It is called alignment probability in OO and denoted by. The research of solution quality evaluation method transfers from the value performance to the ordinal performance, after the definition of the good enough set, selected set, and alignment probability introduced.
Based on this knowledge, Shen et al. So we can use OO ruler to qualify the ordinal performance of solution. One of the intuitive understandings of OO ruler is that uniform samples are taken out from the whole search space and evaluated with a crude but computationally easy model when applying OO. After ordering via the crude performance estimates, the lined-up uniform samples can be seen as an approximate ruler.
By comparing the heuristic design with such a ruler, we can quantify the heuristic design, just as we measure the length of an object with a ruler. If the OO ruler gets from all the solutions, it is an accurate ruler. But this is obviously an ideal situation for practical problems.
It is proved that approximate OO ruler is also effective. Theorem 1 see [ 17 ]. If the solution obtained by optimization algorithm is better than solution of selected set obtained by uniform sampling, we can judge that the solution belongs to the top of the search space at least.
Experimental Methods for the Analysis of Optimization Algorithms (Electronic book text)
And the type II error probability is not larger than. The relation between , , , and is determined by where represents the number of different choices of designed out of distinguished ones. In the case of given parameters of and , we can get relation between and through the list method. For an arbitrary solution obtained by heuristic algorithm, we only need to compare it whether satisfies the conditions of Theorem 1 , then we can make the corresponding judgment, so as to realize the evaluation ordinal performance of solution.
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But OO ruler has a premise. To get OO ruler, uniform sampling for search space is needed. It is also prerequisite for OO. The so-called uniform sampling refers to the same probability of getting arbitrary solution. It is also the reason why the uniform sampling can provide quantitative reference. But, for some problems, it is difficult to achieve uniform sampling, and thus it will not be able to get OO ruler.
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In addition, the price of getting OO ruler for huge solution space is very high. These two problems limit the application of OO ruler in solution evaluation. However, the introduction of ordinal performance has great inspiration for the research of solution quality evaluation for SI. In this section, we take traveling salesman problem TSP as an example to describe experimental analysis method of solution quality evaluation.
For SI, the feature of the algorithm itself determines that the sampling method in the search space is not uniform. Especially by the partial reinforcement effect, it makes the algorithm more and more concentrated in certain regions. So it is not suitable for evaluating method directly using OO ruler.
In addition, the algorithm produces a large number of feasible solutions. The feasible solution contains the search characteristics of some algorithms and the distribution of the solution space.
Experimental Methods for the Analysis of Optimization Algorithms
To obtain the hidden information and its rational utilization through some analysis methods, we need to do some research. It plays an important role in the research of qualtiy evaluation and improving the algorithm performance. Based on the above analysis, this paper presents a general framework of the quality evaluation method for SI. The framework contains three procedures. First, to get some internal approximate uniform subclass, using cluster method, the solution samples corresponding to selected subset of OO were homogeneous processing.
Second, discrete probability distribution solution samples of each subclass and the scale relationship of the subclass are estimated in the fitness space.
Based on the characteristics of the subclass, the presupposition ratio of the good enough set is distributed to each subclass. Last, alignment probability is calculated according to the model of solution quality evaluation, so as to complete the evaluation of the solution quality.
According to the characteristics of discrete space, uniform clustering of samples is that obtaining probability of solution is approximating same. Compared with the continuous space, clustering is very different from discrete space. General discrete spatial distance features are defined with the question, and not as the continuous space as a distance to define general way.
This makes clustering method based on grid no longer applicable, which is used in continuous space such as density clustering and clustering method based on grid. And the huge solution sample set also limits the use of some special clustering method.
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- THE MIRACLE OF THE MISSING PUPPIES.
- Experimental Physics-II (cool Physics Book 2);
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Therefore, we need to design a suitable and efficient clustering algorithm based on demand. Approximate sampling probability is the purpose of clustering. The approximate sampling probability here refers to the neighbor characteristics including the distance and number of nearest neighbors consistent approximation. A feasible method for TSP is to calculate the distance between all solution samples.
Then clustering is done according to the nearest neighbor statistical feature of each sample distance. But it is only applicable to the small size of the solution sample. Another possible method is that the clustering centers are selected from the best solutions. The distance is calculated between each feasible solution and the cluster center. Then the solution samples are clustered according to the distance. The calculation complexity of this algorithm is low. It is more suitable for clustering large scale solution samples.
In the next section, we use this clustering method. The solution alignment probability is calculated using a priori ratio of the good enough set the ration between the good enough set and search space in OO.
- A Solution Quality Assessment Method for Swarm Intelligence Optimization Algorithms;
- A Solution Quality Assessment Method for Swarm Intelligence Optimization Algorithms.
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The ratio of each kind of the good enough sets is needed to know after clustering. The prior ratio requires decomposing prior ratio of each class. This decomposition has a certain relationship with each class distribution of samples and the class size. Therefore, the distribution characteristics of solution in the fitness value, as well as proportional relation of class size, are needed to estimate.
Estimation of distribution of solution in the fitness value is problem of one-dimensional distribution sequence estimation. The purpose of distribution estimation is to obtain the good enough set distribution. If the fitness value is arranged according to the order from small to large, ordered performance curve OPC can be obtained. For the minimization problem, the good enough set is in the first half of the OPC. To obtain a true estimation of the good enough set, you need to consider the types of OPC. The original search space after clustering is divided into approximate uniform partition.
Search space , the good enough set , and selected set of each partition and search space , good enough set , and selected set of the original search space have the following correspondence in the collection and base: Since the probability of any feasible solution pumped into each subclass is the same, for a sampling result has. In this paper, we only concern the selected set whether has at least one solution in good enough set. So we can draw the following conclusions: The main steps to get the evaluation method by the above analysis are described in Algorithm 1. A two-phase local search for the biobjective traveling salesman problem L.
A comparison of the performance of different metaheuristics on the timetabling problem O. Empirical analysis of tabu search for the lexicographic optimization of the examination timetabling problem L. A racing algorithm for configuring metaheuristics M. A study of examination timetabling with multiobjective evolutionary algorithms L.
Quadratic scalarization for bi-objective optimization problems and the rectangular knapsack problem B. Finding representations for an unconstrained bi-objective combinatorial optimization problem A Jesus, L. Hypervolume maximizing representation for the biobjective knapsack problem: The rectangular knapsack problem: Hypervolume maximizing representation B.
Techniques for solution set compression in multiobjective optimization J. Dry climate as a predictor of Chagas' disease irregular clusters: A covariate study L. Transforming constraints into objectives: Finding representative subsets in multiobjective discrete optimization L. Algorithms and applications of biobjective pairwise sequence alignment L. Algorithms for multiobjective sequence alignment L.
Matias 2nd Workshop on Bio-Optimization, Concise representation of nondominated sets in discrete multicriteria optimization L. Spatial cluster detection through constrained dynamic programming G. Efficient paths by local search L. Local search for the bi-objective unconstrained optimization problem A. Finding mines in a Line J. A polynomial time algorithm for a cardinality constrained multicriteria knapsack problem F.
Three algorithms for finding mines in a line L. Finding mines in a line: A biobjective formulation L. Algorithms and data structures for large scale geographic information systems: Visualisation and analysis of geographic information: Local search for bicriteria multiple sequence alignment M.
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Schenker German Conference on Bioinformatics, , Dynamic programming algorithms for biobjective sequence alignment M. Pinheiro Bioinformatics Open Days, 40, Formulation and algorithms M. Personalization of multicriteria decision support systems M. Vanderpooten Personalized Multiobjective Optimization: Educating the community U.
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