Probabilistic Model-building Genetic Algorithms Research Articles

On the Choice of the Update Strength in Estimation-of-Distribution Algorithms and Ant Colony Optimization

Probabilistic model-building Genetic Algorithms (PMBGAs) are a class of metaheuristics that evolve probability distributions favoring optimal solutions in the underlying search space by repeatedly sampling from the distribution and updating it according to promising samples. We provide a rigorous runtime analysis concerning the update strength, a vital parameter in PMBGAs such as the step size 1 / K in the so-called compact Genetic Algorithm (cGA) and the evaporation factor rho in ant colony optimizers (ACO). While a large update strength is desirable for exploitation, there is a general trade-off: too strong updates can lead to unstable behavior and possibly poor performance. We demonstrate this trade-off for the cGA and a simple ACO algorithm on the well-known OneMax function. More precisely, we obtain lower bounds on the expected runtime of {varOmega }(Ksqrt{n} + n log n) and {varOmega }(sqrt{n}/rho + n log n), respectively, suggesting that the update strength should be limited to 1/K, rho = O(1/(sqrt{n} log n)). In fact, choosing 1/K, rho sim 1/(sqrt{n}log n) both algorithms efficiently optimize OneMax in expected time {varTheta }(n log n). Our analyses provide new insights into the stochastic behavior of PMBGAs and propose new guidelines for setting the update strength in global optimization.

A PMBGA to Optimize the Selection of Rules for Job Shop Scheduling Based on the Giffler‐Thompson Algorithm

Most existing research on the job shop scheduling problem has been focused on the minimization of makespan (i.e., the completion time of the last job). However, in the fiercely competitive market nowadays, delivery punctuality is more important for maintaining a high service reputation. So in this paper, we aim at solving job shop scheduling problems with the total weighted tardiness objective. Several dispatching rules are adopted in the Giffler‐Thompson algorithm for constructing active schedules. It is noticeable that the rule selections for scheduling consecutive operations are not mutually independent but actually interrelated. Under such circumstances, a probabilistic model‐building genetic algorithm (PMBGA) is proposed to optimize the sequence of selected rules. First, we use Bayesian networks to model the distribution characteristics of high‐quality solutions in the population. Then, the new generation of individuals is produced by sampling the established Bayesian network. Finally, some elitist individuals are further improved by a special local search module based on parameter perturbation. The superiority of the proposed approach is verified by extensive computational experiments and comparisons.

Towards the Maintenance of Population Diversity: A Hybrid Probabilistic Model Building Genetic Network Programming

Some researchers have investigated that the diversity loss will significantly decrease the performance of Probabilistic Model Building Genetic Algorithm (PMBGA), especially under large search space, leading to the premature convergence and local optimum. However, few work has been done on the diversity maintenance in the Probabilistic Model Building Evolutionary Algorithms (PMBEAs) with more complex chromosome structures, such as tree structure based Probabilistic Model Building Genetic Programming (PMBGP) and graph structure based Probabilistic Model Building Genetic Network Programming (PMBGNP). For the PMBEAs with more complex chromosome structures, the required sample size is usually much larger than that of binary structure based PMBGA. Therefore, these algorithms usually become much more sensitive to the population diversity. In order to obtain enough population diversity, the large population size is needed, which is not the best way. In this paper, the maintenance of the population diversity is studied in PMBGNP, which is a kind of PMBEA, but has its unique characteristics because of its directed graph structure. This paper proposed a hybrid PMBGNP algorithm to maintain the population diversity to avoid the premature convergence and local optimum, and presented a theoretical analysis of the diversity loss in PMBGA, PMBGP and PMBGNP. Two techniques have been proposed for the diversity maintenance when the population size is set at not large values, which are multiple probability vectors and genetic operators. The proposed algorithm is applied and evaluated in a kind of autonomous robot, Khepera robot. The simulation study demonstrates that the proposed hybrid PMBGNP is often able to achieve a better performance than the conventional algorithms.

A hybrid local search algorithm for scheduling real-world job shops with batch-wise pending due dates

This paper aims at solving a real-world job shop scheduling problem with two characteristics, i.e., the existence of pending due dates and job batches. Due date quotation is an important decision process for contemporary companies that adopt the MTO (make to order) strategy. Although the assignment of due dates is usually performed separately with production scheduling, there exist strong interactions between the two tasks. Therefore, we integrate these two decisions into one optimization model. Meanwhile, each order placed by the customer defines a batch of jobs, for which the same due date should be set. Thus, the completion times of these jobs should be close to one another in order to reduce waiting time and cost. For this purpose, we propose a dispatching rule to synchronize their manufacturing progresses. A two-stage local search algorithm based on the PMBGA (probabilistic model-building genetic algorithm) and parameter perturbation is proposed to solve the integrated scheduling problem and its superiority is revealed by the applications to a real-world mechanical factory.

119 多数の近傍を用いた実数値型確率モデルGAの提案

Recently, several heuristic computational methods have been developed for complex real problems. Especially, PMBGAs using statistical information of the good search points have been attracted attention by many researchers and several types of PMBGAs are proposed. In this paper, a novel real-coded probabilistic model-building Genetic Algorithms (PMBGAs) which is called Multiple Neighborhoods Sampling (MNS) is proposed. PMBGAs have a issue that search points converge, while the MNS has a characteristic that search points are maintained different diversities. In the MNS, a new searching point is generated using the neighborhood area. When the neighborhood is narrow, a new search point is generated for the local search. On the other hand, when the neighborhood is wide, a new search point is generated for global search. The MNS has multiple neighborhoods whose width is different respectively. Therefore, search points do not converge and the MNS can run efficiently solution search. Through the standard test functions, the effectiveness of the MNS is examined. The results describe that the MNS shows the better performance than Simple GA.

Edge histogram based sampling with local search for solving permutation problems

A basic scheme for solving permutation problems in the framework of probabilistic model-building genetic algorithms (PMBGAs) that uses edge histogram based sampling techniques was reported in [23]. Two sampling algorithms – sampling without template,

Edge histogram based sampling with local search for solving permutation problems

A basic scheme for solving permutation problems in the framework of probabilistic model-building genetic algorithms (PMBGAs) that uses edge histogram based sampling techniques was reported in [23]....

Gene selection for classification of cancers using probabilistic model building genetic algorithm

Recently, DNA microarray-based gene expression profiles have been used to correlate the clinical behavior of cancers with the differential gene expression levels in cancerous and normal tissues. To this end, after selection of some predictive genes based on signal-to-noise (S2N) ratio, unsupervised learning like clustering and supervised learning like k-nearest neighbor ( k NN) classifier are widely used. Instead of S2N ratio, adaptive searches like Probabilistic Model Building Genetic Algorithm (PMBGA) can be applied for selection of a smaller size gene subset that would classify patient samples more accurately. In this paper, we propose a new PMBGA-based method for identification of informative genes from microarray data. By applying our proposed method to classification of three microarray data sets of binary and multi-type tumors, we demonstrate that the gene subsets selected with our technique yield better classification accuracy.

1103 分散確率モデル遺伝的アルゴリズムにおける解探索能力についての検討(OS22 最適化計算法)

Distributed Probabilistic Model-building Genetic Algorithms (DPMBGAs) are a new type of Genetic Algorithm. In the DPMBGA, when the offspring are generated, Principal Component Analysis (PCA) considers the correlations among the design variables. Moreover, this model applies the island model to maintain population diversity. The effectiveness of DPMBGA has been demonstrated through optimization of continuous functions. This paper describes the effectiveness of the parameters in the DPMBGA. Experiments indicated that these parameters are important factor for maintenance of the diversity of the population.

1310 確率モデル遺伝的アルゴリズムを用いた構造物最適化

1310 確率モデル遺伝的アルゴリズムを用いた構造物最適化

Probabilistic Model Building Based GAs in Permutation Domains Using Edge Histograms.

Recently, there has been a growing interest in developing evolutionary algorithms based on probabilistic modeling. They are called probabilistic model-building genetic algorithms (PMBGAs) or estimation of distribution algorithms (EDAs). In this scheme, the offspring population is generated according to the estimated probability density model of the parent instead of using recombination and mutation operators. In this paper, we have proposed PMBGAs in permutation domains using edge histogram based sampling algorithms (EHBSAs). Two types of sampling algorithms, without template (EHBSA/WO) and with template (EHBSA/WT), are presented. The results were tested in the TSP and showed EHBSA/WT worked fairly well with a small population size in the test problems used. It also worked better than well-known traditional two-parent recombination operators.

111 分散確率モデル遺伝的アルゴリズム

111 分散確率モデル遺伝的アルゴリズム