Simultaneous generalizedhillclimbing (SGHC) algorithms provide a framework for using heuristics to simultaneously address sets of intractable discrete optimization problems where information is shared between the pr...
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Simultaneous generalizedhillclimbing (SGHC) algorithms provide a framework for using heuristics to simultaneously address sets of intractable discrete optimization problems where information is shared between the problems during the algorithm execution. Many well-known heuristics can be embedded within the SGHC algorithm framework. This paper shows that the solutions generated by an SGHC algorithm are a stochastic process that satisfies the Markov property. This allows problem probability mass functions to be formulated for particular sets of problems based on the long-term behavior of the algorithm. Such results can be used to determine the proportion of iterations that an SGHC algorithm will spend optimizing over each discrete optimization problem. Sufficient conditions that guarantee that the algorithm spends an equal number of iterations in each discrete optimization problem are provided. SGHC algorithms can also be formulated such that the overall performance of the algorithm is independent of the initial discrete optimization problem chosen. Sufficient conditions are obtained guaranteeing that an SGHC algorithm will visit the globally optimal solution for each discrete optimization problem. Lastly, rates of convergence for SGHC algorithms are reported that show that given a rate of convergence for the embedded GHC algorithm, the SGHC algorithm can be designed to preserve this rate.
This paper formulates tabu search strategies that guide generalizedhillclimbing (GHC) algorithms for addressing NP-hard discrete optimization problems. The resulting framework, termed tabu guided generalizedhill cl...
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This paper formulates tabu search strategies that guide generalizedhillclimbing (GHC) algorithms for addressing NP-hard discrete optimization problems. The resulting framework, termed tabu guided generalizedhillclimbing (TG(2)HC) algorithms, uses a tabu release parameter that probabilistically accepts solutions currently on the tabu list. TG(2)HC algorithms are modeled as a set of stationary Markov chains, where the tabu list is fixed for each outer loop iteration. This framework provides practitioners with guidelines for developing tabu search strategies to use in conjunction with GHC algorithms that preserve some of the algorithms' known performance properties. In particular, sufficient conditions are obtained that indicate how to design iterations of problem-specific tabu search strategies, where the stationary distributions associated with each of these iterations converge to the distribution with zero weight on all non-optimal solutions.
This thesis presents new solution approaches for land leveling, using optimal earthmoving vehicle routing. It addresses the Shortest Route Cut and Fill Problem (SRCFP) developed by Henderson, Vaughan, Wakefield and J...
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This thesis presents new solution approaches for land leveling, using optimal earthmoving vehicle routing. It addresses the Shortest Route Cut and Fill Problem (SRCFP) developed by Henderson, Vaughan, Wakefield and Jacobson [2000]. The SRCFP is a discrete optimization search problem, proven to be NP-hard. The SRCFP describes the process of reshaping terrain through a series of cuts and fills. This process is commonly done when leveling land for building homes, parking lots, etc. The model used to represent this natural system is a variation of the Traveling Salesman Problem. The model is designed to limit the time needed to operate expensive, earthmoving vehicles. The model finds a vehicle route that minimizes the total time required to travel between cut and fill locations while leveling the site. An optimal route is a route requiring the least amount of travel time for an individual earthmoving vehicle.
This research addresses the SRCFP by evaluating minimum function values across an unknown response surface. The result is a cost estimating strategy that provides construction planners a strategy for contouring terrain as cheaply as possible. Other applications of this research include rapid runway repair, and robotic vehicle routing.
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