Denoising of Smooth Images Using L 1-Fitting

In this paper, denoising of smooth (H¹₀-regular) images is considered. The purpose of the paper is basically twofold. First, to compare the denoising methods based on L¹- and L²-fitting. Second, to analyze and realize an active-set method for solving the non-smooth optimization problem arising from the former approach. More precisely, we formulate the algorithm, proof its convergence, and give an efficient numerical realization. Several numerical experiments are presented, where the convergence of the proposed active-set algorithm is studied and the denoising properties of the methods based on L¹- and L²-fitting are compared. Also a heuristic method for determining the regularization parameter is presented and tested.     

An exterior simplex type algorithm for the Minimum Cost Network Flow Problem

In this paper a new Network Exterior Point Simplex Algorithm (NEPSA) for the Minimum Cost Network Flow Problem (MCNFP) is analytically presented. NEPSA belongs to a special simplex type category and is a modification of the classical network simplex algorithm. The main idea of the algorithm is to compute two flows. One flow is basic but not always feasible and the other is feasible but not always basic. A complete proof of correctness for the proposed algorithm is also presented. Moreover, the computational behavior of NEPSA is shown by an empirical study carried out for randomly generated sparse instances created by the well-known GRIDGEN network problem generator.     

正三角形容器内等圆Packing问题的启发式算法

等圆Packing问题研究如何将n个单位半径的圆形物体互不嵌入地置入一个边长尽量小的正三角形容器内,作为一类经典的NP难度问题,其有着重要的理论价值和广泛的应用背景.模拟退火算法是一种随机的全局寻优算法,通过将启发式格局更新策略与基于梯度法的局部搜索策略融入模拟退火算法,并与二分搜索相结合,提出一种求解正三角形容器内等圆Packing问题的启发式算法.该算法将启发式格局更新策略用来产生新格局和跳坑,用梯度法搜索新产生格局附近能量更低的格局,并用二分搜索得到正三角形容器的最小边长.对41个算例进行测试的实验结果表明,文中算法改进了其中38个实例的目前最优结果,是求解正三角形容器内等圆Packing问题的一种有效算法.     

求解圆形packing问题的拟人退火算法

Circles packing problem is an NP-hard problem and is difficult to solve. In this paper, a hybrid search strategy for circles packing problem is discussed. A way of generating new configuration is presented by simulating the moving of elastic objects, which can avoid the blindness of simulated annealing search and make iteration process converge fast. Inspired by the life experiences of people, an effective personified strategy to jump out of local minima is given. Based on the simulated annealing idea and personification strategy, an effective personified annealing algorithm for circles packing problem is developed. Numerical experiments on benchmark problem instances show that the proposed algorithm outperforms the best algorithm in the literature.     

Blending Set and Interval Arithmetic for Maximal Reliability

In both [3] and [8], the authors review the implementation of the basic operations in interval arithmetic, and in particular discuss the different approaches given in the literature for interval division when the divisor interval contains zero. In these papers, and in the references therein, the basic operations are defined for real or extended real interval operands.Division by an interval containing zero is a special case of an interval function for which the input arguments contain points outside the domain of the underlying point function. A number of approaches exist in the literature, [7], [12], to remove restrictions on the domain of interval functions and hence obtain a closed, exception-free interval system.In this paper, we present an alternative approach to remove restrictions on the domain of interval functions and to guarantee the inclusion property in all situations, even when some input intervals contain points that lie outside the domain of the underlying point function. To achieve this, we allow for the (efficient) set-based representation of non-real results. The computed intervals are sharp, yet contain more information and the resulting interval system is closed and exception-free. We also show how the presented ideas can be implemented in an interval arithmetic library. The performance overhead is negligible compared to the fact that the implementation using the new approach offers 100% reliability in return.The structure of the paper is as follows. We set off with a motivating example in Sect. 1. In Sect. 2, we review various approaches to interval division and then introduce vset-division of real intervals, based on the newly introduced concept of value set or vset. In Sect. 3, we give a formal definition of real vset-intervals and arithmetic on these intervals. We prove a number of essential properties and point out the likenesses and differences with other approaches. Finally, in Sect. 4, we discuss the implementation of vset-interval arithmetic in a floating-point context.Research assistant FWO Vlaanderen.     

Packing unequal circles using formulation space search

In this paper we present a heuristic algorithm for the problem of packing unequal circles in a fixed size container such as the unit circle, the unit square or a rectangle. We view the problem as being one of scaling the radii of the unequal circles so that they can all be packed into the container. Our algorithm is composed of an optimisation phase and an improvement phase. The optimisation phase is based on the formulation space search method whilst the improvement phase creates a perturbation of the current solution by swapping two circles. The instances considered in this work can be categorised into two: instances with large variations in radii and instances with small variations in radii. We consider six different containers: circle, square, rectangle, right-angled isosceles triangle, semicircle and circular quadrant. Computational results show improvements over previous work in the literature.     

求解不等圆Packing问题的一个启发式算法

求解具有NP难度的圆形packing问题具有很高的理论与实用价值.现提出一个启发式方法,求解了货运中常遇到的矩形区域内的不等圆packing问题.此算法首先将待布局圆按半径大小降序排列,然后用占角动作来逐个放置.通过试探性地放入一个或多个待布局圆,给出了占角动作的度以及更全局的有限枚举策略来评价占角动作的优度.在放置每一个圆时,以贪心的方式选取当前具有最大优度的占角动作来放置.最后用测试算例验证了算法的高效性.     

Selection of programme slots of television channels for giving advertisement: A graph theoretic approach

The present paper aims at developing a linear time algorithm to find a solution to the ‘maximum weight 1 colouring’ problem for an interval graph with interval weight. This algorithm has been applied to solve the problem that involves selecting different programme slots telecast on different television channels in a day so as to reach the maximum number of viewers. It is shown that all programmes of all television channels can be modelled as a weighted interval graph with interval numbers as weights. The programme slots are taken as the vertices of the graph and if the time durations of two programme slots have non-empty intersection, the corresponding vertices are considered to be connected by an edge. The number of viewers of a programme is taken as the weight of the vertex. In reality, the number of viewers of a programme is not a fixed one; generally, it lies in an interval. Thus, the weights of the vertices are taken as interval numbers. We assume that a company sets the objective of selecting the popular programme in different channels so as to make its commercial advertisement reach the maximum number of viewers. However, the constraint imposed is that all selected programmes are mutually exclusive in respect of time scheduling. The objective of the paper is, therefore, to helps the companies to select the programme slots, which are mutually exclusive with respect to the time schedule of telecasting time, in such a way that the total number of viewers of the selected programme slots rises to the optimum level. It is shown that the solution of this problem is obtained by solving the maximum weight colouring problem on an interval graph. An algorithm is designed to solve this optimization problem using O(n) time, where n represents the total number of programmes of all channels.     

求解矩形和圆形装填问题的最大穴度算法

在超大规模集成电路设计,裁缝裁剪布料,玻璃切割等工作中提出了矩形和圆形装填问题,即把不同大小的矩形块和圆饼装入一个矩形容器中,以最大化容器的面积利用率为优化目标。对这一问题,可采用模拟退火,遗传算法等国际流行算法进行求解,但这些方法计算时间较长,计算结果的优度也不甚理想。利用人类的智慧和经验,提出了一种求解此问题的最大穴度算法。并对3个随机生成的测试实例进行了实算测试。所得结果的平均面积利用率为90．80％,平均计算时阊为8．38s。测试结果表明,算法对求解矩形和圆形装填问题是行之有效的。     

Constrained circles packing test problems: all the optimal solutions known

Taking a satellite module layout design as engineering background, this paper gives constrained test problems for an unequal circle packing whose optimal solutions are all given. Given a circular container D with radius R, the test problem can be constructed in the following steps. First, M=217 circles are packed into D without overlaps by ‘packing with a tangent circle’ to get the values of radii and centroid coordinates of the circles, which are expressed by R. Then the 217 circles are arranged in descending sequence of radius and are divided into 23 groups according to the radius. Finally, seven test problems are constructed according to the circles of q=1, 2, …, 7 groups. The optimal solution to the test problems as well as its optimality and uniqueness proof are also presented. The experimental results show that the test problems can effectively evaluate performances of different evolutionary algorithms.     

Validation and enclosure of solutions of linear complementarity problems

An inclusion condition is presented to guarantee the existence of the solution of the linear complementarity problem in a given domain. The condition can be tested numerically with very small computational cost. Based on the condition algorithms are designed to compute an interval to enclose the unknown solution. Numerical results are reported to support the theoretical analysis in the paper.     

An improved energy landscape paving algorithm for the problem of packing circles into a larger containing circle

The problem of packing circles into a larger containing circle is a kind of NP-hard problem. It is of high theoretical and practical value. Lacking powerful optimization method is the key obstacle to solving this problem. The energy landscape paving (ELP) method is a class of heuristic global optimization algorithm and a generation of Monte Carlo method. By incorporating new configuration update mechanism into ELP method, an improved energy landscape paving (ELP+) algorithm is put forward. The computational results, on two sets of instances taken from the literature, show the effectiveness of the proposed algorithm.     

A note on circle packing

The problem of packing circles into a domain of prescribed topology is considered. The circles need not have equal radii. The Collins-Stephenson algorithm computes such a circle packing. This algorithm is parallelized in two different ways and its performance is reported for a triangular, planar domain test case. The implementation uses the highly parallel graphics processing unit (GPU) on commodity hardware. The speedups so achieved are discussed based on a number of experiments.     

Parameterized on-line open-end bin packing

This note deals with a new variant of bin packing, the so-called open-end bin packing problem in which a bin can be filled to a level exceeding its capacity by its last item if it is not full immediately before the last is packed. We investigate the on-line version of this problem and give best possible algorithms for parametric cases. This work is supported by the Foundation under State Education Committee of China.     

Derivative Free Inclusion Methods for Polynomial Zeros

Two iterative methods for the simultaneous inclusion of complex zeros of a polynomial are presented. Both methods are realized in circular interval arithmetic and do not use polynomial derivatives. The first method of the fourth order is composed as a combination of interval methods with the order of convergence two and three. The second method is constructed using double application of the inclusion method of Weierstrass’ type in serial mode. It is shown that its R-order of convergence is bounded below by the spectral radius of the corresponding matrix. Numerical examples illustrate the convergence rate of the presented methods     

An improved algorithm for the p-center problem on interval graphs with unit lengths

The p-center problem is to locate p facilities in a network of n   demand points so as to minimize the longest distance between a demand point and its nearest facility. We consider this problem by modelling the network as an interval graph whose edges all have unit lengths. We present an O(n)$O(n)$ time algorithm for the problem under the assumption that the endpoints of the intervals are sorted, which improves on the existing best algorithm for the problem that has a run time of O(pn)$O(\mathit{pn})$.     

Optimal design and operation of a wastewater purification system

Due to the importance of coastal areas, is of the highest interest to implement purification systems that with minimum cost are able to assure water quality standards in agreement with the regional legislations. This work addresses the optimal design (outfall locations) and optimal operation (level of oxygen discharges) of a wastewater treatment system. This problem can be mathematically formulated as a two-objective mixed design and optimal control problem with constraints on the states and the design and control variables.     

Note on: An improved algorithm for the packing of unequal circles within a larger containing circle

This note proposed an improved version of the algorithm proposed by Wang et al. [Wang, H. Q., Huang, W. Q., Zhang, Q., & Xu, D. M. (2002). An improved algorithm for the packing of unequal circles within a larger containing circle. European Journal of Operational Research, 141, 339–347] for solving the disk packing problem with equilibrium constraints. An efficient strategy of accelerating the search process is introduced in the gradient method to shorten the execution time. A number of computational results are presented, showing the effectiveness of the proposed method.     

An action-space-based global optimization algorithm for packing circles into a square container

This paper proposes an action-space-based global optimization (ASGO) approach for the problem of packing unequal circles into a square container such that the size of the square is minimized. Starting from several random configurations, ASGO runs the following potential descent method and basin-hopping strategy iteratively. It finds configurations with the local minimum potential energy by the limited-memory BFGS (LBFGS) algorithm, then selects the circular items having the most deformations and moves them to some large vacant space or randomly chosen vacant space. By adapting the action space defined for the rectangular packing problem, we approximate each circular item as a rectangular item, thus making it much easier to find comparatively larger vacant spaces for any given configuration. The tabu strategy is used to prevent cycling and enhance the diversification during the search procedure. Several other strategies, such as swapping two similar circles or swapping two circles in different quadrants in the container, are combined to increase the diversity of the configurations. We compare the performance of ASGO on 68 benchmark instances at the Packomania website with the state-of-the-art results. ASGO obtains configurations with smaller square containers on 63 instances; at the same time it matches or approaches the current best results on the other five instances.     

An effective hybrid algorithm for the problem of packing circles into a larger containing circle

Simulated annealing is a powerful stochastic search method, but it still has the disadvantage of blind search. Tabu search (TS) which can prevent cycling and enhance diversification, is an adaptive strategy based on tabu list. By reasonably combining simulated annealing with TS, an effective hybrid algorithm for the problem of packing circles into a larger containing circle is presented. Based on a special neighborhood and tabu strategy, some benchmark problem instances can be well solved by the presented hybrid algorithm, and the computational results can compete with the best literature results.