problem because they take too much time to compute an appropriate solution. For this reason a new distributed search algorithm based on stigmergy perceived in ant colony was developed. The algorithm was run on the grid that allows us to solve this optimization problem in much shorter time. As a matter of fact, the computation time can be decreased from half a day to a few hours without any decrease in the solution quality