Karin Zielinski

Parameter Study for Differential Evolution Using a Power Allocation Problem Including Interference Cancellation

The performance of evolutionary algorithms is strongly dependent on the setting of control parameters. Not only the convergence speed is influenced, but also if the optimum of a function is reached at all. For differential evolution premature convergence or even stagnation can occur due to certain parameter settings. In this paper a parameter study for differential evolution is conducted. As basis for the examination a real-world problem is employed that consists of optimizing the power allocation for a CDMA (code division multiple access) system. For the CDMA system interference cancellation methods are applied as the detection performance is significantly degraded by multi-user interference. The convergence of the interference cancellation method establishes a constraint for the single-objective optimization problem. Optimization results for both parallel and successive interference cancellation are given. The findings of the parameter study are compared with results from literature, and recommendations concerning settings of DE control parameters are given.

Constrained Single-Objective Optimization Using Differential Evolution

Differential evolution (DE) is a rather new evolutionary optimization algorithm that has been shown to be fast and simple for unconstrained single-objective optimization problems. In this work DE is employed for the constrained optimization test suite of the special session on constrained real parameter optimization at CEC06. Constraints are handled using a modified selection procedure that does not require additional parameters. For the control parameters of the DE algorithm the best found settings from another examination were used so that almost no parameter tuning was necessary. Most of the test functions are successfully and reliably optimized. Difficulties arise mainly from a high number of equality constraints.

Optimization of Power Allocation for Interference Cancellation With Particle Swarm Optimization

In code division multiple access (CDMA) systems a significant degradation in detection performance due to multiuser interference can be avoided by the utilization of interference cancellation methods. Further enhancement can be obtained by optimizing the power allocation of the users. The resulting constrained single-objective optimization problem is solved here by means of particle swarm optimization (PSO). It is shown that the maximum number of users for a CDMA system can be increased significantly if an optimized power profile is employed. Furthermore, an extensive study of PSO control parameter settings using three different neighborhood topologies is performed on the basis of the power allocation problem, and two constraint-handling techniques are evaluated. Results from the parameter study are compared with examinations from the literature. It is shown that the von-Neumann neighborhood topology performs consistently better than gbest and lbest. However, strong interaction effects and conflicting recommendations for parameter settings are found that emphasize the need for adaptive approaches.

Stopping Criteria for Differential Evolution in Constrained Single-Objective Optimization

Because real-world problems generally include computationally expensive objective and constraint functions, an optimization run should be terminated as soon as convergence to the optimum has been obtained. However, detection of this condition is not a trivial task. Because the global optimum is usually unknown, distance measures cannot be applied for this purpose. Stopping after a predefined number of function evaluations has not only the disadvantage that trial-and-error methods have to be applied for determining a suitable number of function evaluations, but the number of function evaluations at which convergence occurs may also be subject to large fluctuations due to the randomness involved in evolutionary algorithms. Therefore, stopping criteria should be applied which react adaptively to the state of the optimization run. In this work several stopping criteria are introduced that consider the improvement, movement or distribution of population members to derive a suitable time for terminating the Differential Evolution algorithm. Their application for other evolutionary algorithms is also discussed. Based on an extensive test set the criteria are evaluated using Differential Evolution, and it is shown that a distribution-based criterion considering objective space yields the best results concerning the convergence rate as well as the additional computational effort.

Constrained Single-Objective Optimization Using Particle Swarm Optimization

Particle Swarm Optimization (PSO) is an optimization method that is derived from the behavior of social groups like bird flocks or fish schools. In this work PSO is used for the optimization of the constrained test suite of the special session on constrained real parameter optimization at CEC06. Constraint-handling is done by modifying the procedure for determining personal and neighborhood best particles. No additional parameters are needed for the handling of constraints. Numerical results are presented, and statements are given about which types of functions have been successfully optimized and which features present difficulties.

Differential evolution with adaptive parameter setting for multi-objective optimization

Control parameter settings influence the convergence probability and convergence speed of evolutionary algorithms but it is often not obvious how to choose them. In this work an adaptive approach for setting the control parameters of a multi-objective differential evolution algorithm is presented. The adaptive approach is based on methods from design of experiments, so it is able to detect significant performance differences of individual parameters as well as interaction effects between parameters. It is evaluated based on 13 test functions and several performance measures.

Adaptive parameter setting for a multi-objective particle swarm optimization algorithm

To avoid the effort associated with choosing control parameter settings, an adaptive approach for parameter setting of a multi-objective particle swarm optimization algorithm is presented in this work. The adaptive parameter control relies on methods from design of experiments which are able to detect significant performance variations of parameter settings. Furthermore, interaction effects of different parameters can be discovered. The adaptive control is applied to the parameters which are incorporated in the update equations of PSO, so the movement of particles is adapted based on feedback about successes during the search. The adaptive approach is evaluated using 13 test functions and several performance measures.

Comparison of Adaptive Approaches for Differential Evolution

The evaluation of optimization algorithms and especially the analysis of adaptive variants is often complicated because several features are modified concurrently. For Differential Evolution these features may be adaptation of parameters, adjustment of the strategy and addition of local search or other special operators. Thus, it is difficult to analyze which of these procedures is actually responsible for changes in the performance. Therefore, in this work several adaptive algorithms are studied in-depth by monitoring performance changes for individual components of these algorithms to examine their effectiveness. The results show among others that the performance can be significantly improved by employing strategy control.

Variants of Differential Evolution for Multi-Objective Optimization

In multi-objective optimization not only fast convergence is important, but it is also necessary to keep enough diversity so that the whole Pareto-optimal front can be found. In this work four variants of differential evolution are examined that differ in the selection scheme and in the assignment of crowding distance. The assumption is checked that the variants differ in convergence speed and amount of diversity. The performance is shown for 1000 consecutive generations, so that different behavior over time can be detected

Comparison of Differential Evolution and Particle Swarm Optimization for the optimization of a PI cascade control

PI cascade controllers are often used in control applications due to their simplicity. Because of uncertain and varying system parameters, a robust control is needed. However, known methods to generate robust controllers often lead to complicated control structures. Unfortunately, there are no analytical solutions to generate robust controllers with a fixed simple structure like the PI cascade. Therefore, easy-to-use optimization algorithms are needed. In this paper it is shown that for a practical approach using recommended parameter settings from literature both Differential Evolution and Particle Swarm Optimization can be used for the optimization of a PI cascade control. A performance comparison shows similar results, so both of them are useful to field engineers who apply optimization algorithms to real-world problems and are often inexperienced concerning optimization.