Based on Gaussian mixture models（GMM）, speed, flow and occupancy are used together in the cluster analysis of traffic flow data. Compared with other clustering and sorting techniques, as a structural model, the GMM is suitable for various kinds of traffic flow parameters. Gap statistics and domain knowledge of traffic flow are used to determine a proper number of clusters. The expectation-maximization （E-M） algorithm is used to estimate parameters of the GMM model. The clustered traffic flow pattems are then analyzed statistically and utilized for designing maximum likelihood classifiers for grouping real-time traffic flow data when new observations become available. Clustering analysis and pattern recognition can also be used to cluster and classify dynamic traffic flow patterns for freeway on-ramp and off-ramp weaving sections as well as for other facilities or things involving the concept of level of service, such as airports, parking lots, intersections, interrupted-flow pedestrian facilities, etc.
A min-max optimization method is proposed as a new approach to deal with the weight determination problem in the context of the analytic hierarchy process. The priority is obtained through minimizing the maximal absolute difference between the weight vector obtained from each column and the ideal weight vector. By transformation, the. constrained min- max optimization problem is converted to a linear programming problem, which can be solved using either the simplex method or the interior method. The Karush-Kuhn- Tucker condition is also analytically provided. These control thresholds provide a straightforward indication of inconsistency of the pairwise comparison matrix. Numerical computations for several case studies are conducted to compare the performance of the proposed method with three existing methods. This observation illustrates that the min-max method controls maximum deviation and gives more weight to non- dominate factors.
To diagnose the feasibility of the solution of a job-shop scheduling problem（JSSP）,a test algorithm based on diagraph and heuristic search is developed and verified through a case study.Meanwhile,a new repair algorithm for modifying an infeasible solution of the JSSP to become a feasible solution is proposed for the general JSSP.The computational complexity of the test algorithm and the repair algorithm is both O（n） under the worst-case scenario,and O（2J＋M） for the repair algorithm under the best-case scenario.The repair algorithm is not limited to specific optimization methods,such as local tabu search,genetic algorithms and shifting bottleneck procedures for job shop scheduling,but applicable to generic infeasible solutions for the JSSP to achieve feasibility.
