Computing and Information Systems - Theses
Permanent URI for this collection
Search Results
1 - 2 of 2
-
ItemHybrid optimization of vehicle routing problems( 2017)Vehicle routing problems are combinatorial optimization problems that aspire to design vehicle routes that minimize some measure of cost, such as the total distance traveled or the time at which the last vehicle returns to a depot, while adhering to various restrictions. Vehicle routing problems are of profound interest in both academia and industry because they are opportunities to study graph structures and algorithms, and because they underpin practical applications in a multitude of industries, but notably, the transportation and logistics industries. This dissertation presents two applications relevant to industry and develops a fully hybrid method for solving a classical vehicle routing problem. The first application combines vehicle routing with crew scheduling. In industry, vehicle routing and crew scheduling are usually performed in stages due to the large search space of integrated models. The first stage finds minimal-cost vehicle routes with little consideration to crew constraints and objectives. The second stage schedules crews on the routes from the first stage. Disregarding crew constraints in the first stage can lead to suboptimality or even infeasibility of the overall problem in the second stage. To quantify the suboptimality of staged optimization models, two formulations of the integrated problem are developed. The first is an ordinary mixed integer programming model, and the second is a constraint programming model containing a linear relaxation global constraint that performs cost-based filtering. The two integrated models are solved using a branch-and-bound search and a highly specialized large neighborhood search. The large neighborhood search exploits the substructures linking the vehicle routing and crew scheduling elements of the problem, and when executed on the constraint programming model, is shown to perform significantly better than the other approaches. The second application introduces a number of scheduling constraints to the Vehicle Routing Problem with Pickup and Delivery and Time Windows. The scheduling constraints arise from a lack of loading bays or equipment that unloads and loads incoming vehicles. These constraints limit the number of vehicles present or in service at any particular site by requiring the arrival of vehicles to be scheduled around the availabilities of a scarce resource. A mixed integer programming model, a constraint programming model and a sequential model are implemented for the problem but are shown to be inferior to a branch-and-price-and-check model, which hybridizes column generation and constraint programming with nogood learning. This thesis concludes with a hybrid method, named Branch-and-Check with Explanations, that unifies linear programming, constraint programming and Boolean satisfiability. The method begins with a linear programming model that omits several critical constraints. The solver uses the linear programming model to find objective bounds and candidate solutions, which are checked by a constraint programming model for feasibility of the omitted constraints. A Boolean satisfiability model performs conflict analysis on infeasible candidate solutions to derive nogood cuts, which are placed into the linear programming model and the constraint programming model. The method is implemented in a proof-of-concept solver for the Vehicle Routing Problem with Time Windows and is shown to be competitive against a branch-and-cut model while avoiding the intricacies involved in developing the cutting planes and separation algorithms required in branch-and-cut.
-
ItemImproving combinatorial optimization( 2011)Combinatorial Optimization is an important area of computer science that has many theoretical and practical applications. In this thesis, we present important contributions to several different areas of combinatorial optimization, including nogood learning, symmetry breaking, dominance, relaxations and parallelization. We develop a new nogood learning technique based on constraint projection that allows us to exploit subproblem dominances that arise when two different search paths lead to subproblems which are identical on the remaining unlabeled variables. On appropriate problems, this nogood learning technique provides orders of magnitude speedup compared to a base solver which does not learn nogoods. We present a new symmetry breaking technique called SBDS-1UIP, which is an extension of Symmetry Breaking During Search (SBDS). SBDS-1UIP uses symmetric versions of the 1UIP nogoods derived by Lazy Clause Generation solvers to prune symmetric parts of the search space. We show that SBDS-1UIP can exploit at least as many symmetries as SBDS, and that it is strictly more powerful on some problems, allowing us to exploit types of symmetries that no previous general symmetry breaking technique is capable of exploiting. We present two new general methods for exploiting almost symmetries (symmetries which are broken by a small number of constraints). The first is to treat almost symmetries as conditional symmetries and exploit them via conditional symmetry breaking constraints. The second is to modify SDBS-1UIP to handle almost symmetries. Both techniques are capable of producing exponential speedups on appropriate problems. We examine three reasonably well known problems: the Minimization of Open Stacks Problem, the Talent Scheduling Problem (CSPLib prob039), and the Maximum Density Still Life Problem (CSPLib prob032). By applying various powerful techniques such as nogood learning, dynamic programming, dominance and relaxations, we are able to solve these problems many orders of magnitude faster than the previous state of the art. We identify cache contention as a serious bottleneck that severely limit the amount of speedup achievable when parallelizing SAT and LCG solvers on multi-core systems. We alter the data structures used in the state of the art SAT solver MiniSat to be more cache aware, leading to a sequential SAT solver that is some 80% faster on average and a parallel SAT solver that is some 140% faster on average. We examine an important issue in parallel search that has not been properly addressed in the literature. Many work stealing schemes used for load balancing completely ignore the branching heuristic, and instead try to maximize the granularity of the work stolen. This can result in many of the processors searching in unfruitful parts of the search tree. We analyze this problem and develop a new work stealing scheme called confidence based work stealing, which partitions the work based on how strong the branching heuristic is at each node. The new parallel algorithm produced near linear or super linear speedup on all the problems we tested.