Gray Box Optimization for Mk Landscapes (NK Landscapes and MAX-kSAT)

2016 ◽  
Vol 24 (3) ◽  
pp. 491-519 ◽  
Author(s):  
L. Darrell Whitley ◽  
Francisco Chicano ◽  
Brian W. Goldman
Keyword(s):  
Dynamic Programming ◽  
Real World ◽  
Optimization Problems ◽  
Test Problems ◽  
Brute Force ◽  
Local Optima ◽  
Separable Problems ◽  
Boolean Optimization ◽  
Nk Landscapes ◽  
Real World Problems

This article investigates Gray Box Optimization for pseudo-Boolean optimization problems composed of M subfunctions, where each subfunction accepts at most k variables. We will refer to these as Mk Landscapes. In Gray Box Optimization, the optimizer is given access to the set of M subfunctions. We prove Gray Box Optimization can efficiently compute hyperplane averages to solve non-deceptive problems in [Formula: see text] time. Bounded separable problems are also solved in [Formula: see text] time. As a result, Gray Box Optimization is able to solve many commonly used problems from the evolutional computation literature in [Formula: see text] evaluations. We also introduce a more general class of Mk Landscapes that can be solved using dynamic programming and discuss properties of these functions. For certain type of problems Gray Box Optimization makes it possible to enumerate all local optima faster than brute force methods. We also provide evidence that randomly generated test problems are far less structured than those found in real-world problems.

scholarly journals Nature-Inspired Algorithms in Real-World Optimization Problems

MENDEL ◽  
2017 ◽  
Vol 23 (1) ◽  
pp. 7-14 ◽  
Author(s):  
Petr Bujok ◽  
Josef Tvrdik ◽  
Radka Polakova
Keyword(s):  
Differential Evolution ◽  
Real World ◽  
Optimization Problems ◽  
Random Search ◽  
The Other ◽  
Test Problems ◽  
Strong Argument ◽  
Nature Inspired Algorithms ◽  
New Algorithms ◽  
Real World Problems

Eight popular nature inspired algorithms are compared with the blind random search and three advanced adaptive variants of differential evolution (DE) on real-world problems benchmark collected for CEC 2011 algorithms competition. The results show the good performance of the adaptive DE variants and their superiority over the other algorithms in the test problems. Some of the nature-inspired algorithms perform even worse that the blind random search in some problems. This is a strong argument for recommendation for application, where well-verified algorithm successful in competitions should be preferred instead of developing some new algorithms.

Dynamic Swarm Artificial Bee Colony Algorithm

2012 ◽  
Vol 3 (4) ◽  
pp. 19-33 ◽  
Author(s):  
Harish Sharma ◽  
Jagdish Chand Bansal ◽  
K. V. Arya ◽  
Kusum Deep
Keyword(s):  
Global Optimization ◽  
Real World ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Optimization Problems ◽  
Probabilistic Approach ◽  
Population Based ◽  
Test Problems ◽  
Local Optima ◽  
Bee Colony

Artificial Bee Colony (ABC) optimization algorithm is relatively a simple and recent population based probabilistic approach for global optimization. ABC has been outperformed over some Nature Inspired Algorithms (NIAs) when tested over test problems as well as real world optimization problems. This paper presents an attempt to modify ABC to make it less susceptible to stick at local optima and computationally efficient. In the case of local convergence, addition of some external potential solutions may help the swarm to get out of the local valley and if the algorithm is taking too much time to converge then deletion of some swarm members may help to speed up the convergence. Therefore, in this paper a dynamic swarm size strategy in ABC is proposed. The proposed strategy is named as Dynamic Swarm Artificial Bee Colony algorithm (DSABC). To show the performance of DSABC, it is tested over 16 global optimization problems of different complexities and a popular real world optimization problem namely Lennard-Jones potential energy minimization problem. The simulation results show that the proposed strategies outperformed than the basic ABC and three recent variants of ABC, namely, the Gbest-Guided ABC, Best-So-Far ABC and Modified ABC.

Review of Network Flow Algorithms David P. Williamson

2021 ◽  
Vol 52 (1) ◽  
pp. 12-15
Author(s):  
S.V. Nagaraj
Keyword(s):  
Graduate Students ◽  
Real World ◽  
Network Flow ◽  
Network Flows ◽  
Optimization Problems ◽  
Capacity Constraints ◽  
Incoming Flow ◽  
Network Flow Problems ◽  
Flow Problems ◽  
Real World Problems

This book is on algorithms for network flows. Network flow problems are optimization problems where given a flow network, the aim is to construct a flow that respects the capacity constraints of the edges of the network, so that incoming flow equals the outgoing flow for all vertices of the network except designated vertices known as the source and the sink. Network flow algorithms solve many real-world problems. This book is intended to serve graduate students and as a reference. The book is also available in eBook (ISBN 9781316952894/US$ 32.00), and hardback (ISBN 9781107185890/US$99.99) formats. The book has a companion web site www.networkflowalgs.com where a pre-publication version of the book can be downloaded gratis.

Opposition-based learning Multi-Verse Optimizer with disruption operator for optimization problems

2021 ◽  
Author(s):  
Mohammad Shehab ◽  
Laith Abualigah
Keyword(s):  
Real World ◽  
Optimization Problems ◽  
Second Stage ◽  
Opposition Based Learning ◽  
High Fitness ◽  
Fitness Value ◽  
Speed Up ◽  
Disruption Operator ◽  
The Given ◽  
Real World Problems

Abstract Multi-Verse Optimizer (MVO) algorithm is one of the recent metaheuristic algorithms used to solve various problems in different fields. However, MVO suffers from a lack of diversity which may trapping of local minima, and premature convergence. This paper introduces two steps of improving the basic MVO algorithm. The first step using Opposition-based learning (OBL) in MVO, called OMVO. The OBL aids to speed up the searching and improving the learning technique for selecting a better generation of candidate solutions of basic MVO. The second stage, called OMVOD, combines the disturbance operator (DO) and OMVO to improve the consistency of the chosen solution by providing a chance to solve the given problem with a high fitness value and increase diversity. To test the performance of the proposed models, fifteen CEC 2015 benchmark functions problems, thirty CEC 2017 benchmark functions problems, and seven CEC 2011 real-world problems were used in both phases of the enhancement. The second step, known as OMVOD, incorporates the disruption operator (DO) and OMVO to improve the accuracy of the chosen solution by giving a chance to solve the given problem with a high fitness value while also increasing variety. Fifteen CEC 2015 benchmark functions problems, thirty CEC 2017 benchmark functions problems and seven CEC 2011 real-world problems were used in both phases of the upgrade to assess the accuracy of the proposed models.

Development of a Common Platform for Testing Metamodel Based Design Optimization Methods

2013 ◽  
Author(s):  
Adel A. Younis ◽  
George H. Cheng ◽  
G. Gary Wang ◽  
Zuomin Dong
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Computation Time ◽  
Optimization Methods ◽  
Global Optimum ◽  
Test Problems ◽  
Test Bed ◽  
Test Procedures ◽  
Local Optima

Metamodel based design optimization (MBDO) algorithms have attracted considerable interests in recent years due to their special capability in dealing with complex optimization problems with computationally expensive objective and constraint functions and local optima. Conventional unimodal-based optimization algorithms and stochastic global optimization algorithms either miss the global optimum frequently or require unacceptable computation time. In this work, a generic testbed/platform for evaluating various MBDO algorithms has been introduced. The purpose of the platform is to facilitate quantitative comparison of different MBDO algorithms using standard test problems, test procedures, and test outputs, as well as to improve the efficiency of new algorithm testing and improvement. The platform consists of a comprehensive test function database that contains about 100 benchmark functions and engineering problems. The testbed accepts any optimization algorithm to be tested, and only requires minor modifications to meet the test-bed requirements. The testbed is useful in comparing the performance of competing algorithms through execution of same problems. It allows researchers and practitioners to test and choose the most suitable optimization tool for their specific needs. It also helps to increase confidence and reliability of the newly developed MBDO tools. Many new MBDO algorithms, including Mode Pursuing Sampling (MPS), Pareto Set Pursuing (PSP), and Space Exploration and Unimodal Region Elimination (SEUMRE), were tested in this work to demonstrate its functionality and benefits.

scholarly journals A Novel Parent Centric Crossover with the Log-Logistic Probabilistic Approach Using Multimodal Test Problems for Real-Coded Genetic Algorithms

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Ehtasham ul Haq ◽  
Ishfaq Ahmad ◽  
Ibrahim M. Almanjahie
Keyword(s):  
Optimization Problems ◽  
Probabilistic Approach ◽  
Population Diversity ◽  
Test Problems ◽  
Crossover Operator ◽  
Local Optima ◽  
Mutation Operators ◽  
Multiple Comparison Test ◽  
Power Mutation ◽  
Real Coded Genetic Algorithms

In this paper, a comprehensive empirical study is conducted to evaluate the performance of a new real-coded crossover operator called Fisk crossover (FX) operator. The basic aim of the proposed study is to preserve population diversity as well as to avoid local optima. In this context, a new crossover operator is designed and developed which is linked with Log-logistic probability distribution. For its global performance, a realistic comparison is made between FX versus double Pareto crossover (DPX), Laplace crossover (LX), and simulated binary crossover (SBX) operators. Moreover, these crossover operators are also used in conjunction with three mutation operators called power mutation (PM), Makinen, Periaux, and Toivanen mutation (MPTM), and nonuniform mutation (NUM) for inclusive evaluation. The performance of probabilistic-based algorithms is tested on a set of twenty-one well-known nonlinear optimization benchmark functions with diverse features. The empirical results show a substantial dominance of FX over other crossover operators with authentication of performance index (PI). Moreover, we also examined the significance of the proposed crossover scheme by administrating ANOVA and Gabriel pairwise multiple comparison test. Finally, the statistically significant results of the proposed crossover scheme have a definite edge over the other schemes, and it is also expected that FX has a great potential to solve complex optimization problems.

AEGA: A New Real-Coded Genetic AlgorithmTaking Account of Extrapolation

2016 ◽  
Vol 20 (3) ◽  
pp. 429-437 ◽  
Author(s):  
Kento Uemura ◽  
◽  
Isao Ono
Keyword(s):  
Real World ◽  
Optimization Problems ◽  
Function Optimization ◽  
Benchmark Problems ◽  
Lens Design ◽  
Real World Problem ◽  
Real Coded Genetic Algorithm ◽  
Stable Manner ◽  
Ridge Structures ◽  
Real World Problems

This study proposes a new real-coded genetic algorithm (RCGA) taking account of extrapolation, which we call adaptive extrapolation RCGA (AEGA). Real-world problems are often formulated as black-box function optimization problems and sometimes have ridge structures and implicit active constraints. mAREX/JGG is one of the most powerful RCGAs that performs well against these problems. However, mAREX/JGG has a problem of search inefficiency. To overcome this problem, we propose AEGA that generates offspring outside the current population in a more stable manner than mAREX/JGG. Moreover, AEGA adapts the width of the offspring distribution automatically to improve its search efficiency. We evaluate the performance of AEGA using benchmark problems and show that AEGA finds the optimum with fewer evaluations than mAREX/JGG with a maximum reduction ratio of 45%. Furthermore, we apply AEGA to a lens design problem that is known as a difficult real-world problem and show that AEGA reaches the known best solution with approximately 25% fewer evaluations than mAREX/JGG.

scholarly journals A Survey on Meta-heuristic Algorithms for Global Optimization Problems

2020 ◽  
pp. 48-60
Author(s):  
Abdel Nasser H. Zaied ◽  
Mahmoud Ismail ◽  
Salwa El-Sayed ◽  
◽  
◽  
...  
Keyword(s):  
Global Optimization ◽  
Real World ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Traditional Methods ◽  
Complex Problems ◽  
First Choice ◽  
Important Field ◽  
Real World Problems

Optimization is a more important field of research. With increasing the complexity of real-world problems, the more efficient and reliable optimization algorithms vital. Traditional methods are unable to solve these problems so, the first choice for solving these problems becomes meta-heuristic algorithms. Meta-heuristic algorithms proved their ability to solve more complex problems and giving more satisfying results. In this paper, we introduce the more popular meta-heuristic algorithms and their applications in addition to providing the more recent references for these algorithms.

A novel chaotic bat algorithm based on catfish effect for engineering optimization problems

2019 ◽  
Vol 36 (5) ◽  
pp. 1744-1763
Author(s):  
Wensheng Xiao ◽  
Qi Liu ◽  
Linchuan Zhang ◽  
Kang Li ◽  
Lei Wu
Keyword(s):  
Numerical Experiment ◽  
Real World ◽  
Optimization Problems ◽  
Bat Algorithm ◽  
Optimization Method ◽  
Engineering Optimization ◽  
Local Optima ◽  
Content Type ◽  
Engineering Design Problems ◽  
Engineering Optimization Problems

PurposeBat algorithm (BA) is a global optimization method, but has a worse performance on engineering optimization problems. The purpose of this study is to propose a novel chaotic bat algorithm based on catfish effect (CE-CBA), which can effectively deal with optimization problems in real-world applications.Design/methodology/approachIncorporating chaos strategy and catfish effect, the proposed algorithm can not only enhance the ability for local search but also improve the ability to escape from local optima traps. On the one hand, the performance of CE-CBA has been evaluated by a set of numerical experiment based on classical benchmark functions. On the other hand, five benchmark engineering design problems have been also used to test CE-CBA.FindingsThe statistical results of the numerical experiment show the significant improvement of CE-CBA compared with the standard algorithms and improved bat algorithms. Moreover, the feasibility and effectiveness of CE-CBA in solving engineering optimization problems are demonstrated.Originality/valueThis paper proposed a novel BA with two improvement strategies including chaos strategy and catfish effect for the first time. Meanwhile, the proposed algorithm can be used to solve many real-world engineering optimization problems with several decision variables and constraints.

Decomposition Algorithms for a Multi-Hard Problem

2018 ◽  
Vol 26 (3) ◽  
pp. 507-533 ◽  
Author(s):  
M. R. Przybylek ◽  
A. Wierzbicki ◽  
Z. Michalewicz
Keyword(s):  
Systematic Study ◽  
Real World ◽  
Optimization Problems ◽  
Decomposition Algorithms ◽  
Hard Problem ◽  
The Past ◽  
Real World Problems

Real-world optimization problems have been studied in the past, but the work resulted in approaches tailored to individual problems that could not be easily generalized. The reason for this limitation was the lack of appropriate models for the systematic study of salient aspects of real-world problems. The aim of this article is to study one of such aspects: multi-hardness. We propose a variety of decomposition-based algorithms for an abstract multi-hard problem and compare them against the most promising heuristics.

Sign in / Sign up

Export Citation Format

Share Document