FDA -A Scalable Evolutionary Algorithm for the Optimization of Additively Decomposed Functions

1999 ◽  
Vol 7 (4) ◽  
pp. 353-376 ◽  
Author(s):  
Heinz Mühlenbein ◽  
Thilo Mahnig
Keyword(s):  
Genetic Algorithms ◽  
Evolutionary Algorithm ◽  
Discrete Distribution ◽  
Grid Structure ◽  
Approximate Factorization ◽  
Marginal Distributions ◽  
A Chain ◽  
Bayes Networks ◽  
Specific Assignment ◽  
Discrete Functions

The Factorized Distribution Algorithm (FDA) is an evolutionary algorithm which combines mutation and recombination by using a distribution. The distribution is estimated from a set of selected points. In general, a discrete distribution defined for n binary variables has 2n parameters. Therefore it is too expensive to compute. For additively decomposed discrete functions (ADFs) there exist algorithms which factor the distribution into conditional and marginal distributions. This factorization is used by FDA. The scaling of FDA is investigated theoretically and numerically. The scaling depends on the ADF structure and the specific assignment of function values. Difficult functions on a chain or a tree structure are solved in about O(n√n) operations. More standard genetic algorithms are not able to optimize these functions. FDA is not restricted to exact factorizations. It also works for approximate factorizations as is shown for a circle and a grid structure. By using results from Bayes networks, FDA is extended to LFDA. LFDA computes an approximate factorization using only the data, not the ADF structure. The scaling of LFDA is compared to the scaling of FDA.

New Evolutionary Algorithm Based on 2-Opt Local Search to Solve the Vehicle Routing Problem with Private Fleet and Common Carrier

2012 ◽  
pp. 125-148
Author(s):  
Jalel Euchi ◽  
Habib Chabchoub ◽  
Adnan Yassine
Keyword(s):  
Local Search ◽  
Evolutionary Algorithm ◽  
Vehicle Routing ◽  
Cost Savings ◽  
Alternative Mode ◽  
Cost Of Transport ◽  
Routing Problem ◽  
The Cost ◽  
Specific Assignment ◽  
Selection Of

Mismanagement of routing and deliveries between sites of the same company or toward external sites leads to consequences in the cost of transport. When shipping alternatives exist, the selection of the appropriate shipping alternative (mode) for each shipment may result in significant cost savings. In this paper, the authors examine a class of vehicle routing in which a fixed internal fleet is available at the warehouse in the presence of an external transporter. The authors describe hybrid Iterated Density Estimation Evolutionary Algorithm with 2-opt local search to determine the specific assignment of each tour to a private vehicle (internal fleet) or an outside carrier (external fleet). Experimental results show that this method is effective, allowing the discovery of new best solutions for well-known benchmarks.

Optimization of Multi-Modal Discrete Functions Using Genetic Algorithms

1993 ◽  
Vol 207 (1) ◽  
pp. 53-59 ◽  
Author(s):  
D T Pham ◽  
Y Yang
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Optimization Problem ◽  
Approximate Solutions ◽  
Solution Set ◽  
Preliminary Design ◽  
Potential Solution ◽  
Reproduction Cycle ◽  
Fitness Sharing ◽  
Discrete Functions

Four techniques are described which can help a genetic algorithm to locate multiple approximate solutions to a multi-modal optimization problem. These techniques are: fitness sharing, ‘eliminating’ identical solutions, ‘removing’ acceptable solutions from the reproduction cycle and applying heuristics to improve sub-standard solutions. Essentially, all of these techniques operate by encouraging genetic variety in the potential solution set. The preliminary design of a gearbox is presented as an example to illustrate the effectiveness of the proposed techniques.

Evolutionary Algorithm-Based Error Parameterization Methods for Data Assimilation

2011 ◽  
Vol 139 (8) ◽  
pp. 2668-2685 ◽  
Author(s):  
Yulong Bai ◽  
Xin Li
Keyword(s):  
Genetic Algorithms ◽  
Data Assimilation ◽  
Evolutionary Algorithm ◽  
Initial Conditions ◽  
Fitness Function ◽  
Observation Interval ◽  
Substantial Effect ◽  
Model Errors ◽  
Lorenz Model ◽  
Error Adjustment

AbstractThe methods of parameterizing model errors have a substantial effect on the accuracy of ensemble data assimilation. After a review of the current error-handling methods, a new blending error parameterization method was designed to combine the advantages of multiplicative inflation and additive inflation. Motivated by evolutionary algorithm concepts that have been developed in the control engineering field for years, the authors propose a new data assimilation method coupled with crossover principles of genetic algorithms based on ensemble transform Kalman filters (ETKFs). The numerical experiments were developed based on the classic nonlinear model (i.e., the Lorenz model). Convex crossover, affine crossover, direction-based crossover, and blending crossover data assimilation systems were consequently designed. When focusing on convex crossover and affine crossover data assimilation problems, the error adjustment factors were investigated with respect to four aspects, which were the initial conditions of the Lorenz model, the number of ensembles, observation covariance, and the observation interval. A new data assimilation system, coupled with genetic algorithms, is proposed to solve the difficult problem of the error adjustment factor search, which is usually performed using trial-and-error methods. The results show that all of the methods can adaptively obtain the best error factors within the constraints of the fitness function.

scholarly journals Genetic algorithm for binary and functional decision diagrams optimization

2018 ◽  
Vol 31 (2) ◽  
pp. 169-187
Author(s):  
Stojkovic Suzana ◽  
Velickovic Darko ◽  
Moraga Claudio
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Data Structure ◽  
Optimization Problems ◽  
Binary Decision Diagrams ◽  
Size Optimization ◽  
Decision Diagrams ◽  
Crossover Operator ◽  
Binary Decision ◽  
Discrete Functions

Decision diagrams (DD) are a widely used data structure for discrete functions representation. The major problem in DD-based applications is the DD size minimization (reduction of the number of nodes), because their size is dependent on the variables order. Genetic algorithms are often used in different optimization problems including the DD size optimization. In this paper, we apply the genetic algorithm to minimize the size of both Binary Decision Diagrams (BDDs) and Functional Decision Diagrams (FDDs). In both cases, in the proposed algorithm, a Bottom-Up Partially Matched Crossover (BU-PMX) is used as the crossover operator. In the case of BDDs, mutation is done in the standard way by variables exchanging. In the case of FDDs, the mutation by changing the polarity of variables is additionally used. Experimental results of optimization of the BDDs and FDDs of the set of benchmark functions are also presented.

Solving Truck Delivery Problems Using Integrated Evaluation Criteria Based on Neighborhood Degree and Evolutionary Algorithm

2004 ◽  
Vol 8 (3) ◽  
pp. 336-345
Author(s):  
Fangyan Dong ◽  
◽  
Kewei Chen ◽  
Eduardo Masato Iyoda ◽  
Hajime Nobuhara ◽  
...  
Keyword(s):  
Evolutionary Algorithm ◽  
Real World ◽  
Optimal Schedule ◽  
Evaluation Criteria ◽  
Food Product ◽  
Home Delivery ◽  
Computational Time ◽  
Real World Data ◽  
Conflicting Objectives ◽  
A Chain

To solve a real-world truck delivery and dispatch problem (TDDP) that involves multiple mutually conflicting objectives, such as running and loading costs, a concept of neighborhood degree (ND) and an integrated evaluation criteria (IEC) of the solution based on ND are proposed. The IEC makes the weight setting easier than by using conventional methods. To find a high-quality solution to a TDDP in practical computational time, an evolutionary algorithm is proposed. It involves 3 components: (i) a simulated annealing (SA)-based method for finding an optimal or a suboptimal route for each vehicle; (ii) an evolutionary computation (EC)-based method for finding an optimal schedule for a group of vehicles; and (iii) threshold-based evolutionary operations, utilizing the ND concept. The TDDP viewed from real-world application is formulated and the proposed algorithm is implemented on a personal computer using C++. The proposed algorithm is evaluated in 2 experiments involving real-world data representative of the TDDP, and applied to food product delivery to a chain of 46 convenience stores in Saitama Prefecture. In the 2 experiments, our proposed algorithm resulted in a better schedule (with 80%-90% shorter computational time) than a schedule produced by an expert. By incorporating application-specific evaluation criteria, the proposed algorithm is applied to problems such as home-delivery of parcels or mail, and to problems of multidepot delivery and dispatch.

scholarly journals Creating of model of genetic algorithm used to optimization of construction of jet engine element

Mechanik ◽  
2017 ◽  
Vol 90 (7) ◽  
pp. 603-605
Author(s):  
Adam Kozakiewicz ◽  
Rafał Kieszek
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Evolutionary Algorithm ◽  
Optimization Algorithm ◽  
Turbine Engines ◽  
Jet Engine ◽  
Complete Problem ◽  
Traditional Technology ◽  
Np Complete

In this paper authors show results of optimization of compressor discs in turbine engines. The problem of optimizing the thickness of the disc brought to the NP-complete problem, and solved it by using one of the genetic algorithms – evolutionary algorithm. Correctness of model and optimization algorithm were constantly checked. At the end of this paper, compressor disc created due to traditional technology and disc created by BLISK technology were compared.

scholarly journals A Study on the Optimization of Chain Supermarkets’ Distribution Route Based on the Quantum-Inspired Evolutionary Algorithm

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Bi Liang ◽  
Fengmao Lv
Keyword(s):  
Evolutionary Algorithm ◽  
Large Scale ◽  
Optimal Solution ◽  
Distribution Center ◽  
Small Scale ◽  
Optimized Distribution ◽  
A Chain ◽  
Set Up ◽  
The Mathematical Model ◽  
Better Than

The chain supermarket has become a major part of China’s retail industry, and the optimization of chain supermarkets’ distribution route is an important issue that needs to be considered for the distribution center, because for a chain supermarket it affects the logistics cost and the competition in the market directly. In this paper, analyzing the current distribution situation of chain supermarkets both at home and abroad and studying the quantum-inspired evolutionary algorithm (QEA), we set up the mathematical model of chain supermarkets’ distribution route and solve the optimized distribution route throughout QEA. At last, we take Hongqi Chain Supermarket in Chengdu as an example to perform the experiment and compare QEA with the genetic algorithm (GA) in the fields of the convergence, the optimal solution, the search ability, and so on. The experiment results show that the distribution route optimized by QEA behaves better than that by GA, and QEA has stronger global search ability for both a small-scale chain supermarket and a large-scale chain supermarket. Moreover, the success rate of QEA in searching routes is higher than that of GA.

Genetic Algorithms Applied to Discrete Distribution Fitting

2013 ◽  
Author(s):  
Valentina Colla ◽  
Gianluca Nastasi ◽  
Silvia Cateni ◽  
Marco Vannucci ◽  
Marco Vannocci
Keyword(s):  
Genetic Algorithms ◽  
Discrete Distribution ◽  
Distribution Fitting

An Experiment in Meta-Evolution

1996 ◽  
Author(s):  
Thomas Bäck
Keyword(s):  
Genetic Algorithms ◽  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Population Size ◽  
Empirical Work ◽  
Point Of View ◽  
The Self ◽  
Crossover Rate ◽  
Self Adaptation ◽  
Reasonable Choice

So far, the basic knowledge about setting up the parameters of Evolutionary Algorithms stems from a lot of empirical work and few theoretical results. The standard guidelines for parameters such as crossover rate, mutation probability, and population size as well as the standard settings of the recombination operator and selection mechanism were presented in chapter 2 for the Evolutionary Algorithms. In the case of Evolution Strategies and Evolutionary Programming, the self-adaptation mechanism for strategy parameters solves this parameterization problem in an elegant way, while for Genetic Algorithms no such technique is employed. Chapter 6 served to identify a reasonable choice of the mutation rate, but no theoretically confirmed knowledge about the choice of the crossover rate and the crossover operator is available. With respect to the optimal population size for Genetic Algorithms, Goldberg presented some theoretical arguments based on maximizing the number of schemata processed by the algorithm within fixed time, arriving at an optimal size λ* = 3 for serial implementations and extremely small string length [Gol89b]. However, as indicated in section 2.3.7 and chapter 6, it is by no means clear whether the schema processing point of view is appropriately preferred to the convergence velocity investigations presented in section 2.1.7 and chapter 6. As pointed out several times, we prefer the point of view which concentrates on a convergence velocity analysis. Consequently, the search for useful parameter settings of a Genetic Algorithm constitutes an optimization problem by itself, leading to the idea of using an Evolutionary Algorithm on a higher level to evolve optimal parameter settings of Genetic Algorithms. Due to the existence of two logically different levels in such an approach, it is reasonable to call it a meta-evolutionary algorithm. By concentrating on meta-evolution in this chapter, we will radically deviate from the biological model, where no two-level evolution process is to be observed but the self-adaptation principle can well be identified (as argued in chapter 2). However, there are several reasons why meta-evolution promises to yield some helpful insight into the working principles of Evolutionary Algorithms: First, meta-evolution provides the possibility to test whether the basic heuristic and the theoretical knowledge about parameterizations of Genetic Algorithms is also evolvable by the experimental approach, thus allowing us to confirm the heuristics or to point at alternatives.

Optimal Placement of DG Unit in Distribution System

2014 ◽  
Vol 1070-1072 ◽  
pp. 797-803
Author(s):  
Xi Wang ◽  
Gang Chen
Keyword(s):  
Evolutionary Algorithm ◽  
Distributed Generation ◽  
Distribution System ◽  
Discrete Distribution ◽  
Optimal Placement ◽  
Distribution Model ◽  
Distributed Generators ◽  
Power Injection ◽  
On Line ◽  
Line Loss

Interconnection of distributed generators (DG) has obvious impacts on line loss in distribution system and the effects depend on interconnected location, interconnected number and power injection of distributed generation. With discrete distribution model of constant power static load system accessing DG into consideration, establishes the line loss minimum as the objective function of the model and optimizes interconnected location, interconnected number and power injection of DG using a quantum inspired evolutionary algorithm. IEEE33 diffset results show that the application of the model and the quantum-inspired evolutionary algorithm can get reasonable DG interconnected location and power injection, effectively reduce the distribution system line loss.

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