Martin Schütz

Intelligent Mutation Rate Control in Canonical Genetic Algorithms

The role of the mutation rate in canonical genetic algorithms is investigated by comparing a constant setting, a deterministically varying, time-dependent mutation rate schedule, and a self-adaptation mechanism for individual mutation rates following the principle of self-adaptation as used in evolution strategies. The power of the self-adaptation mechanism is illustrated by a time-varying optimization problem, where mutation rates have to adapt continuously in order to follow the optimum. The strengths of the proposed deterministic schedule and the self-adaptation method are demonstrated by a comparison of their performance on difficult combinatorial optimization problems (multiple knapsack, maximum cut and maximum independent set in graphs). Both methods are shown to perform significantly better than the canonical genetic algorithm, and the deterministic schedule yields the best results of all control mechanisms compared.

Design of Graph-Based Evolutionary Algorithms: A Case Study for Chemical Process Networks

This paper describes the adaptation of evolutionary algorithms (EAs) to the structural optimization of chemical engineering plants, using rigorous process simulation combined with realistic costing procedures to calculate target function values. To represent chemical engineering plants, a network representation with typed vertices and variable structure will be introduced. For this representation, we introduce a technique on how to create problem specific search operators and apply them in stochastic optimization procedures. The applicability of the approach is demonstrated by a reference example. The design of the algorithms will be oriented at the systematic framework of metricbased evolutionary algorithms (MBEAs). MBEAs are a special class of evolutionary algorithms, fulfilling certain guidelines for the design of search operators, whose benefits have been proven in theory and practice. MBEAs rely upon a suitable definition of a metric on the search space. The definition of a metric for the graph representation will be one of the main issues discussed in this paper. Although this article deals with the problem domain of chemical plant optimization, the algorithmic design can be easily transferred to similar network optimization problems. A useful distance measure for variable dimensionality search spaces is suggested.

Mixed-Integer Evolution Strategy for Chemical Plant Optimization with Simulators

The optimization of chemical engineering plants is still a challenging task. Economical evaluations of a process flowsheet using rigorous simulation models are very time consuming. Furthermore, many different types of parameters can be involved into the optimization procedure, resulting in highly restricted mixed-integer nonlinear objective functions.

A Comparative Study of a Penalty Function, a Repair Heuristic and Stochastic Operators with the Set-Covering Problem

In this paper we compare the effects of using various stochastic operators with the non-unicost set-covering problem. Four different crossover operators are compared to a repair heuristic which consists in transforming infeasible strings into feasible ones. These stochastic operators are incorporated in GENEsYs, the genetic algorithm we apply to problem instances of the set-covering problem we draw from well known test problems. GENEsYs uses a simple fitness function that has a graded penalty term to penalize infeasibly bred strings. The results are compared to a non GA-based algorithm based on the greedy technique. Our computational results are then compared, shedding some light on the effects of using different operators, a penalty function, and a repair heuristic on a highly constrained combinatorial optimization problem.

Evolutionary Heuristics for the Bin Packing Problem

In this paper we investigate the use of two evolutionary based heuristic to the bin packing problem. The intractability of this problem is a motivation for the pursuit of heuristics that produce approximate solutions. Unlike other evolutionary based heuristics used with optimization problems, ours do not use domain-specific knowledge and has no specialized genetic operators. It uses a straightforward fitness function to which a graded penalty term is added to penalize infeasible strings. The encoding of the problem makes use of strings that are of integer value. Strings do not represent permutations of the objects as is the case in most approaches to this problem. We use a different representation and give justifications for our choice. Several problem instances are used with a greedy heuristic and the evolutionary based algorithms. We compare the results and conclude with some observations, and suggestions on the use of evolutionary heuristics for combinatorial optimization problems.

Mixed integer evolution strategies for parameter optimization

Evolution strategies (ESs) are powerful probabilistic search and optimization algorithms gleaned from biological evolution theory. They have been successfully applied to a wide range of real world applications. The modern ESs are mainly designed for solving continuous parameter optimization problems. Their ability to adapt the parameters of the multivariate normal distribution used for mutation during the optimization run makes them well suited for this domain. In this article we describe and study mixed integer evolution strategies (MIES), which are natural extensions of ES for mixed integer optimization problems. MIES can deal with parameter vectors consisting not only of continuous variables but also with nominal discrete and integer variables. Following the design principles of the canonical evolution strategies, they use specialized mutation operators tailored for the aforementioned mixed parameter classes. For each type of variable, the choice of mutation operators is governed by a natural metric for this variable type, maximal entropy, and symmetry considerations. All distributions used for mutation can be controlled in their shape by means of scaling parameters, allowing self-adaptation to be implemented. After introducing and motivating the conceptual design of the MIES, we study the optimality of the self-adaptation of step sizes and mutation rates on a generalized (weighted) sphere model. Moreover, we prove global convergence of the MIES on a very general class of problems. The remainder of the article is devoted to performance studies on artificial landscapes (barrier functions and mixed integer NK landscapes), and a case study in the optimization of medical image analysis systems. In addition, we show that with proper constraint handling techniques, MIES can also be applied to classical mixed integer nonlinear programming problems.