The first important conclusion to infer from the tests in this chapter is that a large portion of the scheduling problems that arise in the considered domain is not solvable optimally. Therefore the usage of heuristic optimization algorithms is indeed necessary. This deduction follows directly from the results obtained in the first section of this chapter. Even a sophisticated MIP solver like CPLEX is not able to solve MRCPSP/max instances optimally or often to find a solution at all.
The second section is concerned with the solution of the best mode assignment subproblem that occur in multimodal scheduling problems. We suggested algorithms that do not only take the validity and the duration of a underlying project into account, but also consider the fact that in general a more diverse population leads to better overall results when genetic algorithms are used. It was shown that the methods indeed increase the diversity in the resulting population.
This directly results in more variability for the initial population in the second stage of the algorithm.
This second stage is examined in the third section of this chapter. There we present the results of the best configuration of the algorithm that has been found in the course of this work and show that these configurations cannot be improved by changing a single parameter. The following observations may be stated concerning a good parameter and operator selection:
• There are some operators that consistently deliver better results than their alternative. First of all the initialization method using the LST rule to generate the candidate’s priority struc-ture is clearly preferable to choosing the priority randomly. The idea to further diversify the initial population did not pay off.
Also the stochastic universal sampling method seems to be a robust choice for the se-lection strategy. Neither rank nor tournament sese-lection could increase the quality of the solutions.
However the strongest impact on performance had the choice of the recombination method.
The proposed cycle-based crossover clearly outperformed the X-point methods. The worst choice being the uniform crossover which obtained the weakest results consistently.
• The best choice of the encoding/decoding scheme on the other hand is not an obvious one.
The activity list representation performed best in two of the three cases, but the random key representation outperfomed it for the largest instances. Also the choice of the SGS is not trivial. Especially because the mixed scheme achieved good results for the large instances and even the best ones after a medium runtime (5000generated schedules).
• The same holds for the used BMAP algorithm. Here the steady-state roulette approach inspired by the original DGA performed good, but was outperformed by the generation similarity-tournament algorithm proposed in this work. The similarity-roulette implemen-tation that was meant as a tradeoff between the two could not achieve the same results.
In summary it can be said that the survey showed that the optimization library implemented in the course of this work fulfills the requirements. It is parameterizable in many ways which should allow the user to solve a variety of scheduling problems with different characteristics. It
was also shown, that the results delivered by the library are competitive, compared to the most sophisticated implementations in the literature.
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CHAPTER 5
Summary
5.1 Summary
This thesis is concerned with the resolution of scheduling problems that arise in the context of IT automation. The concrete use case at hand is the domain of the UC4 Operations Manager.
The first chapter is started with an introduction of the objects and concepts within the UC4 OM.
After that we state the desired result of this work, which is the creation of a software library that is capable of generating high quality solutions for the scheduling problems. Currently this step is executed by hand as the UC4 OM provides only rudimentary mechanisms of automated scheduling. This manual scheduling gets tedious when the controlled procedures reach a certain level of complexity. For these cases it is desirable to move this task to an optimization program.
In order to create such an optimization program it is mandatory to formalize the problem do-main in a mathematical model. The decision process that resulted in the actual formalization is documented in section 1.3. Together with experts from UC4 the problem domain described in a number of machine scheduling problems from the literature. Since these are not flexible enough to model all the concepts, it was decided to use more complex multi-mode resource-constrained project scheduling problems.
The second chapter provides a thorough mathematical discussion of various versions of this problem, a description of different objective functions to evaluate their performance and a pro-cedure to translate the actual scheduling problems into the mathematical formulation. After that we outline exact and heuristic optimization approaches of the problem from the literature. This research and a preliminary study strongly suggest that only a heuristic optimization method is capable of solving problem instances with the size and complexity that are inherent in a typical UC4 OM system. The decision to use the a genetic algorithm approach is based on the fact that this solution approach is chosen and documented in a number of scientific papers. Also the approach has been proven to be very successful for similar problems. Furthermore the fact that objective functions are relatively flexible is appealing, because in IT environments which often are regulated by legal service level agreements, the measure of quality is not only overall time.
It may be a more complex cost function based on missed deadlines.
After the identification of the MRCPSP/max as the most suitable problem formalization, a sur-vey of the concepts for genetic algorithms to tackle this problem is given. Because it is possible to reduce the MRCPSP/max to an MRCPSP instance we also provide an overview of works on this problem. Furthermore do not examine the operators alone, but examine different possi-bilities for the representation and the population management of such algorithms. Namely we present different approaches to solve the BMAP, introduce a crossover operator based on the cycle-based crossover of Barrios et al. [1] and evaluate the random keys representation.
In the last section we present a number of results obtained in the course of this work. First of all the findings of the preliminary study are shown. These support our decision to discard the idea of using an MIP solver to generate optimal solutions.
After that we present the results for the best mode assignment problem (BMAP) which is a sub-problem of the MRCPSP/max. There we evaluate the modifications we proposed in this work with respect to solution quality and diversity. It could be shown that the introduced changes have desirable effects on the obtained solutions.
For the results in the last section a number of runs were executed with benchmarks used in the scientific community. With these standardized test instances we could verify that our imple-mentation is suitable for problem instances showing a variety of different characteristics. This verification is important, because there is no typical UC4 OM scheduling problem since the clients use the software in very different ways. Furthermore these tests allowed us to compare our work with the state of the art implementations, where they proved to be competitive.