Combinatorial Surrogate-Assisted Optimization for Bus Stops Spacing Problem

International audienceThe distribution of transit stations constitutes an ubiquitous task in large urban areas. In particular, bus stops spacing is a crucial factor that directly affects transit ridership travel time. Hence, planners often rely on traffic surveys and virtual simulations of urban journeys to design sustainable public transport routes. However, the combinator-ial structure of the search space in addition to the time-consuming and black-box traffic simulations require computationally expensive efforts. This imposes serious constraints on the number of potential configurations to be explored. Recently, powerful techniques from discrete optimization and machine learning showed convincing to overcome these limitations. In this preliminary work, we build combinatorial surrogate models to approximate the costly traffic simulations. These so-trained surrog-ates are embedded in an optimization framework. More specifically, this article is the first to make use of a fresh surrogate-assisted optimization algorithm based on the mathematical foundations of discrete Walsh functions in order to solve the real-world bus stops spacing optimization problem. We conduct our experiments with the sialac benchmark in the city of Calais, France. We compare state-of-the-art approaches and we highlight the accuracy and the optimization efficiency of the proposed methods

Fourier Transform-based Surrogates for Permutation Problems

In the context of pseudo-Boolean optimization, surrogate functions based on the Walsh-Hadamard transform have been recently proposed with great success. It has been shown that lower-order components of the Walsh-Hadamard transform have usually a larger influence on the value of the objective function. Thus, creating a surrogate model using the lower-order components of the transform can provide a good approximation to the objective function. The Walsh-Hadamard transform in pseudo-Boolean optimization is a particularization in the binary representation of a Fourier transform over a finite group, precisely defined in the framework of group representation theory. Using this more general definition, it is possible to define a Fourier transform for the functions over permutations. We propose in this paper the use of surrogate functions based on the Fourier transforms over the permutation space. We check how similar the proposed surrogate models are to the original objective function and we also apply regression to learn a surrogate model based on the Fourier transform. The experimental setting includes two permutation problems for which the exact Fourier transform is unknown based on the problem parameters: the Asteroid Routing Problem and the Single Machine Total Weighted Tardiness.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Ministerio de Ciencia, Innovación y Universidades del Gobierno de España under grants PID 2020-116727RB-I00 and PRX21/00669, and by EU Horizon 2020 research and innovative program (grant 952215, TAILOR ICT-48 network). Thanks to the Supercomputing and Bioinnovation Center (SCBI) of Universidad de Málaga for their provision of computational resources and support

Surrogate-assisted Multi-objective Combinatorial Optimization based on Decomposition and Walsh Basis

International audienceWe consider the design and analysis of surrogate-assisted algorithms for expensive multi-objective combinatorial optimization. Focusing on pseudo-boolean functions, we leverage existing techniques based on Walsh basis to operate under the decomposition framework of MOEA/D. We investigate two design components for the cheap generation of a promising pool of offspring and the actual selection of one solution for expensive evaluation. We propose different variants, ranging from a filtering approach that selects the most promising solution at each iteration by using the constructed Walsh surrogates to discriminate between a pool of offspring generated by variation, to a substitution approach that selects a solution to evaluate by optimizing the Walsh surrogates in a multi-objective manner. Considering bi-objective NK landscapes as benchmark problems offering different degree of non-linearity, we conduct a comprehensive empirical analysis including the properties of the achievable approximation sets, the anytime performance, and the impact of the order used to train the Walsh surrogates. Our empirical findings show that, although our surrogate-assisted design is effective, the optimal integration of Walsh models within a multi-objective evolutionary search process gives rise to particular questions for which different trade-off answers can be obtained

A surrogate model based on Walsh decomposition for pseudo-boolean functions

International audienceExtensive efforts so far have been devoted to the design of effective surrogate models aiming at reducing the computational cost for solving expensive black-box continuous optimization problems. There are, however, relatively few investigations on the development of methodologies for combinatorial domains. In this work, we rely on the mathematical foundations of discrete Walsh functions in order to derive a surrogate model for pseudo-boolean optimization functions. Specifically, we model such functions by means of Walsh expansion. By conducting a comprehensive set of experiments on nk-landscapes, we provide empirical evidence on the accuracy of the proposed model. In particular, we show that a Walsh-based surrogate model can outperform the recently-proposed discrete model based on Kriging