A BRANCH-AND-BOUND ALGORITHM FOR A PSEUDO-BOOLEAN OPTIMIZATION PROBLEM WITH BLACK-BOX FUNCTIONS

We consider a conditional pseudo-Boolean optimization problem with both the objective function and all constraint functions given algorithmically (black-box functions) and defined on {0, 1}n only. We suppose that these functions have certain properties, for example, unimodality and monotonicity. To solve problems of this type, we propose an optimization algorithm based on finding boundary points of the feasible region and the branch-and-bound method. The developed algorithm is aimed at the reception of an exact solution of an optimization problem. In addition, this algorithm can be used as an improvement of approximate algorithms such as the greedy heuristic and the random search algorithms for finding boundary points. Even after a small number of iterations (branchings), a significant improvement of the found feasible solution is achieved

Solving real-world ATSP instances by branch-and-cut

Recently, Fischetti, Lodi and Toth [15] surveyed exact methods for the Asymmetric Traveling Salesman Problem (ATSP) and computationally compared branch-and-bound and branch-and-cut codes. The results of this comparison proved that branch-and-cut is the most effective method to solve hard ATSP instances. In the present paper the branch-and-cut algorithms by Fischetti and Toth [17] and by Applegate, Bixby, Chvátal and Cook [2] are considered and tested on a set of 35 real-world instances including 16 new instances recently presented in [12]. © Springer-Verlag Berlin Heidelberg 2003

Entscheidungsunterstützung für die Angebotserstellung im internationalen Großanlagenbau

The intensive competition in the international market for plant engineering is characterized by high pricing pressure, increase of local content requirements and decrease of project durations. This leads to intricate problems with regard to the choice of production locations and project scheduling. These interacting decisions are to be considered in the bidding phase of a plant project already. This dissertation proposes a mixed-integer optimization model to determine the lower bound of the bid price. ProGen benchmark suits developed in the field of resource-constrained project scheduling problems are extended to evaluate the model. To solve problems with large size and high complexity, a solution method using the Branch & Bound paradigm is developed. Computational results demonstrate the advantage of the solution method in comparison with the application of the commercial software package ILOG CPLEX. Finally, the decision support of the developed model for bidding is demonstrated in an application case using real data from an international plant manufacturing company.Der verschärfte Wettbewerb im globalen Markt für Großanlagen ist durch einen hohen Preisdruck, erhöhtes Local Content Requirement und verkürzte Projektlaufzeiten gekennzeichnet. Daraus resultieren komplexe Problemstellungen für die Standortwahl und das Projekt-Scheduling. Diese Entscheidungen beeinflussen sich gegenseitig und sollten deshalb bereits in der Angebotsphase berücksichtigt werden. Die vorliegende Dissertation setzt sich mit der Modellierung dieses Problems auseinander und unterstützt die Ermittlung der Untergrenze des Angebotspreises durch Kostenminimierung. ProGen-Benchmark-Instanzen für das Resource-Constrained Project Scheduling Problem (RCPSP) werden erweitert, um das Model zu evaluieren. Zur Lösung großer und komplexer Probleme wird eine Methode mit Hilfe des Branch-and-Bound-Ansatzes entwickelt. Die Ergebnisse belegen die Überlegenheit des Lösungsverfahrens im Vergleich zur kommerziellen Optimierungssoftware ILOG CPLEX. Anhand einer Fallstudie für einen internationalen Großanlagenbauer wird das entwickelte Modell auf Basis von Realdaten implementiert

New local search in the space of infeasible solutions framework for the routing of vehicles

Combinatorial optimisation problems (COPs) have been at the origin of the design of many optimal and heuristic solution frameworks such as branch-and-bound algorithms, branch-and-cut algorithms, classical local search methods, metaheuristics, and hyperheuristics. This thesis proposes a refined generic and parametrised infeasible local search (GPILS) algorithm for solving COPs and customises it to solve the traveling salesman problem (TSP), for illustration purposes. In addition, a rule-based heuristic is proposed to initialise infeasible local search, referred to as the parameterised infeasible heuristic (PIH), which allows the analyst to have some control over the features of the infeasible solution he/she might want to start the infeasible search with. A recursive infeasible neighbourhood search (RINS) as well as a generic patching procedure to search the infeasible space are also proposed. These procedures are designed in a generic manner, so they can be adapted to any choice of parameters of the GPILS, where the set of parameters, in fact for simplicity, refers to set of parameters, components, criteria and rules. Furthermore, a hyperheuristic framework is proposed for optimizing the parameters of GPILS referred to as HH-GPILS. Experiments have been run for both sequential (i.e. simulated annealing, variable neighbourhood search, and tabu search) and parallel hyperheuristics (i.e., genetic algorithms / GAs) to empirically assess the performance of the proposed HH-GPILS in solving TSP using instances from the TSPLIB. Empirical results suggest that HH-GPILS delivers an outstanding performance. Finally, an offline learning mechanism is proposed as a seeding technique to improve the performance and speed of the proposed parallel HH-GPILS. The proposed offline learning mechanism makes use of a knowledge-base to keep track of the best performing chromosomes and their scores. Empirical results suggest that this learning mechanism is a promising technique to initialise the GA’s population