Volker Nissen

Solving the quadratic assignment problem with clues from nature

This paper describes a new evolutionary approach to solving quadratic assignment problems. The proposed technique is based loosely on a class of search and optimization algorithms known as evolution strategies (ES). These methods are inspired by the mechanics of biological evolution and have been applied successfully to a variety of difficult problems, particularly in continuous optimization. The combinatorial variant of ES presented here performs very well on the given test problems as compared with the standard 2-Opt heuristic and results with simulated annealing and tabu search. Extensions for practical applications in factory layout are described.

On the robustness of population-based versus point-based optimization in the presence of noise

Practical optimization problems often require the evaluation of solutions through experimentation, stochastic simulation, sampling, or even interaction with the user. Thus, most practical problems involve noise. We address the robustness of population-based versus point-based optimization on a range of parameter optimization problems when noise is added to the deterministic objective function values. Population-based optimization is realized by a genetic algorithm and an evolution strategy. Point-based optimization is implemented as the classical Hooke-Jeeves pattern search strategy and threshold accepting as a modern local search technique. We investigate the performance of these optimization methods for varying levels of additive normally distributed fitness-independent noise and different sample sizes for evaluating individual solutions. Our results strongly favour population-based optimization, and the evolution strategy in particular.

Supply Chain Event Management

Viele Probleme, die im Rahmen von Supply Chain Management auftreten, lassen sich auf eine mangelnde unternehmensübergreifende Visibilität kritischer Logistikprozesse zurückführen. Da sich Störungen im Leistungserstellungsprozess niemals vollständig eliminieren lassen, müssen Planabweichungen in der Wertschöpfungskette zeitnah erkannt werden, um so zeitnah Gegensteuerungsmaßnahmen einleiten zu können. Dieser Problematik widmet sich das Supply Chain Event Management, welches die methodische Lücke zwischen der mittelbis langfristigen Supply Chain Planung und der operativen Prozessdurchführung zu schließen vermag.

A modification of threshold accepting and its application to the quadratic assignment problem

In this paper we propose a modification of the threshold accepting heuristic by Dueck and Scheuer. Instead of using discrete threshold values a threshold function similar to the cooling schedule of simulated annealing is used. Furthermore, the number of iterations during each step of the heuristic is a function of the current and the initial threshold value. Using this scheme, we investigate the trade-off between solution quality and convergence speed on different instances of the well known quadratic assignment problem. In a second set of experiments the results of a multistart-version of TA are compared with the results of unique long runs at identical CPU-requirements to identify the better optimization strategy. Since, generally, in the literature the number of starting solutions for QAP-heuristics appears to be chosen on a rather arbitrary basis, we also highlight how varying this number influences the TA-results.ZusammenfassungIm vorliegenden Beitrag wird eine Modifizierung der Threshold Accepting Heuristik von Dueck und Scheuer vorgeschlagen. Anstelle diskreter Schwellenwerte wird eine Schwellenwertfunktion verwendet, die vom Abkühlungsplan beim Simulated Annealing inspiriert ist. Desweiteren ist die Iterationszahl auf jeder Ebene des Verfahrens nunmehr eine Funktion des aktuellen sowie des Ausgangsschwellenwertes. Anhand dieses Vorgehensschemas untersuchen wir den Trade-off von Lösungsqualität und Konvergenzgeschwindigkeit bei verschiedenen Standardbeispielen des bekannten Quadratischen Zuordnungsproblems. Auch die Qualität und Zuverlässigkeit einer Multistart-Version kurzer TA-Läufe wird mit den Ergebnissen ausführlicher Läufe bei gleichen CPU-Zeiten verglichen, um Rückschlüsse auf die sinnvollere Optimierungsstrategie zu erhalten. In der Literatur verwenden unterschiedliche Autoren häufig sehr verschiedene Anzahlen zufälliger Startlösungen in ihren numerischen Experimenten. Wir untersuchen daher auch, wie sich eine Variation dieser Anzahl auf die TA-Ergebnisse auswirkt.

Combinations of simulation and Evolutionary Algorithms in management science and economics

Evolutionary Algorithms are robust search methods that mimic basic principles of evolution. We discuss different combinations of Evolutionary Algorithms and the versatile simulation method resulting in powerful tools not only for complex decision situations but explanatory models also. Realised and suggested applications from the domains of management and economics demonstrate the relevance of this approach. In a practical example three EA-variants produce better results than two conventional methods when optimising the decision variables of a stochastic inventory simulation. We show that EA are also more robust optimisers when only few simulations of each trial solution are performed. This characteristic may be used to reduce the generally higher CPU-requirements of population-based search methods like EA as opposed to point-based traditional optimisation techniques.

Supply Chain Management mit SAP

Kurzfassung Der Ausdruck Supply Chain Management (SCM) bezeichnet die betriebsübergreifende, meist systemunterstützte Planung, Abwicklung und Überwachung der Logistik. Insbesondere in produzierenden Unternehmen steht dieses Thema auf der Tagesordnung an oberster Stelle. Globaler Wettbewerb, immer kürzere Produktlebenszyklen und steigende Ansprüche der Kunden erfordern eine Optimierung der logistischen Prozesse. Ungenutzte Potenziale liegen vor allem in der Beschleunigung des Materialflusses, dem Abbau von Bestandsüberhängen, der Verbesserung der Transparenz logistischer Abläufe sowie in der Erhöhung der Lieferbereitschaft. Eine Schlüsselfunktion kommt dabei der Absatzplanung zu.

Optimization with Noisy Function Evaluations

In the optimization literature it is frequently assumed that the quality of solutions can be determined by calculating deterministic objective function values. Practical optimization problems, however, often require the evaluation of solutions through experimentation, stochastic simulation, sampling, or even interaction with the user. Thus, most practical problems involve noise. We empirically investigate the robustness of population-based versus point-based optimization methods on a range of parameter optimization problems when noise is added. Our results favor population-based optimization, and the evolution strategy in particular.

On Using Penalty Functions and Multicriteria Optimisation Techniques in Facility Layout

Constrained optimisation is a research field of great practical relevance. For facility layout problems zoning constraints are typical restrictions. This type of constraint is awkward to deal with using common measures like a tailored solution representation or problem-specific search operators, a repair algorithm or special decoding scheme. Penalty functions are frequently applied in such situations. The general understanding seems to be that well-chosen, graded penalties are better than harsh penalties. We compare different approaches to deal with zoning constraints, and find that laborious finetuning of penalty factors is unnecessary in our application, even when there are only few valid solutions. We also implement two multiobjective optimisation approaches where the minimisation of violated constraints becomes a second objective. One of them employs so called Paretoselection, the second a best-per-objective selection scheme. The results establish the superiority of the Pareto-selection scheme over the other, when finding an evenly distributed set of efficient (non-dominated) solutions is desired. Both multicriteria techniques are inferior to the other approaches, though, when one is primarily interested in a single valid and good solution.

An Overview of Evolutionary Algorithms in Management Applications

In this paper an evaluation of the current situation regarding Evolutionary Algorithms (EA) in management applications is given. While assembling as many references as possible, the overview is, of course, not complete, but should give a representative account of current focuses of research and practical applications. EA-references are divided in three major categories: practical applications in business, applications-oriented research (mainly at universities), and abstract standard operations research problems with relevance beyond the domain of management.

An Introduction to Evolutionary Algorithms

We discuss the mainstream directions of Evolutionary Algorithms (EA), a class of stochastic search and optimisation techniques with heuristic character. EA have recently attracted many researchers and practitioners, not only in the management domain, due to their applicability to very complex problems. In this paper, we describe, next to the standard forms of Genetic Algorithms, Genetic Programming, Evolution Strategies and Evolutionary Programming, also Learning Classifier Systems, and some other hybrid approaches that integrate different technologies. Our focus, however, is on Genetic Algorithms as the most prominent and diversified EA-type.