scholarly journals Inferring Future Landscapes: Sampling the Local Optima Level

2020 ◽  
Vol 28 (4) ◽  
pp. 621-641 ◽  
Author(s):  
Sarah L. Thomson ◽  
Gabriela Ochoa ◽  
Sébastien Verel ◽  
Nadarajen Veerapen
Keyword(s):  
Fitness Landscape ◽  
Quadratic Assignment Problem ◽  
Real Life ◽  
Quadratic Assignment ◽  
Search Performance ◽  
Local Optima ◽  
Sampling Algorithms ◽  
Local Optima Networks ◽  
Almost All ◽  
Construction Algorithms

Connection patterns among Local Optima Networks (LONs) can inform heuristic design for optimisation. LON research has predominantly required complete enumeration of a fitness landscape, thereby restricting analysis to problems diminutive in size compared to real-life situations. LON sampling algorithms are therefore important. In this article, we study LON construction algorithms for the Quadratic Assignment Problem (QAP). Using machine learning, we use estimated LON features to predict search performance for competitive heuristics used in the QAP domain. The results show that by using random forest regression, LON construction algorithms produce fitness landscape features which can explain almost all search variance. We find that LON samples better relate to search than enumerated LONs do. The importance of fitness levels of sampled LONs in search predictions is crystallised. Features from LONs produced by different algorithms are combined in predictions for the first time, with promising results for this “super-sampling”: a model to predict tabu search success explained 99% of variance. Arguments are made for the use-case of each LON algorithm and for combining the exploitative process of one with the exploratory optimisation of the other.

Identifying Features of Fitness Landscapes and Relating Them to Problem Difficulty

2017 ◽  
Vol 25 (3) ◽  
pp. 407-437 ◽  
Author(s):  
I. Moser ◽  
M. Gheorghita ◽  
A. Aleti
Keyword(s):  
Fitness Landscape ◽  
Quadratic Assignment Problem ◽  
Combinatorial Problem ◽  
Combinatorial Problems ◽  
Quadratic Assignment ◽  
Problem Difficulty ◽  
Local Optima ◽  
Fitness Distance Correlation ◽  
Problem Instances

Complex combinatorial problems are most often optimised with heuristic solvers, which usually deliver acceptable results without any indication of the quality obtained. Recently, predictive diagnostic optimisation was proposed as a means of characterising the fitness landscape while optimising a combinatorial problem. The scalars produced by predictive diagnostic optimisation appear to describe the difficulty of the problem with relative reliability. In this study, we record more scalars that may be helpful in determining problem difficulty during the optimisation process and analyse these in combination with other well-known landscape descriptors by using exploratory factor analysis on four landscapes that arise from different search operators, applied to a varied set of quadratic assignment problem instances. Factors are designed to capture properties by combining the collinear variances of several variables. The extracted factors can be interpreted as the features of landscapes detected by the variables, but disappoint in their weak correlations with the result quality achieved by the optimiser, which we regard as the most reliable indicator of difficulty available. It appears that only the prediction error of predictive diagnostic optimisation has a strong correlation with the quality of the results produced, followed by a medium correlation of the fitness distance correlation of the local optima.

scholarly journals Local Optima Networks, Landscape Autocorrelation and Heuristic Search Performance

2012 ◽  
pp. 337-347 ◽  
Author(s):  
Francisco Chicano ◽  
Fabio Daolio ◽  
Gabriela Ochoa ◽  
Sébastien Vérel ◽  
Marco Tomassini ◽  
...  
Keyword(s):  
Heuristic Search ◽  
Search Performance ◽  
Local Optima ◽  
Local Optima Networks

scholarly journals EFFICIENT METAHEURISTIC ALGORITHMS FOR THE MULTI-STRIPE TRAVELLING SALESMAN PROBLEM

2020 ◽  
Vol 36 (3) ◽  
pp. 233-250
Author(s):  
Ban Ha Bang
Keyword(s):  
Quadratic Assignment Problem ◽  
Travelling Salesman Problem ◽  
Computation Time ◽  
Metaheuristic Algorithms ◽  
Neighborhood Search ◽  
Quadratic Assignment ◽  
Travelling Salesman ◽  
Local Optima ◽  
Benchmark Instances ◽  
Main Components

The Multi-stripe Travelling Salesman Problem (Ms-TSP) is an extension of the Travelling Salesman Problem (TSP). In the \textit{q}-stripe TSP with $q \geq 1$, the objective function sums the costs for travelling from one customer to each of the next \textit{q} customers along the tour. The resulting \textit{q}-stripe TSP generalizes the TSP and forms a special case of the Quadratic Assignment Problem. To solve medium and large size instances, a metaheuristic algorithm is proposed. The proposed algorithm has two main components, which are construction and improvement phases. The construction phase generates a solution using Greedy Randomized Adaptive Search Procedure (GRASP) while the optimization phase improves the solution with several variants of Variable Neighborhood Search, both coupled with a technique called Shaking Technique to escape from local optima. In addition, Adaptive Memory is integrated into our algorithms to balance between the diversification and intensification. To show the efficiency of our proposed metaheuristic algorithms, we extensively experiment on benchmark instances. The results indicate that the developed algorithms can produce efficient and effective solutions at a reasonable computation time.

A Modified Migrating Bird Optimization For University Course Timetabling Problem

2014 ◽  
Vol 72 (1) ◽  
Author(s):  
Lam Way Shen ◽  
Hishammuddin Asmuni ◽  
Fong Cheng Weng
Keyword(s):  
Quadratic Assignment Problem ◽  
Iterated Local Search ◽  
Quadratic Assignment ◽  
Local Optima ◽  
Course Timetabling ◽  
Timetabling Problem ◽  
University Course Timetabling ◽  
Benchmark Datasets ◽  
Course Timetabling Problem ◽  
University Course

University course timetabling problem is a dilemma which educational institutions are facing due to  various demands to be achieved in limited resources. Migrating bird optimization (MBO) algorithm is a new meta-heuristic algorithm which is inspired by flying formation of migrating birds. It has been applied successfully in tackling quadratic assignment problem and credit cards fraud detection problem. However, it was reported that MBO will get stuck in local optima easily. Therefore, a modified migrating bird optimization algorithm is proposed to solve post enrolment-based course timetabling. An improved neighbourhood sharing mechanism is used with the aim of escaping from local optima. Besides that, iterated local search is selected to be hybridized with the migrating bird optimization in order to further enhance its exploitation ability. The proposed method was tested using Socha’s benchmark datasets. The experimental results show that the proposed method outperformed the basic MBO and it is capable of producing comparable results as compared with existing methods that have been presented in literature. Indeed, the proposed method is capable of addressing university course timetabling problem and promising results were obtained.

scholarly journals The fractal geometry of fitness landscapes at the local optima level

2020 ◽  
Author(s):  
Sarah L. Thomson ◽  
Gabriela Ochoa ◽  
Sébastien Verel
Keyword(s):  
Fractal Dimension ◽  
Visual Analysis ◽  
Fitness Landscape ◽  
Fractal Dimensions ◽  
Machine Learning Techniques ◽  
Search Performance ◽  
Algorithm Performance ◽  
Local Optima ◽  
Learning Techniques ◽  
Insight Into

AbstractA local optima network (LON) encodes local optima connectivity in the fitness landscape of a combinatorial optimisation problem. Recently, LONs have been studied for their fractal dimension. Fractal dimension is a complexity index where a non-integer dimension can be assigned to a pattern. This paper investigates the fractal nature of LONs and how that nature relates to metaheuristic performance on the underlying problem. We use visual analysis, correlation analysis, and machine learning techniques to demonstrate that relationships exist and that fractal features of LONs can contribute to explaining and predicting algorithm performance. The results show that the extent of multifractality and high fractal dimensions in the LON can contribute in this way when placed in regression models with other predictors. Features are also individually correlated with search performance, and visual analysis of LONs shows insight into this relationship.

A TISSUE P SYSTEM BASED SOLUTION TO QUADRATIC ASSIGNMENT PROBLEM

2012 ◽  
Vol 23 (07) ◽  
pp. 1511-1522 ◽  
Author(s):  
YUNYUN NIU ◽  
K. G. SUBRAMANIAN ◽  
IBRAHIM VENKAT ◽  
ROSNI ABDULLAH
Keyword(s):  
Assignment Problem ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Real Life ◽  
Computation Time ◽  
Polynomial Time Algorithm ◽  
P Systems ◽  
Quadratic Assignment ◽  
P System ◽  
Combinatorial Optimization Problems

The quadratic assignment problem (QAP) is one of the fundamental combinatorial optimization problems, which models many real-life problems. However, it is considered as one of the most difficult NP-hard problems, which means that no polynomial-time algorithm is known to solve this intractable problem effectively. Even small instances of QAP may require vast computation time. In this work, a uniform cellular solution to QAP is proposed in the framework of membrane computing by using a family of recognizer tissue P systems with cell division. In the design of the solution, we encode the given instances in binary notations. The paper can be considered as a contribution to the study of considering a binary encoding of the information in P systems.

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