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- W1858552305 abstract "We present a real time heuristic learning algorithm. This algorithm is characterized by the complete heuristic learning process, which consists of state selection, heuristic learning, and search path review. The execution of the search path review is controlled by the user specified heuristic learning threshold. The algorithm will return an optimal solution with zero threshold, and near-optimal solutions with nonzero thresholds. We base on the dynamic nature of the resources of a project scheduling problem to present an application approach, which includes definition of states, state transition operator, and the cost of transition between states. Important results with the Patterson’s110 problems are presented. Introduction The project scheduling problems with resource constraints (PSRC) have been shown by Blazewicz to be NP-Complete. Its complexity has led to the development of many solution methods since early 1960s. Among them the enumerative branchand-bound procedures appears to be more effective than others. Some of the major works and reviews in this area include Elmaghraby, Demeulemeester et al, Sampson and Weiss, Demeulemeester and Herroelen, and the earlier works by Christofides et al and Stinson et al. The works by Patterson et al, who apply a backtracking algorithm to solve the PSRC problems, and Bell and Park, who apply the A* algorithm to solve the PSRC problems, represent another approach in implementing techniques of Artificial Intelligence to address this problem. In this research, we present a heuristic learning algorithm SLAT*, and an approach to facilitate its applications to solve the PSRC problems. The development of SLAT* algorithm is based on the real time heuristic search algorithm LRTA*, which is a much improved version of the original A* algorithm. The LRTA* Algorithm and The SLAT* Algorithm The Learning Real Time A* (LRTA*) algorithm assumes non-overestimating initial heuristic estimates from every state to the goals state, and positive edge costs between states. At a front state i, a neighboring state j with the minimum heuristic function f(j) = k(i,j) + h(j) is selected, where k(i,j) is the edge cost from i to j, and h(j) is the heuristic estimate of j. Based on the rationale that the farther away a state is from the goal state the larger its solution estimate should be, the heuristic learning for state i is for the algorithm to update h(i) to the value of f(j) should the latter be greater than the former, and then the search continues from j. Otherwise, there will be no heuristic learning, and from j the algorithm continues the search. It has been shown that repetitive application of the algorithm to a problem will eventually find an optimal. We add a path review component to LRTA* to form the SLAT* algorithm (Search and Learning with Threshold), and control its execution with the user specified heuristic learning threshold. The path review is carried out only when the accumulated heuristic learning has exceeded the given threshold. When that happens, from the front state i, the algorithm backtracks to its previous state i-1 and applies the same rationale to see if h(i-1) can be improved as a result of the improved h(i). The improvement of h(i-1) will lead to further backtracking to state i-2, and this backtracking procedure will continue until a state is reached where its heuristic remains unchanged or the root state, then the forward search resumes. This review procedure will ensure that, before the occurrence of the subsequent heuristic learning, the search path remains a minimum path. Hence when the goal state is found, the solution will be a near-optimal one within the range of the specified threshold. When zero threshold is provided, the algorithm, called SLA* algorithm, backtracks every time a front state experiencing heuristic learning, and hence the solution will be an optimal one. The Approach for Solving Project Scheduling Problems Definition of states : Based on the status of all activities of a project, we define a state as a partial schedule, which consists of all activities of a project in three sets completed, in-progress, and unscheduled. The completed set consists of all activities which have been completed at the time a state is being considered. The in-progress set consists of activities to be scheduled at that moment and those activities which have been scheduled but not yet completed. The unscheduled set" @default.
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- W1858552305 date "1998-01-01" @default.
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- W1858552305 title "A Heuristic Learning Algorithm and its Application to Project Scheduling Problems" @default.
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