Selected Topics in Network Optimization: Aligning Binary Decision Diagrams for a Facility Location Problem and a Search Method for Dynamic Shortest Path Interdiction

This work deals with three different combinatorial optimization problems: minimizing the total size of a pair of binary decision diagrams (BDDs) under a certain structural property, a variant of the facility location problem, and a dynamic version of the Shortest-Path Interdiction (DSPI) problem. However, these problems all have the following core idea in common: They all stem from representing an optimization problem as a decision diagram. We begin from cases in which such a diagram representation of reasonable size might exist, but finding a small diagram is difficult to achieve. The first problem develops a heuristic for enforcing a structural property for a collection of BDDs, which allows them to be merged into a single one efficiently. In the second problem, we consider a specific combinatorial problem that allows for a natural representation by a pair of BDDs. We use the previous result and ideas developed earlier in the literature to reformulate this problem as a linear program over a single BDD. This approach enables us to obtain sensitivity information, while often enjoying runtimes comparable to a mixed integer program solved with a commercial solver, after we pay the computational overhead of building the diagram (e.g., when re-solving the problem using different costs, but the same graph topology). In the last part, we examine DSPI, for which building the full decision diagram is generally impractical. We formalize the concept of a game tree for the DSPI and design a heuristic based on the idea of building only selected parts of this exponentially-sized decision diagram (which is not binary any more). We use a Monte Carlo Tree Search framework to establish policies that are near optimal. To mitigate the size of the game tree, we leverage previously derived bounds for the DSPI and employ an alpha–beta pruning technique for minimax optimization. We highlight the practicality of these ideas in a series of numerical experiments

SPEA2-based safety system multi-objective optimization

Safety systems are designed to prevent the occurrence of certain conditions and their future development into a hazardous situation. The consequence of the failure of a safety system of a potentially hazardous industrial system or process varies from minor inconvenience and cost to personal injury, significant economic loss and death. To minimise the likelihood of a hazardous situation, safety systems must be designed to maximise their availability. Therefore, the purpose of this thesis is to propose an effective safety system design optimization scheme. A multi-objective genetic algorithm has been adopted, where the criteria catered for includes unavailability, cost, spurious trip and maintenance down time. Analyses of individual system designs are carried out using the latest advantages of the fault tree analysis technique and the binary decision diagram approach (BDD). The improved strength Pareto evolutionary approach (SPEA2) is chosen to perform the system optimization resulting in the final design specifications. The practicality of the developed approach is demonstrated initially through application to a High Integrity Protection System (HIPS) and subsequently to test scalability using the more complex Firewater Deluge System (FDS). Computer code has been developed to carry out the analysis. The results for both systems are compared to those using a single objective optimization approach (GASSOP) and exhaustive search. The overall conclusions show a number of benefits of the SPEA2 based technique application to the safety system design optimization. It is common for safety systems to feature dependency relationships between its components. To enable the use of the fault tree analysis technique and the BDD approach for such systems, the Markov method is incorporated into the optimization process. The main types of dependency which can exist between the safety system component failures are identified. The Markov model generation algorithms are suggested for each type of dependency. The modified optimization tool is tested on the HIPS and FDS. Results comparison shows the benefit of using the modified technique for safety system optimization. Finally the effectiveness and application to general safety systems is discussed

Genetic algorithm approach to find the best input variable partitioning

Conference PaperThis paper presents a variable partition algorithm which combines the quasi-reduced ordered multiple-terminal multiple-valued decision diagrams and genetic algorithms (GAs). The algorithm is better than the previous techniques which find a good functional decomposition by non-exhaustive search and expands the range of searching for the best decomposition providing the optimal subtable multiplicity. The possible solutions are evaluated using the gain of decomposition for a multiple-output multiple-valued logic function. The distinct feature of GA is the possible solutions being coded by real numbers. Here the simplex-based crossover is proposed to use for the recombination stage of GA. It permits to increase the GA coverag