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1.
Solving Planning and Design Problems in the Process Industry Using Mixed Integer and Global Optimization 总被引:1,自引:0,他引:1
Josef Kallrath 《Annals of Operations Research》2005,140(1):339-373
This contribution gives an overview on the state-of-the-art and recent advances in mixed integer optimization to solve planning
and design problems in the process industry. In some case studies specific aspects are stressed and the typical difficulties
of real world problems are addressed.
Mixed integer linear optimization is widely used to solve supply chain planning problems. Some of the complicating features
such as origin tracing and shelf life constraints are discussed in more detail. If properly done the planning models can also
be used to do product and customer portfolio analysis.
We also stress the importance of multi-criteria optimization and correct modeling for optimization under uncertainty. Stochastic
programming for continuous LP problems is now part of most optimization packages, and there is encouraging progress in the
field of stochastic MILP and robust MILP.
Process and network design problems often lead to nonconvex mixed integer nonlinear programming models. If the time to compute
the solution is not bounded, there are already a commercial solvers available which can compute the global optima of such
problems within hours. If time is more restricted, then tailored solution techniques are required. 相似文献
2.
Simulated Annealing Algorithms for Continuous Global Optimization: Convergence Conditions 总被引:3,自引:0,他引:3
M. Locatelli 《Journal of Optimization Theory and Applications》2000,104(1):121-133
In this paper, simulated annealing algorithms for continuous global optimization are considered. After a review of recent convergence results from the literature, a class of algorithms is presented for which strong convergence results can be proved without introducing assumptions which are too restrictive. The main idea of the paper is that of relating both the temperature value and the support dimension of the next candidate point, so that they are small at points with function value close to the current record and bounded away from zero otherwise. 相似文献
3.
A class of simulated annealing algorithms for continuous global optimization is considered in this paper. The global convergence property is analyzed with respect to the objective value sequence and the minimum objective value sequence induced by simulated annealing algorithms. The convergence analysis provides the appropriate conditions on both the generation probability density function and the temperature updating function. Different forms of temperature updating functions are obtained with respect to different kinds of generation probability density functions, leading to different types of simulated annealing algorithms which all guarantee the convergence to the global optimum. 相似文献
4.
Global Optimization Techniques for Solving the General Quadratic Integer Programming Problem 总被引:3,自引:0,他引:3
Nguyen Van Thoai 《Computational Optimization and Applications》1998,10(2):149-163
We consider the problem of minimizing a general quadratic function over a polytope in the n-dimensional space with integrality restrictions on all of the variables. (This class of problems contains, e.g., the quadratic 0-1 program as a special case.) A finite branch and bound algorithm is established, in which the branching procedure is the so-called integral rectangular partition, and the bound estimation is performed by solving a concave programming problem with a special structure. Three methods for solving this special concave program are proposed. 相似文献
5.
This paper presents an interactive method for solving general 0-1 multiobjective linear programs using Simulated Annealing and Tabu Search. The interactive protocol with the decision maker is based on the specification of reservation levels for the objective function values. These reservation levels narrow the scope of the search in each interaction in order to identify regions of major interest to the decision maker. Metaheuristic approaches are used to generate potentially nondominated solutions in the computational phases. Generic versions of Simulated Annealing and Tabu Search for 0-1 single objective linear problems were developed which include a general routine for repairing unfeasible solutions. This routine improves significantly the results of single objective problems and, consequently, the quality of the potentially nondominated solutions generated for the multiobjective problems. Computational results and examples are presented. 相似文献
6.
In this paper, a simulated-annealing-based method called Filter Simulated Annealing (FSA) method is proposed to deal with
the constrained global optimization problem. The considered problem is reformulated so as to take the form of optimizing two
functions, the objective function and the constraint violation function. Then, the FSA method is applied to solve the reformulated
problem. The FSA method invokes a multi-start diversification scheme in order to achieve an efficient exploration process.
To deal with the considered problem, a filter-set-based procedure is built in the FSA structure. Finally, an intensification
scheme is applied as a final stage of the proposed method in order to overcome the slow convergence of SA-based methods. The
computational results obtained by the FSA method are promising and show a superior performance of the proposed method, which
is a point-to-point method, against population-based methods. 相似文献
7.
The method of partitioned random search has been proposed in recent years to obtain an as good as possible solution for the global optimization problem (1). A practical algorithm has been developed and applied to real-life problems. However, the design of this algorithm was based mainly on intuition. The theoretical foundation of the method is an important issue in the development of efficient algorithms for such problems. In this paper, we generalize previous theoretical results and propose a sequential sampling policy for the partitioned random search for global optimization with sampling cost and discounting factor. A proof of the optimality of the proposed sequential sampling policy is given by using the theory of optimal stopping. 相似文献
8.
M. Locatelli 《Journal of Global Optimization》2000,18(3):219-233
In this paper a simulated annealing algorithm for continuous global optimization will be considered. The algorithm, in which a cooling schedule based on the distance between the function value in the current point and an estimate of the global optimum value is employed, has been first introduced in Bohachevsky, Johnson and Stein (1986) [2], but without any proof of convergence. Here it will be proved that, under suitable assumptions, the algorithm is convergent 相似文献
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11.
Pierre Courrieu 《Journal of Global Optimization》1997,10(1):37-55
This article presents a new algorithm, called theHyperbell Algorithm, that searches for the global extrema ofnumerical functions of numerical variables. The algorithm relies on theprinciple of a monotone improving random walk whose steps aregenerated around the current position according to a gradually scaleddown Cauchy distribution. The convergence of the algorithm is provenand its rate of convergence is discussed. Its performance is tested onsome hard test functions and compared to that of other recentalgorithms and possible variants. An experimental study of complexityis also provided, and simple tuning procedures for applications areproposed. 相似文献
12.
We suggested some modifications to the controlled random search (CRS) algorithm for global optimization. We introduce new trial point generation schemes in CRS, in particular, point generation schemes using linear interpolation and mutation. Central to our modifications is the probabilistic adaptation of point generation schemes within the CRS algorithm.A numerical study is carried out using a set of 50 test problems many of which are inspired by practical applications. Numerical experiments indicate that the resulting algorithms are considerably better than the previous versions. Thus, they offer a reasonable alternative to many currently available stochastic algorithms, especially for problems requiring direct search type methods. 相似文献
13.
Simulated annealing for constrained global optimization 总被引:10,自引:0,他引:10
Hide-and-Seek is a powerful yet simple and easily implemented continuous simulated annealing algorithm for finding the maximum of a continuous function over an arbitrary closed, bounded and full-dimensional body. The function may be nondifferentiable and the feasible region may be nonconvex or even disconnected. The algorithm begins with any feasible interior point. In each iteration it generates a candidate successor point by generating a uniformly distributed point along a direction chosen at random from the current iteration point. In contrast to the discrete case, a single step of this algorithm may generateany point in the feasible region as a candidate point. The candidate point is then accepted as the next iteration point according to the Metropolis criterion parametrized by anadaptive cooling schedule. Again in contrast to discrete simulated annealing, the sequence of iteration points converges in probability to a global optimum regardless of how rapidly the temperatures converge to zero. Empirical comparisons with other algorithms suggest competitive performance by Hide-and-Seek.This material is based on work supported by a NATO Collaborative Research Grant, no. 0119/89. 相似文献
14.
Romeijn H. E. Zabinsky Z. B. Graesser D. L. Neogi S. 《Journal of Optimization Theory and Applications》1999,101(2):403-427
To reduce the well-known jamming problem in global optimization algorithms, we propose a new generator for the simulated annealing algorithm based on the idea of reflection. Furthermore, we give conditions under which the sequence of points generated by this simulated annealing algorithm converges in probability to the global optimum for mixed-integer/continuous global optimization problems. Finally, we present numerical results on some artificial test problems as well as on a composite structural design problem. 相似文献
15.
Christian Kanzow 《Journal of Global Optimization》2000,16(1):1-21
We investigate the theoretical and numerical properties of two global optimization techniques for the solution of mixed complementarity problems. More precisely, using a standard semismooth Newton-type method as a basic solver for complementarity problems, we describe how the performance of this method can be improved by incorporating two well-known global optimization algorithms, namely a tunneling and a filled function method. These methods are tested and compared with each other on a couple of very difficult test examples. 相似文献
16.
Effective Heuristics for the GPS Survey Network of Malta: Simulated Annealing and Tabu Search Techniques 总被引:1,自引:0,他引:1
A GPS network can be defined as a set of stations, co-ordinated by a series of sessions formed by placing receivers on the stations. This paper shows how to search for the best order in which to observe these sessions giving the cheapest schedule. The complexity of observing GPS networks increases with their size and become highly difficult to solve effectively. To obtain good methods to solve this problem a new area of research is implemented. This area is based on developed heuristic techniques that provide an optimal or near optimal solution for large networks. Comparing their outcome in terms of solution quality and computational effort proves the performance of the developed techniques. 相似文献
17.
一种改进的禁忌搜索算法及其在连续全局优化中的应用 总被引:2,自引:1,他引:1
禁忌搜索算法是一种元启发式的全局优化算法,是局部搜索算法的一种推广,已被成功地应用于许多组合优化问题中。本文针对有界闭区域上的连续函数全局优化问题,提出了一种改进的禁忌搜索算法,并进行了理论分析和数值实验。数值实验表明,对于连续函数全局优化问题的求解该算法是可行有效的,并且结构简单,迭代次数较少,是一种较好的全局启发式优化算法。 相似文献
18.
考虑了一种矩形优化排样系统中遗传算法和模拟退火算法的结合算法.首先建立了该系统的通用数学模型.然后给出了求解该问题的遗传模拟退火算法.最后用VC++6.0模拟算例的结果表明该算法是一种行之有效的方法. 相似文献
19.
求解全局优化问题的填充函数算法 总被引:1,自引:0,他引:1
填充函数法是求解多变量、多极值函数全局优化问题的有效方法.这种方法的关键是构造填充函数.本文在无Lipschitz连续条件下,对一般无约束最优化问题提出了一类单参数填充函数.讨论了其填充性质,并设计了一个求解约束全局优化问题的填充函数算法,数值实验表明,算法是有效的. 相似文献
20.
Monotone optimization problems are an important class of global optimization problems with various applications. In this paper,
we propose a new exact method for monotone optimization problems. The method is of branch-and-bound framework that combines
three basic strategies: partition, convexification and local search. The partition scheme is used to construct a union of
subboxes that covers the boundary of the feasible region. The convexification outer approximation is then applied to each
subbox to obtain an upper bound of the objective function on the subbox. The performance of the method can be further improved
by incorporating the method with local search procedure. Illustrative examples describe how the method works. Computational
results for small randomly generated problems are reported.
Dedicated to Professor Alex Rubinov on the occasion of his 65th birthday. The authors appreciate very much the discussions
with Professor Alex Rubinov and his suggestion of using local search. Research supported by the National Natural Science Foundation
of China under Grants 10571116 and 10261001, and Guangxi University Scientific Research Foundation (No. X051022). 相似文献