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Handwritten Character Recognition
Published in Edward R. Dougherty, Digital Image Processing Methods, 2020
Paul Gader, Andrew Gillies, Daniel Hepp
There is no closed-form solution to this problem unless k = 2, in which case we have a linear problem, as discussed previously. The backpropagation algorithm is used as an attempt to find the minimum value of E. The backpropagation algorithm uses a technique called gradient descent, illustrated in Fig. 12. Gradient descent is sometimes referred to as hill climbing. A value is chosen for the parameters and the gradient is computed at a point. The gradient “points” in the direction of maximum rate of change and so can be used to find the direction to change the parameters. The algorithm is a “greedy” algorithm in that it tries to take the fastest route to the minimum. As can be seen in Fig. 12, if the starting point is not chosen in a lucky spot, gradient descent will not find the global minimum value of the function. This is because the gradient uses only local information.
Collective Intelligence in Networking
Published in Phan Cong Vinh, Nature-Inspired Networking: Theory and Applications, 2018
In computer science, hill climbing is a mathematical optimization technique that belongs to the family of local search. It is an iterative algorithm that starts with an arbitrary solution to a problem, then attempts to find a better solution by incrementally changing a single element of the solution. If the change produces a better solution, an incremental change is made to the new solution, repeating until no further improvements can be found. For example, hill climbing can be applied to the travelling salesman problem. It is easy to find an initial solution that visits all the cities but will be very poor compared to the optimal solution. The algorithm starts with such a solution and makes small improvements to it, such as switching the order in which two cities are visited. Eventually, a much shorter route is likely to be obtained [64].
Application of a new clustering method for automatic identification of rock joint sets
Published in Vladimir Litvinenko, Geomechanics and Geodynamics of Rock Masses: Selected Papers from the 2018 European Rock Mechanics Symposium, 2018
Sayedalireza Fereshtenejad, Jae-Joon Song
In this method, hill-climbing algorithm is designed to search for the best partition of data which optimizes the applied clustering criterion. This is a generic term covering many algorithms trying to reach an optimum by determining the optimum along successive directions (Besset, 2015). In fact, Hill-climbing is an iterative algorithm that starts with an arbitrary solution to a problem, then attempts to find a better solution by incremental change in a single element of the solution. The following steps elaborate how the algorithm minimizes the proposed optimization criterion.
Optimisation problems and resolution methods in satellite scheduling and space-craft operation: a survey
Published in Enterprise Information Systems, 2021
Simulated Annealing (SA) generalises Hill Climbing with the aim to overcome the premature convergence to local optima. Indeed, by moving always to neighbouring solutions of better fitness, HC soon reaches to a solution where improvements are no more possible. This new mechanism in SA is implemented via a cooling procedure, namely, using a temperature parameter. According to the cooling mechanism, high-temperature values almost all candidate neighbouring moves can be accepted, while for low-temperature values neighbouring solution selection is more restrictive. The acceptability criterion uses both the function and a temperature parameter . Then, a new move is accepted with probability if . Clearly, the larger the temperature value , the larger is the probability of accepting a new move. The algorithms starts with a high value of and keeps decreasing its value systematically at each iteration of the algorithm according to a priori established cooling procedure. It should, therefore, be noted that tuning the cooling procedure directly affects the convergence of the SA algorithm. A standard template of SA can be found in Alg. 2.
Application of the covariance matrix clustering algorithm for partitioning joint sets having various joint pole sizes and densities
Published in Geosystem Engineering, 2020
Sayedalireza Fereshtenejad, Dong-Ho Yoon, Jae-Joon Song
In this method, hill-climbing algorithm is used to find the best cluster of data to optimise the applied clustering criterion. This is a generic term covering many algorithms trying to reach an optimum by determining the optimum along successive directions (Besset, 2015). The hill-climbing algorithm is an iterative algorithm that works with an arbitrary solution to a problem and then searches for a better solution by making incremental changes in a single element of the solution. The following steps elaborate on how the algorithm minimizes the proposed optimization criterion.
Optimal orientations of discrete global grids and the Poles of Inaccessibility
Published in International Journal of Digital Earth, 2020
For each initial value, the hillclimbing algorithm was run several times. Using several initial values, repeated runs, and annealing all help hillclimbing algorithms to avoid local optima and find global optima (Russell and Norvig 2002, §4.3; Skiena 2012, §7.5.2). In addition, as shown in Figure 5, the search space was characterized by smooth isolines and broad basins of attraction, which meant the hillclimber had a favourable working environment.