A Note on Problem Difficulty Measures in Black-Box Optimization: Classification, Realizations and Predictability

Various methods have been defined to measure the hardness of a fitness function for evolutionary algorithms and other black-box heuristics. Examples include fitness landscape analysis, epistasis, fitness-distance correlations etc., all of which are relatively easy to describe. However, they do not always correctly specify the hardness of the function. Some measures are easy to implement, others are more intuitive and hard to formalize. This paper rigorously defines difficulty measures in black-box optimization and proposes a classification. Different types of realizations of such measures are studied, namely exact and approximate ones. For both types of realizations, it is proven that predictive versions that run in polynomial time in general do not exist unless certain complexity-theoretical assumptions are wrong.

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Fitness Landscape Analysis and Edge Weighting-Based Optimization of Vehicle Routing Problems

Processes ◽

10.3390/pr8111363 ◽

2020 ◽

Vol 8 (11) ◽

pp. 1363

Author(s):

László Kovács ◽

Anita Agárdi ◽

Tamás Bányai

Keyword(s):

Vehicle Routing ◽

Vehicle Routing Problem ◽

Fitness Landscape ◽

Fitness Function ◽

Search Space ◽

Landscape Analysis ◽

Discrete Optimization Problem ◽

Routing Problem ◽

Fitness Landscape Analysis ◽

Fitness Value

Vehicle routing problem (VRP) is a highly investigated discrete optimization problem. The first paper was published in 1959, and later, many vehicle routing problem variants appeared to simulate real logistical systems. Since vehicle routing problem is an NP-difficult task, the problem can be solved by approximation algorithms. Metaheuristics give a “good” result within an “acceptable” time. When developing a new metaheuristic algorithm, researchers usually use only their intuition and test results to verify the efficiency of the algorithm, comparing it to the efficiency of other algorithms. However, it may also be necessary to analyze the search operators of the algorithms for deeper investigation. The fitness landscape is a tool for that purpose, describing the possible states of the search space, the neighborhood operator, and the fitness function. The goal of fitness landscape analysis is to measure the complexity and efficiency of the applicable operators. The paper aims to investigate the fitness landscape of a complex vehicle routing problem. The efficiency of the following operators is investigated: 2-opt, order crossover, partially matched crossover, cycle crossover. The results show that the most efficient one is the 2-opt operator. Based on the results of fitness landscape analysis, we propose a novel traveling salesman problem genetic algorithm optimization variant where the edges are the elementary units having a fitness value. The optimal route is constructed from the edges having good fitness value. The fitness value of an edge depends on the quality of the container routes. Based on the performed comparison tests, the proposed method significantly dominates many other optimization approaches.

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Generalised Pattern Search with Restarting Fitness Landscape Analysis

SN Computer Science ◽

10.1007/s42979-021-00989-8 ◽

2021 ◽

Vol 3 (2) ◽

Author(s):

Ferrante Neri

Keyword(s):

Fitness Landscape ◽

Black Box ◽

Pattern Search ◽

Numerical Results ◽

Landscape Analysis ◽

Computationally Efficient ◽

Fitness Landscape Analysis ◽

Explainable Ai ◽

Pattern Matrix ◽

Algorithmic Design

AbstractFitness landscape analysis for optimisation is a technique that involves analysing black-box optimisation problems to extract pieces of information about the problem, which can beneficially inform the design of the optimiser. Thus, the design of the algorithm aims to address the specific features detected during the analysis of the problem. Similarly, the designer aims to understand the behaviour of the algorithm, even though the problem is unknown and the optimisation is performed via a metaheuristic method. Thus, the algorithmic design made using fitness landscape analysis can be seen as an example of explainable AI in the optimisation domain. The present paper proposes a framework that performs fitness landscape analysis and designs a Pattern Search (PS) algorithm on the basis of the results of the analysis. The algorithm is implemented in a restarting fashion: at each restart, the fitness landscape analysis refines the analysis of the problem and updates the pattern matrix used by PS. A computationally efficient implementation is also presented in this study. Numerical results show that the proposed framework clearly outperforms standard PS and another PS implementation based on fitness landscape analysis. Furthermore, the two instances of the proposed framework considered in this study are competitive with popular algorithms present in the literature.

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