Claus Hillermeier

An Application of Genetic Algorithms and Neural Networks to Scheduling Power Generating Systems

This paper presents an effective strategy to schedule fossilfuel power plant systems with so-called power-heat coupling. Due to the simultaneous production of electricity, heat and steam such systems reach a higher efficiency than pure electric power plants. The goal is to minimize the total costs for the production of the predicted load demand of the next day. We employ a genetic algorithm to determine the unit commitment, while the economically optimal load distribution among the operating units is performed by a conventional constraint optimization method. Our approach is based on exact thermodynamic simulations of the unit efficiency, taking into account the current plant state and environmental conditions. In order to make this high modeling precision available within short computation times we employ neural networks for the storage and interpolation of simulation data.

Routing optimization in corporate networks by evolutionary algorithms

The purpose of the research reported in this chapter is to meet the increasing and rapidly changing communication demands in a private telecommunication network. The goal is to improve the performance of a telecommunication system just by changes in its software components. The network topology and the trunk capacities are viewed as fixed parameters, because a change in these components is very expensive. The algorithm of how to use this network is stored in a routing table that consists of alternative paths between the nodes that are supposed to be connected. So the goal of the evolutionary algorithm is to find a routing table that increases the performance of the network by reducing the probability of end-to-end-blocking. The investigated non-hierarchical networks require a fixed alternate routing (FAR) with sequential office control (SOC). The chapter presents a new approach based on evolutionary algorithms to solve this problem.

Optimization of Power Plant Design: Stochastic and Adaptive Solution Concepts

Optimizing the design of industrial plants requires making optimal structural decisions (concerning the selection and arrangement of various components) as well as optimizing all continuous design variables. This paper presents genetic and stochastic optimization strategies which are based on a representation of the plant by means of a modified decision tree. By taking into account hierarchical dependencies of decisions this representation guarantees that designs generated by mutation operators automatically comply with an important class of constraints. The method is explained and its potential is demonstrated with the example of an important industrial application problem: The design optimization of feed-water heater strings in fossil-fueled power plants. For the treatment of the structural and continuous design variables two strategies have been implemented and tested. The first approach considers structural decisions as the primary problem, which is solved by means of a Metropolis algorithm, and regards the optimization of the continuous variables as a subproblem, which is solved by Sequential Quadratic Programming for each generated plant structure. The second strategy is an evolutionary one-level algorithm which simultaneously optimizes both types of variables. In the design problem which is investigated here, the one-level Evolutionary computation algorithm performs slightly better than the hierarchical method. This result is explained by analyzing the objective function.

The Manifold of Stationary Points

The further examinations presuppose that the feasible setRis defined by m equality constraints h i (x) = 0, i = 1,…, m. In this case the necessary condition — according to Kuhn and Tucker — for Pareto optimal points has the form of a system of equations. The set of all points which fulfill this condition can therefore be interpreted as a zero manifold in an extended variable space, the product space formed by the actual variables x, the Lagrange multipliers λ and the weight vectors α. On certain conditions this zero manifold is a (k− 1)-dimensional differentiable manifold.

Principles and Methods of Vector Optimization

Let an operation point or a plant design be characterized by n real-valued variables x 1,…,x n . The variables can be combined to a vector x := (x 1,…, x n )T ∈ ℝn and are supposed to vary freely within a feasible set R ⊆ ℝn.

Vector Optimization in Industrial Applications

Application problems of vector optimization that arise in the science of engineering are documented in literature in great numbers (see e.g. [STADLER, 1988] and [DAs, 1997]). Instead of listing these quotations here again, we will present the multiobjective problems which originate in optimization applications within the configuration of industrial systems. Subsequently we will discuss in detail two multiobjective problems which arise in the concrete practice of the plant manufacturer SIEMENS.

The Connection with Scalar-Valued Optimization

A necessary condition for Pareto optimality given by Kuhn and Tucker builds the bridge between vector optimization and scalar-valued optimization: On the assumption that the constraints meet a certain constraint qualification, necessarily for a Pareto optimal point x* there exists a convex combination of the objectives \({g_\alpha }(x): = \sum _{i = 1}^k{\alpha _i}{f_i}(x)\), so that x* is a Karush-Kuhn-Tucker point of the scalar-valued function g α.