scholarly journals Evolutionary Squeaky Wheel Optimization: A New Framework for Analysis

2011 ◽  
Vol 19 (3) ◽  
pp. 405-428 ◽  
Author(s):  
Jingpeng Li ◽  
Andrew J. Parkes ◽  
Edmund K. Burke
Keyword(s):  
Simulated Annealing ◽  
Search Space ◽  
Simple Problem ◽  
Problem Instance ◽  
Search Process ◽  
Distribution Probability ◽  
Formal Framework ◽  
Recent Extension ◽  
New Framework ◽  
Real World Problems

Squeaky wheel optimization (SWO) is a relatively new metaheuristic that has been shown to be effective for many real-world problems. At each iteration SWO does a complete construction of a solution starting from the empty assignment. Although the construction uses information from previous iterations, the complete rebuilding does mean that SWO is generally effective at diversification but can suffer from a relatively weak intensification. Evolutionary SWO (ESWO) is a recent extension to SWO that is designed to improve the intensification by keeping the good components of solutions and only using SWO to reconstruct other poorer components of the solution. In such algorithms a standard challenge is to understand how the various parameters affect the search process. In order to support the future study of such issues, we propose a formal framework for the analysis of ESWO. The framework is based on Markov chains, and the main novelty arises because ESWO moves through the space of partial assignments. This makes it significantly different from the analyses used in local search (such as simulated annealing) which only move through complete assignments. Generally, the exact details of ESWO will depend on various heuristics; so we focus our approach on a case of ESWO that we call ESWO-II and that has probabilistic as opposed to heuristic selection and construction operators. For ESWO-II, we study a simple problem instance and explicitly compute the stationary distribution probability over the states of the search space. We find interesting properties of the distribution. In particular, we find that the probabilities of states generally, but not always, increase with their fitness. This nonmonotonocity is quite different from the monotonicity expected in algorithms such as simulated annealing.

Theoretical Convergence Guarantees for Cooperative Coevolutionary Algorithms

2010 ◽  
Vol 18 (4) ◽  
pp. 581-615 ◽  
Author(s):  
Liviu Panait
Keyword(s):  
Theoretical Foundation ◽  
Formal Model ◽  
Optimal Solution ◽  
Theoretical Work ◽  
Search Space ◽  
Simple Problem ◽  
Search Process ◽  
Coevolutionary Algorithms ◽  
Suboptimal Solutions ◽  
Speed Up

Cooperative coevolutionary algorithms have the potential to significantly speed up the search process by dividing the space into parts that can each be conquered separately. However, recent research presented theoretical and empirical arguments that these algorithms tend to converge to suboptimal solutions in the search space, and are thus not fit for optimization tasks. This paper details an extended formal model for cooperative coevolutionary algorithms, and uses it to explore possible reasons these algorithms converge to optimal or suboptimal solutions. We demonstrate that, under specific conditions, this theoretical model will converge to the globally optimal solution. The proofs provide the underlying theoretical foundation for a better application of cooperative coevolutionary algorithms. We demonstrate the practical advantages of applying ideas from this theoretical work to a simple problem domain.

An Integrated Design Optimization Approach for Quantitative and Qualitative Search Space

2003 ◽  
Author(s):  
Victor Oduguwa ◽  
Rajkumar Roy ◽  
Didier Farrugia
Keyword(s):  
Real World ◽  
Design Problem ◽  
Integrated Design ◽  
Search Space ◽  
Optimization Approach ◽  
Design Optimisation ◽  
Solution Approach ◽  
Rod Rolling ◽  
Algorithmic Engineering ◽  
Real World Problems

Most of the algorithmic engineering design optimisation approaches reported in the literature aims to find the best set of solutions within a quantitative (QT) search space of the given problem while ignoring related qualitative (QL) issues. These QL issues can be very important and by ignoring them in the optimisation search, can have expensive consequences especially for real world problems. This paper presents a new integrated design optimisation approach for QT and QL search space. The proposed solution approach is based on design of experiment methods and fuzzy logic principles for building the required QL models, and evolutionary multi-objective optimisation technique for solving the design problem. The proposed technique was applied to a two objectives rod rolling problem. The results obtained demonstrate that the proposed solution approach can be used to solve real world problems taking into account the related QL evaluation of the design problem.

scholarly journals Bootstrapping Bloch bands

2021 ◽  
Author(s):  
Serguei Tchoumakov ◽  
Serge Florens
Keyword(s):  
Search Space ◽  
Quantum Field Theories ◽  
New Techniques ◽  
Bootstrap Methods ◽  
Quantum Operator ◽  
Canonical Variables ◽  
Distribution Probability ◽  
Anharmonic Potential ◽  
Bloch Band ◽  
Band Spectra

Abstract Bootstrap methods, initially developed for solving statistical and quantum field theories, have recently been shown to capture the discrete spectrum of quantum mechanical problems, such as the single particle Schrödinger equation with an anharmonic potential. The core of bootstrap methods builds on exact recursion relations of arbitrary moments of some quantum operator and the use of an adequate set of positivity criteria. We extend this methodology to models with continuous Bloch band spectra, by considering a single quantum particle in a periodic cosine potential. We find that the band structure can be obtained accurately provided the bootstrap uses moments involving both position and momentum variables. We also introduce several new techniques that can apply generally to other bootstrap studies. First, we devise a trick to reduce by one unit the dimensionality of the search space for the variables parametrizing the bootstrap. Second, we employ statistical techniques to reconstruct the distribution probability allowing to compute observables that are analytic functions of the canonical variables. This method is used to extract the Bloch momentum, a quantity that is not readily available from the bootstrap recursion itself.

Convergence of Simulated Annealing with Feedback Temperature Schedules

1997 ◽  
Vol 11 (3) ◽  
pp. 279-304 ◽  
Author(s):  
M. Kolonko ◽  
M. T. Tran
Keyword(s):  
Simulated Annealing ◽  
Cost Function ◽  
Job Shop ◽  
Job Shop Scheduling ◽  
Optimization Method ◽  
Search Process ◽  
Local Optimum ◽  
Fixed Sequence ◽  
Temperature Parameter ◽  
The Cost

It is well known that the standard simulated annealing optimization method converges in distribution to the minimum of the cost function if the probability a for accepting an increase in costs goes to 0. α is controlled by the “temperature” parameter, which in the standard setup is a fixed sequence of values converging slowly to 0. We study a more general model in which the temperature may depend on the state of the search process. This allows us to adapt the temperature to the landscape of the cost function. The temperature may temporarily rise such that the process can leave a local optimum more easily. We give weak conditions on the temperature schedules such that the process of solutions finally concentrates near the optimal solutions. We also briefly sketch computational results for the job shop scheduling problem.

Development and research of a genetic method for the analysis and determination of the location of power grid objects

2020 ◽  
Vol 25 (1) ◽  
pp. 20-42
Author(s):  
Fedorchenko I. ◽  
◽  
Oliinyk A. ◽  
Korniienko S. ◽  
Kharchenko A. ◽  
...  
Keyword(s):  
Power Supply ◽  
Narrow Range ◽  
Search Space ◽  
Distribution Networks ◽  
Power Supplies ◽  
Search Process ◽  
Stable Convergence ◽  
Genetic Method

The problem of combinatorial optimization is considered in relation to the choice of the location of the location of power supplies when solving the problem of the development of urban distribution networks of power supply. Two methods have been developed for placing power supplies and assigning consumers to them to solve this problem. The first developed method consists in placing power supplies of the same standard sizes, and the second - of different standard sizes. The fundamental difference between the created methods and the existing ones is that the proposed methods take into account all the material of the problem and have specialized methods for coding possible solutions, modified operators of crossing and selection. The proposed methods effectively solve the problem of low inheritance, topological unfeasibility of the found solutions, as a result of which the execution time is significantly reduced and the accuracy of calculations is increased. In the developed methods, the lack of taking into account the restrictions on the placement of new power supplies is realized, which made it possible to solve the problem of applying the methods for a narrow range of problems. A comparative analysis of the results obtained by placing power supplies of the same standard sizes and known methods was carried out, and it was found that the developed method works faster than the known methods. It is shown that the proposed approach ensures stable convergence of the search process by an acceptable number of steps without artificial limitation of the search space and the use of additional expert information on the feasibility of possible solutions. The results obtained allow us to propose effective methods to improve the quality of decisions made on the choice of the location of power supply facilities in the design of urban electrical.

A Novel Non-Decreasing Temperature Based Simulated Annealing for Flow Shop Problems

2015 ◽  
Vol 764-765 ◽  
pp. 1390-1394
Author(s):  
Ruey Maw Chen ◽  
Frode Eika Sandnes
Keyword(s):  
Simulated Annealing ◽  
Flow Shop ◽  
State Of The Art ◽  
Computation Time ◽  
Search Space ◽  
Control Mechanisms ◽  
Flow Shop Problem ◽  
Simple Implementation ◽  
Two Phases ◽  
Permutation Schedule

The permutation flow shop problem (PFSP) is an NP-hard permutation sequencing scheduling problem, many meta-heuristics based schemes have been proposed for finding near optimal solutions. A simple insertion simulated annealing (SISA) scheme consisting of two phases is proposed for solving PFSP. First, to reduce the complexity, a simple insertion local search is conducted for constructing the solution. Second, to ensure continuous exploration in the search space, two non-decreasing temperature control mechanisms named Heating SA and Steady SA are introduced in a simulated annealing (SA) procedure. The Heating SA increases the exploration search ability and the Steady SA enhances the exploitation search ability. The most important feature of SISA is its simple implementation and low computation time complexity. Experimental results are compared with other state-of-the-art algorithms and reveal that SISA is able to efficiently yield good permutation schedule.

Global search in single-solution-based metaheuristics

2020 ◽  
Vol 54 (3) ◽  
pp. 275-296 ◽  
Author(s):  
Najmeh Sadat Jaddi ◽  
Salwani Abdullah
Keyword(s):  
Search Space ◽  
Population Based ◽  
Global Optimum ◽  
Global Search ◽  
Hill Climbing ◽  
Search Process ◽  
Local Optimum ◽  
Content Type ◽  
Solution Algorithms ◽  
Single Solution

PurposeMetaheuristic algorithms are classified into two categories namely: single-solution and population-based algorithms. Single-solution algorithms perform local search process by employing a single candidate solution trying to improve this solution in its neighborhood. In contrast, population-based algorithms guide the search process by maintaining multiple solutions located in different points of search space. However, the main drawback of single-solution algorithms is that the global optimum may not reach and it may get stuck in local optimum. On the other hand, population-based algorithms with several starting points that maintain the diversity of the solutions globally in the search space and results are of better exploration during the search process. In this paper more chance of finding global optimum is provided for single-solution-based algorithms by searching different regions of the search space.Design/methodology/approachIn this method, different starting points in initial step, searching locally in neighborhood of each solution, construct a global search in search space for the single-solution algorithm.FindingsThe proposed method was tested based on three single-solution algorithms involving hill-climbing (HC), simulated annealing (SA) and tabu search (TS) algorithms when they were applied on 25 benchmark test functions. The results of the basic version of these algorithms were then compared with the same algorithms integrated with the global search proposed in this paper. The statistical analysis of the results proves outperforming of the proposed method. Finally, 18 benchmark feature selection problems were used to test the algorithms and were compared with recent methods proposed in the literature.Originality/valueIn this paper more chance of finding global optimum is provided for single-solution-based algorithms by searching different regions of the search space.

Evolving Particle Swarm Optimization Implemented by a Genetic Algorithm

2008 ◽  
Vol 12 (3) ◽  
pp. 284-289 ◽  
Author(s):  
Jenn-Long Liu ◽  
Keyword(s):  
Genetic Algorithm ◽  
Particle Swarm Optimization ◽  
Social Learning ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Search Space ◽  
Design Parameters ◽  
Search Process ◽  
Swarm Optimization ◽  
Learning Rates

Particle swarm optimization (PSO) is a promising evolutionary approach related to a particle moves over the search space with velocity, which is adjusted according to the flying experiences of the particle and its neighbors, and flies towards the better and better search area over the course of search process. Although the PSO is effective in solving the global optimization problems, there are some crucial user-input parameters, such as cognitive and social learning rates, affect the performance of algorithm since the search process of a PSO algorithm is nonlinear and complex. Consequently, a PSO with well-selected parameter settings may result in good performance. This work develops an evolving PSO based on the Clerc’s PSO to evaluate the fitness of objective function and a genetic algorithm (GA) to evolve the optimal design parameters to provide the usage of PSO. The crucial design parameters studied herein include the cognitive and social learning rates as well as constriction factor for the Clerc’s PSO. Several benchmarking cases are experimented to generalize a set of optimal parameters via the evolving PSO. Furthermore, the better parameters are applied to the engineering optimization of a pressure vessel design.

Hierarchical simulated annealing vs. a Gauss‐Newton scheme applying analytical Jacobians for the solution of a source current distribution problem

2001 ◽  
Vol 20 (2) ◽  
pp. 497-506
Author(s):  
Bernhard Brandstätter ◽  
Christian Magele
Keyword(s):  
Simulated Annealing ◽  
Linear Problem ◽  
Computational Cost ◽  
Search Space ◽  
Quadratic Program ◽  
Source Current ◽  
Ill Posed ◽  
Newton Scheme ◽  
Future Work ◽  
The Magnetic Field

Considers, without loss of generality, a simple linear problem, where in a certain domain the magnetic field, generated by infinitely long conductors, whose locations as well as the currents are unknown, has to meet a certain figure. The problem is solved by applying hierarchical simulated annealing, which iteratively reduces the dimension of the search space to save computational cost. A Gauss‐Newton scheme, making use of analytical Jacobians, preceding a sequential quadratic program (SQP), will be applied as a second approach to tackle this severely ill‐posed problem. The results of these two techniques will be analyzed and discussed and some comments on future work will be given.

MEMBRANE ALGORITHM WITH BROWNIAN SUBALGORITHM AND GENETIC SUBALGORITHM

2007 ◽  
Vol 18 (06) ◽  
pp. 1353-1360 ◽  
Author(s):  
TAISHIN Y. NISHIDA
Keyword(s):  
Simulated Annealing ◽  
Approximate Solutions ◽  
Search Space ◽  
Traveling Salesman ◽  
Benchmark Problems ◽  
Wide Range ◽  
Membrane Algorithm ◽  
Thermal Movement ◽  
The Traveling Salesman Problem ◽  
Cooling Schedule

Membrane algorithms with subalgorithms inspired by simulated annealing are treated in this paper. Simulated annealing is inherently a kind of local search but it modifies a solution to a worse one with a probability determined by "temperature". The temperature of simulated annealing is changed according to "cooling schedule". On the other hand, the subalgorithm introduced here has constant temperature which is determined by the region where the subalgorithm is. It is called Brownian subalgorithm since the subalgorithm incorporates "thermal movement" of a solution in the search space but does not simulate "annealing". Computer simulations show that a membrane algorithm which has three regions and has a Brownian subalgorithm in each region can obtain very good approximate solutions for several benchmark problems of the traveling salesman problem. However, the algorithm, occasionally, gets quite bad solutions (twice as large as the optimum) for a problem. A membrane algorithm which has both Brownian and genetic subalgorithms never gets such a bad solution (only 8% worse than the optimum) for all problems examined, although, in average, it is not as good as the algorithm with Brownian only. The result indicates that membrane algorithm with subalgorithms under different approximate mechanisms may be robust under a wide range of problems.

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