共查询到20条相似文献,搜索用时 46 毫秒
1.
E J Anderson 《The Journal of the Operational Research Society》2002,53(6):630-636
When local search methods are applied to combinatorial optimisation problems it is the characteristics of the solution surface that determine the effectiveness of the method. This paper aims to advance our understanding of solution surface characteristics. The focus is on the basin of attraction associated with each local minimum; that is the set of solutions from which a particular local minimum is reached by following downhill local search. A Markov chain model is proposed for the behaviour of the function values occurring in a random walk on the solution surface. The probability transition matrix can be estimated and this is used to estimate both the shape and the size of the basins of attraction. In order to test this approach a study is made of the problem of minimising weighted flowtime on unrelated parallel machines. 相似文献
2.
Typically local search methods for solving constraint satisfaction problems such as GSAT, WalkSAT, DLM, and ESG treat the
problem as an optimisation problem. Each constraint contributes part of a penalty function in assessing trial valuations.
Local search examines the neighbours of the current valuation, using the penalty function to determine a “better” neighbour
valuation to move to, until finally a solution which satisfies all the constraints is found. In this paper we investigate
using some of the constraints as “hard” constraints, that are always satisfied by every trial valuation visited, rather than
as part of a penalty function. In this way these constraints reduce the possible neighbours in each move and also the overall
search space. The treating of some constraints as hard requires that the space of valuations that are satisfied is “connected”
in order to guarantee that a solution can be found from any starting position within the region; thus the concept of islands
and the name “island confinement method” arises. Treating some constraints as hard provides new difficulties for the search
mechanism since the search space becomes more jagged, and there are more deep local minima. A new escape strategy is needed.
To demonstrate the feasibility and generality of our approach, we show how the island confinement method can be incorporated
in, and significantly improve, the search performance of two successful local search procedures, DLM and ESG, on SAT problems
arising from binary CSPs.
A preliminary version of this paper appeared in AAAI’2002. 相似文献
3.
This paper describes the development of a novel metaheuristic that combines an electromagnetic-like mechanism (EM) and the
great deluge algorithm (GD) for the University course timetabling problem. This well-known timetabling problem assigns lectures
to specific numbers of timeslots and rooms maximizing the overall quality of the timetable while taking various constraints
into account. EM is a population-based stochastic global optimization algorithm that is based on the theory of physics, simulating
attraction and repulsion of sample points in moving toward optimality. GD is a local search procedure that allows worse solutions
to be accepted based on some given upper boundary or ‘level’. In this paper, the dynamic force calculated from the attraction-repulsion
mechanism is used as a decreasing rate to update the ‘level’ within the search process. The proposed method has been applied
to a range of benchmark university course timetabling test problems from the literature. Moreover, the viability of the method
has been tested by comparing its results with other reported results from the literature, demonstrating that the method is
able to produce improved solutions to those currently published. We believe this is due to the combination of both approaches
and the ability of the resultant algorithm to converge all solutions at every search process. 相似文献
4.
In this paper a new heuristic hybrid technique for bound-constrained global optimization is proposed. We developed iterative algorithm called GLPτS that uses genetic algorithms, LPτ low-discrepancy sequences of points and heuristic rules to find regions of attraction when searching a global minimum of an objective function. Subsequently Nelder–Mead Simplex local search technique is used to refine the solution. The combination of the three techniques (Genetic algorithms, LPτO Low-discrepancy search and Simplex search) provides a powerful hybrid heuristic optimization method which is tested on a number of benchmark multimodal functions with 10–150 dimensions, and the method properties – applicability, convergence, consistency and stability are discussed in detail. 相似文献
5.
Generalized hill climbing algorithms provide a framework to describe and analyze metaheuristics for addressing intractable discrete optimization problems. The performance of such algorithms can be assessed asymptotically, either through convergence results or by comparison to other algorithms. This paper presents necessary and sufficient convergence conditions for generalized hill climbing algorithms. These conditions are shown to be equivalent to necessary and sufficient convergence conditions for simulated annealing when the generalized hill climbing algorithm is restricted to simulated annealing. Performance measures are also introduced that permit generalized hill climbing algorithms to be compared using random restart local search. These results identify a solution landscape parameter based on the basins of attraction for local optima that determines whether simulated annealing or random restart local search is more effective in visiting a global optimum. The implications and limitations of these results are discussed. 相似文献
6.
The effectiveness of local search algorithms on discrete optimization problems is influenced by the choice of the neighborhood function. A neighborhood function that results in all local minima being global minima is said to have zero L-locals. A polynomially sized neighborhood function with zero L-locals would ensure that at each iteration, a local search algorithm would be able to find an improving solution or conclude that the current solution is a global minimum. This paper presents a recursive relationship for computing the number of neighborhood functions over a generic solution space that results in zero L-locals. Expressions are also given for the number of tree neighborhood functions with zero L-locals. These results provide a first step towards developing expressions that are applicable to discrete optimization problems, as well as providing results that add to the collection of solved graphical enumeration problems. 相似文献
7.
D. W. Bulger 《Journal of Optimization Theory and Applications》2007,133(3):289-301
Grover’s quantum algorithm promises a quadratic acceleration for any problem formulable as a search. For unstructured search
problems, its implementation and performance are well understood. The curse of dimensionality and the intractability of the
general global optimization problem require any identifiable structure or regularity to be incorporated into a solution method.
This paper addresses the application of Grover’s algorithm when a local search technique is available, thereby combining the
quadratic acceleration with the acceleration seen in the multistart method.
The author thanks Dr. Bill Baritompa for helpful discussions. 相似文献
8.
This paper gives a quantum algorithm for global optimization. The heart of such approaches employ Grover’s database search
(1996; Phys Rev Lett 79(23):4709–4712, 1997a; 79(2):325–328, 1997b). Chi and Kim (1998) show that when the phases of the generalized Grover database search operator are optimally chosen, it is capable of finding
a solution by a single query. To apply this method to global optimization requires knowledge of the number of marked points
m to calculate the optimal phases, but this value is seldom known. This paper focuses on overcoming this hurdle by showing
that an estimate of the optimal phases can be found and used to replace the optimal phases while maintaining a high probability
of finding a solution. Merging this finding with a recently discovered dynamic quantum global optimization algorithm (BBW2D)
that reduces the problem to finding successively improving regions using Grover’s search, we present a hybrid method that
improves the efficiency and reduces the variance of the search algorithm when empirically compared to other existing quantum
search algorithms. 相似文献
9.
Experiments with a new selection criterion in a fast interval optimization algorithm 总被引:3,自引:0,他引:3
Usually, interval global optimization algorithms use local search methods to obtain a good upper (lower) bound of the solution. These local methods are based on point evaluations. This paper investigates a new local search method based on interval analysis information and on a new selection criterion to direct the search. When this new method is used alone, the guarantee to obtain a global solution is lost. To maintain this guarantee, the new local search method can be incorporated to a standard interval GO algorithm, not only to find a good upper bound of the solution, but also to simultaneously carry out part of the work of the interval B&B algorithm. Moreover, the new method permits improvement of the guaranteed upper bound of the solution with the memory requirements established by the user. Thus, the user can avoid the possible memory problems arising in interval GO algorithms, mainly when derivative information is not used. The chance of reaching the global solution with this algorithm may depend on the established memory limitations. The algorithm has been evaluated numerically using a wide set of test functions which includes easy and hard problems. The numerical results show that it is possible to obtain accurate solutions for all the easy functions and also for the investigated hard problems. 相似文献
10.
There is a lack of a representative set of test problems for comparing global optimization methods. To remedy this a classification of essentially unconstrained global optimization problems into unimodal, easy, moderately difficult, and difficult problems is proposed. The problem features giving this classification are the chance to miss the region of attraction of the global minimum, embeddedness of the global minimum, and the number of minimizers. The classification of some often used test problems are given and it is recognized that most of them are easy and some even unimodal. Global optimization solution techniques treated are global, local, and adaptive search and their use for tackling different classes of problems is discussed. The problem of fair comparison of methods is then adressed. Further possible components of a general global optimization tool based on the problem classes and solution techniques is presented. 相似文献
11.
Inverse problems in geophysics are usually described as data misfit minimization problems, which are difficult to solve because
of various mathematical features, such as multi-parameters, nonlinearity and ill-posedness. Local optimization based on function
gradient can not guarantee to find out globally optimal solutions, unless a starting point is sufficiently close to the solution.
Some global optimization methods based on stochastic searching mechanisms converge in the limit to a globally optimal solution
with probability 1. However, finding the global optimum of a complex function is still a great challenge and practically impossible
for some problems so far. This work develops a multiscale deterministic global optimization method which divides definition
space into sub-domains. Each of these sub-domains contains the same local optimal solution. Local optimization methods and
attraction field searching algorithms are combined to determine the attraction basin near the local solution at different
function smoothness scales. With Multiscale Parameter Space Partition method, all attraction fields are to be determined after
finite steps of parameter space partition, which can prevent redundant searching near the known local solutions. Numerical
examples demonstrate the efficiency, global searching ability and stability of this method. 相似文献
12.
On the Design of Optimization Strategies Based on Global Response Surface Approximation Models 总被引:1,自引:0,他引:1
Striking the correct balance between global exploration of search spaces and local exploitation of promising basins of attraction
is one of the principal concerns in the design of global optimization algorithms. This is true in the case of techniques based
on global response surface approximation models as well. After constructing such a model using some initial database of designs
it is far from obvious how to select further points to examine so that the appropriate mix of exploration and exploitation
is achieved. In this paper we propose a selection criterion based on the expected improvement measure, which allows relatively
precise control of the scope of the search. We investigate its behavior through a set of artificial test functions and two
structural optimization problems. We also look at another aspect of setting up search heuristics of this type: the choice
of the size of the database that the initial approximation is built upon. 相似文献
13.
Alexander G. Nikolaev Sheldon H. Jacobson Shane N. Hall Darrall Henderson 《Computational Optimization and Applications》2011,49(3):407-433
This paper presents a framework for analyzing and comparing sub-optimal performance of local search algorithms for hard discrete
optimization problems. The β-acceptable solution probability is introduced that captures how effectively an algorithm has performed to date and how effectively
an algorithm can be expected to perform in the future. Using this probability, the necessary conditions for a local search
algorithm to converge in probability to β-acceptable solutions are derived. To evaluate and compare the effectiveness of local search algorithms, two estimators for
the expected number of iterations to visit a β-acceptable solution are obtained. Computational experiments are reported with simulated annealing and tabu search applied
to four small traveling salesman problem instances, and the Lin-Kernighan-Helsgaun algorithm applied to eight medium to large
traveling salesman problem instances (all with known optimal solutions), to illustrate the application of these estimators. 相似文献
14.
We study a “hard” optimization problem for metaheuristic search, where a natural neighborhood (that consists of moves for
flipping the values of zero-one variables) confronts two local optima, separated by a maximum possible number of moves in
the feasible space. Once a descent method reaches the first local optimum, all sequences of feasible moves to reach the second,
which is the global optimum, must ultimately pass through solutions that are progressively worse until reaching the worst
solution of all, which is adjacent to the global optimum. 相似文献
15.
In this paper we present a chaos-based evolutionary algorithm (EA) for solving nonlinear programming problems named chaotic genetic algorithm (CGA). CGA integrates genetic algorithm (GA) and chaotic local search (CLS) strategy to accelerate the optimum seeking operation and to speed the convergence to the global solution. The integration of global search represented in genetic algorithm and CLS procedures should offer the advantages of both optimization methods while offsetting their disadvantages. By this way, it is intended to enhance the global convergence and to prevent to stick on a local solution. The inherent characteristics of chaos can enhance optimization algorithms by enabling it to escape from local solutions and increase the convergence to reach to the global solution. Twelve chaotic maps have been analyzed in the proposed approach. The simulation results using the set of CEC’2005 show that the application of chaotic mapping may be an effective strategy to improve the performances of EAs. 相似文献
16.
17.
A. É. Filippov 《Theoretical and Mathematical Physics》1998,117(3):1423-1433
We investigate the global phase-portrait structure of a local version of the exact renormalization group (RG) equation for
a fluctuating scalar field of the order parameter. All the physical branches of the RG equation solution for the fixed points
belong to the attractor subspace to which the local density of the Ginzburg-Landau-Wilson functional is attracted for largely
arbitrary initial configurations. The solution of the RG equation corresponding to the nontrivial fixed point determining
the critical behavior under the second-order phase transition is a fixed saddle point of this attractor subspace separating
the attraction domains of two stable solutions corresponding to the high- and low-temperature thermodynamic regimes.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 3, pp. 397–410, December, 1998. 相似文献
18.
Gerald L. Thompson 《Computational Optimization and Applications》2002,22(3):351-367
In this paper a local integral simplex algorithm will be described which, starting with the initial tableau of a set partitioning problem, makes pivots using the pivot on one rule until no more such pivots are possible because a local optimum has been found. If the local optimum is also a global optimum the process stops. Otherwise, a global integral simplex algorithm creates and solves the problems in a search tree consisting of a polynomial number of subproblems, subproblems of subproblems, etc. The solution to at least one of these subproblems is guaranteed to be an optimal solution to the original problem. If that solution has a bounded objective then it is an optimal set partitioning solution of the original problem, but if it has an unbounded objective then the original problem has no feasible solution. It will be shown that the total number of pivots required for the global integral simplex method to solve a set partitioning problem having m rows, where m is an arbitrary but fixed positive integer, is bounded by a polynomial function of n.A method for programming the algorithms in this paper to run on parallel computers is discussed briefly. 相似文献
19.
Consider the multi-homogeneous homotopy continuation method for solving a system of polynomial equations. For any partition of variables, the multi-homogeneous Bézout number bounds the number of isolated solution curves one has to follow in the method. This paper presents a local search method for finding a partition of variables with minimal multi-homogeneous Bézout number. As with any other local search method, it may give a local minimum rather than the minimum over all possible homogenizations. Numerical examples show the efficiency of this local search method.
20.
Random search technique is the simplest one of the heuristic algorithms. It is stated in the literature that the probability of finding global minimum is equal to 1 by using the basic random search technique, but it takes too much time to reach the global minimum. Improving the basic random search technique may decrease the solution time. In this study, in order to obtain the global minimum fastly, a new random search algorithm is suggested. This algorithm is called as the Dynamic Random Search Technique (DRASET). DRASET consists of two phases, which are general search and local search based on general solution. Knowledge related to the best solution found in the process of general search is kept and then that knowledge is used as initial value of local search. DRASET’s performance was experimented with 15 test problems and satisfactory results were obtained. 相似文献