Iterative Hill Climbing Research Articles

Parallel iterative hill climbing algorithm to solve TSP on GPU

SummaryTraveling Salesman Problem (TSP) is an NP‐hard combinatorial optimization problem. Heuristic algorithms provide satisfactory solutions to large instance TSP in a reasonable amount of time. However, heuristic methods result in suboptimal solutions as they do not cover the search space adequately. Sequential heuristic approaches spend significant CPU time in neighborhood generation for large input instances. Neighborhood generation time can be reduced by generating in parallel. GPUs have been shown to be effective in exploiting data and memory level parallelism in large complex problems. This work presents a GPU‐based Parallel Iterative Hill Climbing (PIHC) algorithm using the nearest neighborhood heuristic to arrive at near‐optimal solutions of large TSPLIB instances in a reasonable amount of time. Multiple construction heuristics approaches, thread mapping strategies, and data structures for TSPLIB instances have been evaluated. We demonstrate improved cost quality on symmetric TSPLIB instances up to 85,900 cities. The PIHC GPU implementation gives up to 193× speedup over its sequential counterpart and up to 979.96× speedup over a state‐of‐the‐art GPU‐based TSP solver. The PIHC implementation gives a cost quality with error rate 0.72% in the best case and 8.06% in the worst case.

Construction of RSBFs with improved cryptographic properties to resist differential fault attack on grain family of stream ciphers

In recent literature, the differential fault analysis (DFA) on Grain family of stream ciphers has been shown to exploit the low algebraic degree of the derivative of the nonlinear combining function h of the stream cipher, h(x) ? h(x ? ?). The low algebraic degree allows the DFA adversary to create a linearly independent system of equations generated from the faulty and fault-free keystreams and use these equations to extract the initial state of the NFSR and LFSR stages in the stream cipher. In this paper, we propose a construction scheme for rotation symmetric Boolean functions (RSBFs) h(x) along with an orbit-tuple flip based iterative hill-climbing based construction algorithm for balanced RSBFs with high nonlinearity, low absolute indicator value of global avalanche characteristics (GAC), and high algebraic degree of h(x) ? h(x ? ?). The construction algorithm is scalable for higher input variables like n = 9,10,11 as shown in the paper. We find some interesting autocorrelation spectra and Walsh spectra properties for the class of RSBFs and then use them in the construction of RSBFs with improved cryptographic properties. We present the cryptographic properties of the RSBFs constructed for high input variables which can be used to make DFA attack harder using the existing techniques.

Development and simulation of sensor-based irrigation control strategies for cotton using the VARIwise simulation framework

Feedback control systems offer opportunities to accommodate spatial and temporal differences in crop water requirement and to improve the automated irrigation of field crops via real-time data from in-field plant, soil–water and evaporation sensing. This paper describes two sensor-based strategies applied to irrigation control, ‘Iterative Learning Control’ (ILC) and custom-designed ‘Iterative Hill Climbing Control’ (IHCC), implemented in the control simulation and evaluation framework ‘VARIwise’. Simulation of an irrigated cotton crop using soils and merged 1999–2004 weather data of SE Queensland, Australia, and represented by the performance of the well-validated cotton growth and production model OZCOT, permitted the relative performance of differing sensor data types and availability to be evaluated (both as alternatives and in combination) in meeting the requirement to optimise either crop yield or water use efficiency. These simulations indicated that ILC would perform better at maintaining soil–water deficit, whilst IHCC would be better at maximising crop yield when plant and soil sensors were utilised in combination. This work demonstrates that the optimal choice of field sensor(s) and control strategy will be a function of the irrigation objective and the spatial and temporal availability and type of field measurements.

Fast and comprehensive fitting of complex mathematical models to massive amounts of empirical data

The new method for parameterising a high number of observed curves in terms of nonlinear functions, presented by Isaeva et al. is here applied to noisy data and tested with respect to computational speed, ease of use and estimation precision. The method employs conventional least squares minimisation of the lack-of-fit residuals. But algorithmically it replaces traditional, time-consuming iterative hill-climbing (e.g., simplex optimisation) by a fast, non-iterative linear projection. Each nonlinear function is emulated by its multivariate metamodel (a low-dimensional bi-linear principal component analysis model of its behaviour), and yields parameter estimates by a simple projection plus a data base look-up.For setting up a generic, fast modelling system for line curvature, a set of 38 widely different mathematical functions - most of them nonlinear - were selected for their ability to give sigmoid curves. For each model, its behavioural repertoire was established by designed computer simulation, and its multivariate metamodel was estimated. Then the new curve fitting approach was compared to conventional simplex optimisation, by fitting artificial, but noisy curves to the 38 curve-functions, in order to identify the correct function type and parameter values. Finally, the new method was adapted to heteroscedastic noise and employed for parameterisation of >170,000 sigmoid curves from time lapse monitoring of proteomic 2D Gel Electrophoresis (2DGE) image development.The new method gave at least as precise parameter estimates as the simplex optimisation and worked well both for homoscedastic and heteroscedastic noise. It speeded up the parameter estimation in the nonlinear models by a factor of about 24 compared to the simplex optimisation.Moreover, per definition it avoids the problems of having to select starting values and ending up in locally optimal solutions. And it reduced the problem of subjective, possibly erroneous choice of nonlinear model specification.

An iterative hillclimbing algorithm for discrete optimization on images: application to joint encoding of image transform coefficients

We develop an iterative, hillclimbing-based assignment algorithm for the approximate solution of discrete-parameter cost minimization problems defined on the pixel sites of an image. While the method is applicable to a number of problems including encoding, decoding, and segmentation, this article focuses on entropy-constrained encoding. For typical statistical image models, the globally optimal solution requires an intractable exhaustive search, while standard greedy methods, though tractable in computation, may be quite suboptimal. Alternatively, our method is guaranteed to perform no worse (and typically performs significantly better) than greedy encoding, yet with manageable increases in complexity. The new approach uses dynamic programming as a local optimization step, repeatedly applied to the rows (or columns) of the image, until convergence. For a DCT framework, with entropy-constrained TCQ applied to the coefficient sources, the new method gains as much as 0.8 dB over standard greedy encoding.