The conventional information used to guide automobile drivers in selecting their driving routes is the shortest-distance path (SDP). As several researchers have pointed out, driver route selection is a multiple criteria decision process. This research proposes a multiobjective path optimisation (MOPO) decision model to make a more precise simulation of the decision-making behaviour of driver route selection. Seven single-objective path optimisation (SOPO) decision models are taken into account to establish the MOPO decision model. They relate to travel time, travel cost, cumulative distance, roadway capacity, roadway grade, passed intersections and number of turns. To solve the MOPO problem, a two-stage technique which incorporates shortest path (SP) algorithms and techniques for solving the multiobjective programming problem and a path genetic algorithm (PGA) are proposed. In addition, algorithms such as Dijkstra, A* and GA are reviewed and algorithms that are applicable for solving the MOPO problems are suggested. Furthermore, new algorithms for solving least-node path (LNP) problem, corresponding to the objective of passed intersections, as well as minimum-turn path (MTP) problem, corresponding to the objective of number of turns, are developed. To conduct the empirical study, a software tool - the multiobjective path optimisation analysis tool (MOPOAT) - was implemented. It contains tools for constructing a road network and its corresponding network topology, the environment of coding techniques for solving the MOPO problems and tools for the manipulation, statistics, analysis and display of experimental results. The purpose of implementing the MOPOAT software is to provide more efficient, convenient and user-friendly tools for solving MOPO and SOPO problems so that an empirical study of real road networks can be carried out more easily. To demonstrate the advantages of the proposed model in supporting more diverse information to drivers to assist in route selection, several experiments were conducted utilising three real road networks with different roadway types and numbers of nodes and links. Techniques and algorithms such as the two-stage approach, Dijkstra and the PGA for solving the MOPO problem, and the Dijkstra, LNP and MTP algorithms for solving the SOPO problems were applied. Finally, to deal with improvements in computational efficiency for identifying SPs in a large road network and for population initialisation of the PGA, the critical-section (CS) approach and the seed-path expansion (SPE) approach are proposed. To compare the run time between the conventional SP and CS algorithms as well as the PGA and the SPE algorithms, tools were implemented with commercial GIS, and experimental tests were conducted using road networks with a large amount of nodes and links and different roadway types. Through these theoretical and empirical studies, several useful contributions and conclusions were obtained. Some of the most significant findings are: 1. The experimental results demonstrate the advantages of integration with commercial GIS packages in supporting both spatial and attribute data displays. It can be safely said that, assisted by the MOPOAT software, it is easy for automobile drivers to obtain the optimal paths of the SDP, LNP, MTP and MOPO problems in seconds, despite these problems being highly complex and difficult to resolve manually. 2. According to the experimental results, the proposed LNP, MTP and MOPO decision models give automobile drivers richer information for choosing their driving routes in a more diverse way. 3. It is shown by the experimental results that the SDP and LNP mostly locate different paths in both radial-circumferential and grid-type road networks, and that the total passed intersections by the SDP are greater than passed by the LNP. Moreover, it is revealed that ambiguous turns might occur in both radial-circumferential and grid-type road networks. 4. It is found that the number of nodes of the SDP is in general greater than the number of nodes of the LNP and MTP irrespective of the type of road network. 5. A sensitivity analysis for weights shows that as the weighting value of the SDP objective incrementally increases by 0.1 units, the corresponding SDP??s objective value varies either low or high. The same results also occur for the LNP and MTP objectives. This verifies the fact that the weighting coefficients do not reflect proportionally the relative importance of the objectives. Moreover, the MTP objective has the higher sensitivity in comparison with the other two objectives. 6. Despite utilising Dijkstra or PGA algorithms for solving the MOPO problem, the LNP and MTP algorithms have to be employed to solve the non-commeasurable problem, whereby the standardisation objective value can be obtained. In addition, without any assisting information the PGA might fail to reach the best-compromise solution. 7. It is found that the total run time for solving the MOPO problem by applying the Dijkstra algorithm is much faster than by the PGA. However, if the run time excludes the time needed for population initialisation, the PGA is much faster than the Dijkstra algorithm. 8. Based on calculated bottlenecks, the proposed CS approach partitions a SP into many critical sections in advance, with the result that a long SP can be obtained by combining all SPs of all CSs. The experimental results show that the run time of the CS algorithm is much faster than Dijkstra??s algorithm. Moreover, the test result for the P-pointer indicates that if the total number of nodes of a SP grows the computational efficiency of the CS algorithm becomes significantly better than the Dijkstra algorithm, and that the CS approach has the best performance. 9. The experimental result for the E-pointer reveals that the computational efficiency of the CS algorithm will decrease gradually as the number of selected CSs increases. Therefore, the total percentage of selected CSs suggested by the experimental result is no more than 30 percent. 10. According to the experimental results, the performance order among SDP, LNP and MTP algorithms from fast to slow is SDP, MTP and LNP, and the LNP algorithm requires much more time than the other two algorithms. 11. As the total nodes of a path increase, most of the run time for SDP and LNP also increases. However, there are still some paths that violate the above rule. This result verifies that the run time needed for solving SDP and LNP is not only affected by the node numbers but also depends on the network topology. 12. Run time for solving the MOPO problem by applying the PGA is faster than applying the Dijkstra algorithm, if the run time of the former algorithm does not take into account the population initialisation time. Nevertheless, if the run time of the former algorithm does take into account the population initialisation time, the latter algorithm is much faster than the former algorithm. 13. In comparing the run time for population initialisation, the run time of the evolution process by applying the PGA is quite small, and the bottleneck of the run time for solving MOPO problem by applying the PGA is the population initialisation. 14. The population initialisation time is reduced significantly by applying the SPE algorithm, and increases at a very slow rate as the number of nodes of a path increases. As the total nodes of a path grow ever larger, the computing time is reduced more noticeably.

The conventional information used to guide automobile drivers in selecting their driving routes is the shortest-distance path (SDP). As several researchers have pointed out, driver route selection is a multiple criteria decision process. This research proposes a multiobjective path optimisation (MOPO) decision model to make a more precise simulation of the decision-making behaviour of driver route selection. Seven single-objective path optimisation (SOPO) decision models are taken into account to establish the MOPO decision model. They relate to travel time, travel cost, cumulative distance, roadway capacity, roadway grade, passed intersections and number of turns. To solve the MOPO problem, a two-stage technique which incorporates shortest path (SP) algorithms and techniques for solving the multiobjective programming problem and a path genetic algorithm (PGA) are proposed. In addition, algorithms such as Dijkstra, A* and GA are reviewed and algorithms that are applicable for solving the MOPO problems are suggested. Furthermore, new algorithms for solving least-node path (LNP) problem, corresponding to the objective of passed intersections, as well as minimum-turn path (MTP) problem, corresponding to the objective of number of turns, are developed. To conduct the empirical study, a software tool - the multiobjective path optimisation analysis tool (MOPOAT) - was implemented. It contains tools for constructing a road network and its corresponding network topology, the environment of coding techniques for solving the MOPO problems and tools for the manipulation, statistics, analysis and display of experimental results. The purpose of implementing the MOPOAT software is to provide more efficient, convenient and user-friendly tools for solving MOPO and SOPO problems so that an empirical study of real road networks can be carried out more easily. To demonstrate the advantages of the proposed model in supporting more diverse information to drivers to assist in route selection, several experiments were conducted utilising three real road networks with different roadway types and numbers of nodes and links. Techniques and algorithms such as the two-stage approach, Dijkstra and the PGA for solving the MOPO problem, and the Dijkstra, LNP and MTP algorithms for solving the SOPO problems were applied. Finally, to deal with improvements in computational efficiency for identifying SPs in a large road network and for population initialisation of the PGA, the critical-section (CS) approach and the seed-path expansion (SPE) approach are proposed. To compare the run time between the conventional SP and CS algorithms as well as the PGA and the SPE algorithms, tools were implemented with commercial GIS, and experimental tests were conducted using road networks with a large amount of nodes and links and different roadway types. Through these theoretical and empirical studies, several useful contributions and conclusions were obtained. Some of the most significant findings are: 1. The experimental results demonstrate the advantages of integration with commercial GIS packages in supporting both spatial and attribute data displays. It can be safely said that, assisted by the MOPOAT software, it is easy for automobile drivers to obtain the optimal paths of the SDP, LNP, MTP and MOPO problems in seconds, despite these problems being highly complex and difficult to resolve manually. 2. According to the experimental results, the proposed LNP, MTP and MOPO decision models give automobile drivers richer information for choosing their driving routes in a more diverse way. 3. It is shown by the experimental results that the SDP and LNP mostly locate different paths in both radial-circumferential and grid-type road networks, and that the total passed intersections by the SDP are greater than passed by the LNP. Moreover, it is revealed that ambiguous turns might occur in both radial-circumferential and grid-type road networks. 4. It is found that the number of nodes of the SDP is in general greater than the number of nodes of the LNP and MTP irrespective of the type of road network. 5. A sensitivity analysis for weights shows that as the weighting value of the SDP objective incrementally increases by 0.1 units, the corresponding SDP??s objective value varies either low or high. The same results also occur for the LNP and MTP objectives. This verifies the fact that the weighting coefficients do not reflect proportionally the relative importance of the objectives. Moreover, the MTP objective has the higher sensitivity in comparison with the other two objectives. 6. Despite utilising Dijkstra or PGA algorithms for solving the MOPO problem, the LNP and MTP algorithms have to be employed to solve the non-commeasurable problem, whereby the standardisation objective value can be obtained. In addition, without any assisting information the PGA might fail to reach the best-compromise solution. 7. It is found that the total run time for solving the MOPO problem by applying the Dijkstra algorithm is much faster than by the PGA. However, if the run time excludes the time needed for population initialisation, the PGA is much faster than the Dijkstra algorithm. 8. Based on calculated bottlenecks, the proposed CS approach partitions a SP into many critical sections in advance, with the result that a long SP can be obtained by combining all SPs of all CSs. The experimental results show that the run time of the CS algorithm is much faster than Dijkstra??s algorithm. Moreover, the test result for the P-pointer indicates that if the total number of nodes of a SP grows the computational efficiency of the CS algorithm becomes significantly better than the Dijkstra algorithm, and that the CS approach has the best performance. 9. The experimental result for the E-pointer reveals that the computational efficiency of the CS algorithm will decrease gradually as the number of selected CSs increases. Therefore, the total percentage of selected CSs suggested by the experimental result is no more than 30 percent. 10. According to the experimental results, the performance order among SDP, LNP and MTP algorithms from fast to slow is SDP, MTP and LNP, and the LNP algorithm requires much more time than the other two algorithms. 11. As the total nodes of a path increase, most of the run time for SDP and LNP also increases. However, there are still some paths that violate the above rule. This result verifies that the run time needed for solving SDP and LNP is not only affected by the node numbers but also depends on the network topology. 12. Run time for solving the MOPO problem by applying the PGA is faster than applying the Dijkstra algorithm, if the run time of the former algorithm does not take into account the population initialisation time. Nevertheless, if the run time of the former algorithm does take into account the population initialisation time, the latter algorithm is much faster than the former algorithm. 13. In comparing the run time for population initialisation, the run time of the evolution process by applying the PGA is quite small, and the bottleneck of the run time for solving MOPO problem by applying the PGA is the population initialisation. 14. The population initialisation time is reduced significantly by applying the SPE algorithm, and increases at a very slow rate as the number of nodes of a path increases. As the total nodes of a path grow ever larger, the computing time is reduced more noticeably.

An efficient algorithm which finds collision free paths for a manipulator with 5 or 6 revolute joints is described. It solves the problem for four degree of freedom pick and place operations. Examples are given of paths found by the algorithm in tightly cluttered workspaces. The algorithm first describes free space in two ways: as freeways for the hand and payload ensemble and as freeways for the upperarm. Freeways match volumes swept out by manipulator motions and can be "inverted" to find a class of topologically equivalent path segments. The two freeway spaces are searched concurrently under projection of constraints determined by motion of the forearm.

A hierarchical representation for configuration space is presented, along with an algorithm for searching that space for collision-free paths. The detail of the algorithm are presented for polygonal obstacles and a moving object with two translational and one rotational degrees of freedom.

This paper deals with the class of problems that involve finding where to place or how to move a solid object in the presence of obstacles. The solution to this class of problems is essential to the automatic planning of manipulator transfer movements, i.e. the motions to grasp a part and place it at some destination. This paper presents algorithms for planning manipulator paths that avoid collisions with objects in the workspace and for choosing safe grasp points on objects. These algorithms allow planning transfer movements for Cartesian manipulators. The approach is based on a method of computing an explicit representation of the manipulator configurations that would bring about a collision.

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In this paper a partial least squares (PLS) approach to dynamic modelling with latent variables is proposed. Let Y be a matrix of manifest variables and H the matrix of the corresponding latent variables. And let H = BH+ε be a structural PLS model with a coefficient matrix B. Then this model can be made a dynamic one by substituting for B a matrix F = B + CL containing the lag operator L. Then the structural dynamic model H = FH+ε is formally estimated like an ordinary PLS model. In an exploratory way the model can be used for forecasting purposes. The procedure is being programmed in ISP.

Dendritic shapes are commonplace in the natural world such as trees, lichens, coral and lightning. Models of dendritic shapes are widely needed in many areas. Because of their branching fractal and erratic structures modeling dendritic shapes is a tricky task. Existing methods for modeling dendritic shapes are slow and complicated.<p>In this thesis we present a procedural algorithm of using path planning to model dendritic shapes. We generate a dendrite by finding the least-cost paths from multiple endpoints to a common generator and use the dendrite to build the geometric model. With the control handles of endpoint placement, fractal shape, edge weights distribution and path width, we create different shapes of dendrites that simulate different kinds of dendritic shapes very well. Compared with some existing methods, our algorithm is fast and simple.

Variable Selection has always been a very important problem in statistics. We often meet situations where a huge data set is given and we want to find out the relationship between the response and the corresponding variables. With a huge number of variables, we often end up with a big model even if we delete those that are insignificant. There are two reasons why we are unsatisfied with a final model with too many variables. The first reason is the prediction accuracy. Though the prediction bias might be small under a big model, the variance is usually very high. The second reason is interpretation. With a large number of variables in the model, it's hard to determine a clear relationship and explain the effects of variables we are interested in. A lot of variable selection methods have been proposed. However, one disadvantage of variable selection is that different sizes of model require different tuning parameters in the analysis, which is hard to choose for non-statisticians. Xin and Zhu advocate variable ranking instead of variable selection. Once variables are ranked properly, we can make the selection by adopting a threshold rule. In this thesis, we try to rank the variables using Least Angle Regression (LARS). Some shrinkage methods like Lasso and LARS can shrink the coefficients to zero. The advantage of this kind of methods is that they can give a solution path which describes the order that variables enter the model. This provides an intuitive way to rank variables based on the path. However, Lasso can sometimes be difficult to apply to variable ranking directly. This is because that in a Lasso solution path, variables might enter the model and then get dropped. This dropping issue makes it hard to rank based on the order of entrance. However, LARS, which is a modified version of Lasso, doesn't have this problem. We'll make use of this property and rank variables using LARS solution path.

Dendritic shapes are commonplace in the natural world such as trees, lichens, coral and lightning. Models of dendritic shapes are widely needed in many areas. Because of their branching fractal and erratic structures modeling dendritic shapes is a tricky task. Existing methods for modeling dendritic shapes are slow and complicated.<p>In this thesis we present a procedural algorithm of using path planning to model dendritic shapes. We generate a dendrite by finding the least-cost paths from multiple endpoints to a common generator and use the dendrite to build the geometric model. With the control handles of endpoint placement, fractal shape, edge weights distribution and path width, we create different shapes of dendrites that simulate different kinds of dendritic shapes very well. Compared with some existing methods, our algorithm is fast and simple.