Browsing by Subject "heuristics"
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Item A Study of Heuristic Approaches for Runway Scheduling for the Dallas-Fort Worth Airport(2010-01-16) Stiverson, Paul W.Recent work in air transit efficiency has increased en-route efficiency to a point that airport efficiency is the bottleneck. With the expected expansion of air transit it will become important to get the most out of airport capacity. Departure scheduling is an area where efficiency stands to be improved, but due to the complicated nature of the problem an optimal solution is not always forthcoming. A heuristic approach can be used to find a sub-optimal take-off order in a significantly faster time than the optimal solution can be found using known methods. The aim of this research is to explore such heuristics and catalog their solution characteristics. A greedy approach as well as a k-interchange approach were developed to find improved takeoff sequences. When possible, the optimal solution was found to benchmark the performance of the heuristics, in general the heuristic solutions were within 10-15% of the optimal solution. The heuristic solutions showed improvements of up to 15% over the first-in first-out order with a running time around 4 ms.Item Conceptual design of long-span trusses using multi-stage heuristics(Texas A&M University, 2006-08-16) Agarwal, PranabA hybrid method that addresses the design and optimization of long-span steel trusses is presented. By utilizing advancements in present day computing and biologically inspired analysis and design, an effort has been made to automate the process of evolving optimal trusses in an unstructured problem domain. Topology, geometry and sizing optimization of trusses are simultaneously addressed using a three stage methodology. Multi-objective genetic algorithms are used to optimize the member section sizes of truss topologies and geometries. Converting constraints into additional objectives provides a robust algorithm that results in improved convergence to the pareto-optimal set of solutions. In addition, the pareto-curve plotted based on how well the different objectives are satisfied helps in identifying the trade-offs that exist between these objectives, while also providing an efficient way to rank the population of solutions during the search process. A comparison study between multi-objective genetic algorithms, simulated annealing, and reactive taboo search is conducted to evaluate the efficiency of each method with relation to its overall performance, computational expense, sensitivity to initial parameter settings, and repeatability of finding near-global optimal designs. The benefit of using a three stage approach, and also implementing the entire model on parallel computers, is the high level of computational efficiency that is obtained for the entire process and the near-optimal solutions obtained. The overall efficiency and effectiveness of this method has been established by comparing the truss design results obtained using this method on bridge and roof truss benchmark problems with truss designs obtained by other researchers. One of the salient features of thisresearch is the large number of optimal trusses that are produced as the final result. The range of designs available provides the user with the flexibility to select the truss design that best matches their design requirements. By supporting human-computer interactions between these stages, the program also incorporates subjective aesthetic criteria, which assist in producing final designs in consonance with the user's requirements.Item Improved formulations, heuristics and metaheuristics for the dynamic demand coordinated lot-sizing problem(2009-06-02) Narayanan, ArunachalamCoordinated lot sizing problems, which assume a joint setup is shared by a product family, are commonly encountered in supply chain contexts. Total system costs include a joint set-up charge each time period any item in the product family is replenished, an item set-up cost for each item replenished in each time period, and inventory holding costs. Silver (1979) and subsequent researchers note the occurrence of coordinated replenishment problems within manufacturing, procurement, and transportation contexts. Due to their mathematical complexity and importance in industry, coordinated lot-size problems are frequently studied in the operations management literature. In this research, we address both uncapacitated and capacitated variants of the problem. For each variant we propose new problem formulations, one or more construction heuristics, and a simulated annealing metaheuristic (SAM). We first propose new tight mathematical formulations for the uncapacitated problem and document their improved computational efficiency over earlier models. We then develop two forward-pass heuristics, a two-phase heuristic, and SAM to solve the uncapacitated version of the problem. The two-phase and SAM find solutions with an average optimality gap of 0.56% and 0.2% respectively. The corresponding average computational requirements are less than 0.05 and 0.18 CPU seconds. Next, we propose tight mathematical formulations for the capacitated problem and evaluate their performance against existing approaches. We then extend the two-phase heuristic to solve this more general capacitated version. We further embed the six-phase heuristic in a SAM framework, which improves heuristic performance at minimal additional computational expense. The metaheuristic finds solutions with an average optimality gap of 0.43% and within an average time of 0.25 CPU seconds. This represents an improvement over those reported in the literature. Overall the heuristics provide a general approach to the dynamic demand lot-size problem that is capable of being applied as a stand-alone solver, an algorithm embedded with supply chain planning software, or as an upper-bounding procedure within an optimization based algorithm. Finally, this research investigates the performance of alternative coordinated lotsizing procedures when implemented in a rolling schedule environment. We find the perturbation metaheuristic to be the most suitable heuristic for implementation in rolling schedules.Item Optimization in Geometric Graphs: Complexity and Approximation(2011-02-22) Kahruman-Anderoglu, SeraWe consider several related problems arising in geometric graphs. In particular, we investigate the computational complexity and approximability properties of several optimization problems in unit ball graphs and develop algorithms to find exact and approximate solutions. In addition, we establish complexity-based theoretical justifications for several greedy heuristics. Unit ball graphs, which are defined in the three dimensional Euclidian space, have several application areas such as computational geometry, facility location and, particularly, wireless communication networks. Efficient operation of wireless networks involves several decision problems that can be reduced to well known optimization problems in graph theory. For instance, the notion of a \virtual backbone" in a wire- less network is strongly related to a minimum connected dominating set in its graph theoretic representation. Motivated by the vastness of application areas, we study several problems including maximum independent set, minimum vertex coloring, minimum clique partition, max-cut and min-bisection. Although these problems have been widely studied in the context of unit disk graphs, which are the two dimensional version of unit ball graphs, there is no established result on the complexity and approximation status for some of them in unit ball graphs. Furthermore, unit ball graphs can provide a better representation of real networks since the nodes are deployed in the three dimensional space. We prove complexity results and propose solution procedures for several problems using geometrical properties of these graphs. We outline a matching-based branch and bound solution procedure for the maximum k-clique problem in unit disk graphs and demonstrate its effectiveness through computational tests. We propose using minimum bottleneck connected dominating set problem in order to determine the optimal transmission range of a wireless network that will ensure a certain size of "virtual backbone". We prove that this problem is NP-hard in general graphs but solvable in polynomial time in unit disk and unit ball graphs. We also demonstrate work on theoretical foundations for simple greedy heuristics. Particularly, similar to the notion of "best" approximation algorithms with respect to their approximation ratios, we prove that several simple greedy heuristics are "best" in the sense that it is NP-hard to recognize the gap between the greedy solution and the optimal solution. We show results for several well known problems such as maximum clique, maximum independent set, minimum vertex coloring and discuss extensions of these results to a more general class of problems. In addition, we propose a "worst-out" heuristic based on edge contractions for the max-cut problem and provide analytical and experimental comparisons with a well known "best-in" approach and its modified versions.