Parameter Control of Genetic Algorithms by Learning and Simulation of Bayesian Networks — A Case Study for the Optimal Ordering of Tables

Parameter setting for evolutionary algorithms is still an important issue in evolutionary computation. There are two main approaches to parameter setting: parameter tuning and parameter control. In this paper, we introduce self-adaptive parameter control of a genetic algorithm based on Bayesian network learning and simulation. The nodes of this Bayesian network are genetic algorithm parameters to be controlled. Its structure captures probabilistic conditional (in)dependence relationships between the parameters. They are learned from the best individuals, i.e., the best configurations of the genetic algorithm. Individuals are evaluated by running the genetic algorithm for the respective parameter configuration. Since all these runs are time-consuming tasks, each genetic algorithm uses a small-sized population and is stopped before convergence. In this way promising individuals should not be lost. Experiments with an optimal search problem for simultaneous row and column orderings yield the same optima as state-of-the-art methods but with a sharp reduction in computational time. Moreover, our approach can cope with as yet unsolved high-dimensional problems.     

Natural killer or T-lymphocyte cells: Which is the best immune therapeutic agent for cancer? An optimal control approach

Therapeutic vaccines are being developed as a promising new approach to treatment for cancer patients. There are still many unanswered questions about which kind of therapeutic vaccines are the best for the cancer treatments? In this paper we consider a mathematical model, in the form of a system of ordinary differential equations (ODE), this system is an example from a class of mathematical models for immunotherapy of the tumor that were derived from a biologically validated model by Lisette G. de Pillis. The problem how to schedule a variable amount of which vaccines to achieve a maximum reduction in the primary cancer volume is consider as an optimal control problem and it is shown that optimal control is quadratic with 0 denoting a trajectory corresponding to no treatment and 1 a trajectory with treatment at maximum dose along that all therapeutics are being exhausted. The ODE system dynamics characterized by locating equilibrium points and stability properties are determined by using appropriate Lyapunov functions. Especially we attend a parametric sensitivity analysis, which indicates the dependency of the optimal solution with respect to disturbances in model parameters.