MULTI OBJECTIVE DECISION MAKING – SOLUTIONS FOR THE OPTIMIZATION OF MANUFACTURING PROCESSES

There is no doubt about the need of optimizing the factor of time in today’s production. Several optimization methods are in use. The optimization is often based on a single objective, e.g. the makespan. In practice, more than one time-related objectives are to be optimized. We focus on simulation based optimization of manufacturing processes. Therefore, control strategies are searched using several metaheuristic methods like Simulated Annealing, Genetic Algorithms, or Tabu Search and evaluated by running a simulation of the modeled manufacturing system repeatedly. Best results are proposed to be scheduled. The simulation yields in a big amount of data which is reduced to several time-related objectives like machine utilization, due date keeping, lead time, cycle time and others. Of course, these objectives have different dimensions and are contradictory in some cases. This makes the goal setting process very difficult. Several objectives have to be combined to a fitness value, which is used for optimization. Algorithms for combining the objectives are user-dependent, preferences need to be set, and interdependencies between different goals need to be detected. We present methods for interactive goal setting, dynamic objective observation, filtering of interdependencies between objectives and finding of fitness functions with consideration of user preferences. The normalization of different objectives allows the comparison between various dimensions and the detection of correlation between indifferent objectives. Relations between objectives are shown in correlation diagrams. Only competitive goals are used for the fitness and graphically presented during the optimization process (Petal Diagram and Modified Star Graph). Sometimes the hardest part of optimization can be solved using these methods. The basic theories will be shown and explained with the results of some optimized scheduling problems of our industry partners. INTRODUCTION The scheduling of manufacturing processes is one of the most important tasks of an enterprise. This is not only important for saving costs, but also for maintaning competitiveness in a more and more turbulent market. Today it is not enough to have a single objective for optimization of a flexible manufacturing system. Instead of this a set of objectives is needed, e.g. the makespan, throughput time, machine utilization or job lead time, which represent an objective vector. Though the theory of multi objective decision making (MODM) knows several kinds of hierarchies and dependencies between the single objectives, these are often unknown in a practical application. Because of that we have examined several methods for the representation of a large number of n-dimensional objective vectors. The purpose is to recognize the relations inside a real objective system. A further problem is, that the single components of a given objective system do not have the same value range. So it is difficult to compare different objective types, e.g. the makespan and the machine utilization. In general the subjective preferences of the objectives are described by weights. The higher the value of a weight, the more important the related objective. But this is only right in the case of the comparability of all components. The solution of this dilemma seems to be the well known normalization of objectives where the maximum of a component is related to 1 and its minimum to 0. This is possible after the optimization process was stopped and the set of vectors is enclosed. But during a running optimization the normalization is actually impossible, because we do not know the real maximum and minimum of a particular vector component. This means, we need a modified normalization method which is suitable for an interactive optimization system. OPTIMIZATION BY SIMULATION Unfortunately, most of the real scheduling problems are often NP-complete or NP-hard, so that they are not solvable by effective mathematical algorithms. In general the only way to optimize the schedule of a complex flexible manufacturing system is its simulation. Usually a model of the manufacturing system is created by using one of the available simulation systems. In this model you can easily change several parameters, e.g. input sequences, stock capacities or processing times. The simulation makes it possible to predict the influence of these parameter changes to the manufacturing process. If the simulation process is sufficiently rapid, a lot of variants of schedules can be tried during a short time period. Among these variants you can choose the one, which seems to be the best solution for using in the real manufacturing system. This is the principle of an optimization process which uses the simulation. Of course, the word “optimization” is not quite right and “improvement” fits better to this approach. The basic idea is to regard the manufacturing system as a so called black box in this case the simulation model itself with an input (influence values) and an output (assessment values). Disturbances are not considered in the following. In order to complete the optimization loop we need an additional search system, which generates new influence values as an output. If we connect the output of the search system with the input of our simulation system and vice versa, the optimization loop is closed and can work automatically. We have developed such an optimization system, which we have already introduced in [1] and [2]. One of the most important questions is the definition of suitable influence values. Our simulation system ROSI knows two object-types of influence or control values: • Permutation-objects for the modeling of sequences • Adjustment-objects for the modeling of scalable parameters On the other side there is one object-type for the output, a so called assessment-object, which describes an objective of our optimization problem. The user can define any number he likes of influenceand assessment-objects. For example, if a manufacturing system is controlled by the input sequence of jobs and by the capacity value of two stocks, one permutation-object and two adjustment-objects are necessary to be defined. If the user is interested in optimization of the makespan, the machine utilization as well as the average lead time of some tagged jobs, he has to define three assessment-objects with types belonging to these objectives. Each objective vector is a possible solution of our optimization problem, a so called alternative (By the way, the simulation model does not only assess the alternative but also guarantees the observance of all the constraints.). In addition each objective can be given a weight, which correlates to its importance. This weight is really a subjective value, only determined by the user. Now the optimization process can be started. For searching a control strategy several heuristic algorithms are used, e.g. Genetic Algorithms, Simulated Annealing, Tabu Search or other algorithms which are implemented. The common characteristic of all these algorithms is the stochastic generation of a large number of alternatives. If the simulation model is not too complex, thousands of alternatives are generated in a few minutes. This becomes the data basis for the examination of the objective-space. In this case our system is not only an optimization system but more a generator of data. In the meaning of Genetic Algorithms, each alternative is a so called individual, the fitness of which is in general the weighted sum of all single objective values.[3][4][5] Most of the optimization algorithms need such a substitute objective function like fitness. INTERDEPENDENCIES BETWEEN OBJECTIVES Our optimization system generates a set of n-dimensional objective vectors during its work. Each vector is represented by a point in the n-dimensional objective-space, as shown for e.g. n=3 in Figure 1 bottom right. We can recognize there a cloud of points in the 3-dimensional space. All vectors appear without normalization or any other transformation. Moving around this cloud we can study its structure. If we look from above, from right or from left to the cloud we get the three 2dimensional pictures. Figure 1. Example of three 2-dimensional objective-spaces derived from a 3-dimensionl space In order to analyze simulation data, normalization is necessary. Different normalization has been examined in decision theory. We transform the data into a range between 0 and 1. Practice has m a ke sp an