Discrete Tomography Based on DC Programming and DCA Le Thi Hoai An; Nguyen Trong Phuc; Pham Dinh Tao
2010 IEEE RIVF International Conference on Computing & Communication Technologies, Research, Innovation, and Vision for the Future (RIVF),
2010-Nov.
Conference Proceeding
In this article, we present a new continuous approach based on DC (Difference of Convex functions) programming and DC algorithms (DCA) to the Discrete Tomography. We are concerned with the ...reconstruction of binary images from their projections in a smaller number of directions. We treat this problem as DC programs. DC programming and DCA, becoming now classic, have been introduced by PHAM DINH T. in 1985 and extensively developed by LE THI H. A. and PHAM DINH T. since 1994. The DCA has been successfully applied to a lot of various large-scale differentiable or nondifferentiable nonconvex programs for which it has provided quite often global solutions (see, and references therein). Preliminary numerical experiments show the efficiency of the proposed algorithms.
In this paper a new evolutionary algorithm (EA) is described for the unconstrained Binary Quadratic Problem, which is to be used with small, medium and large scale problems as well. This method can ...be divided into two stages, where each stage is a steady-state EA. The first stage improves the quality of the initial population. The second stage uses concatenated, complex neighbourhood structures for the mutations and improves the quality of the solutions with a randomized k-opt local search procedure. The bit selection by mutation is based on an explicit collective memory (EC-memory) that is a modification of the flee-mutation operator (Sebag et al. 1997). We tested our algorithm on all the benchmark problems of the OR-Library. Comparing the results with other heuristic methods, we can conclude that our algorithm belongs to the best methods of this problem scope.
We review some of the recent enhancements of interior-point methods for the improved solution of semidefinite relaxations in combinatorial optimization and binary quadratic programming. Central ...topics include general interior-point cutting-plane schemes, handling of linear inequalities, and several warm-starting strategies. A practical implementation and computational results are also discussed.
When an evolutionary algorithm addresses a sequence of instances of the same problem, it can seed its population with solutions that it found for previous instances. This technique is called case ...injection. How similar must the instances be for case injection to help an EA's search? We consider this question by applying a genetic algorithm, without and with case injection, to sequences of instances of binary quadratic programming. When the instances are similar, case injection helps; when the instances differ sufficiently, case injection is no help at all.
Binary Quadratic Programming (BQP) problems arise frecuently in robust MPC when min-max techniques are used. In this paper, an efficient algorithm that solves the problem for L-Band matrix structures ...is presented. The L-Band matrix algorithm has a direct application to min-max MPC. The computational burden of the L-Band max algorithm is polynomial with the dimension of the optimization variable and exponential with L, the band size. The proposed algorithm makes the implementation in real time of min-max predictive controllers possible.
The thematic object in a commercial video is representative of its content. The authors propose a data-mining method for thematic object discovery in commercials by finding spatially collocated ...visual features.
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