A self-supervised learning model for graph clustering optimization problems

Mining large-scale graphs is increasingly important, as it provides a powerful way of extracting useful information from real-world data. Efficient processing of that volume of information requires partitioning the graph across multiple nodes in a distributed system. However, traversing edges across distributed partitions results in significant performance penalty due to the additional cost of inter-partition communication. Minimising the number of cut edges between partitions improves communication cost between neighbouring vertices; balanced graph partitioning is required for load balancing [2].

In this paper we consider the problem of (k, υ)-balanced graph partitioning - dividing the vertices of a graph into k almost equal size components (each of size less than υ • nk) so that the capacity of edges between different components is minimized. This problem is a natural generalization of several other problems such as minimum bisection, which is the (2,1)-balanced partitioning problem. We present a bicriteria polynomial time approximation algorithm with an O(log2n)-approximation for any constant υ > 1. For υ = 1 we show that no polytime approximation algorithm can guarantee a finite approximation ratio unless P=NP. Previous work has only considered the (k, υ)-balanced partitioning problem for υ ≥ 2.

k-median and facility location problems are classical NP-hard combinatorial optimization problems. Although there are many experimental studies on them, their theoretical results are relatively few. This paper mainly contributes to investigating the approximation performance of two evolutionary algorithms for the k-median and facility location problems from a theoretical perspective. For k-median problem, we show that the evolutionary algorithms with standard bit mutation (SBM) operator can obtain approximation ratios 5 and $$3{+}2/p$$ in expected polynomial time while the evolutionary algorithm with somatic contiguous hypermutation (CHM) operator cannot obtain them. For facility location problem, we show that the evolutionary algorithms with SBM operator can obtain approximation ratio 3 in expected polynomial time while the evolutionary algorithm with CHM operator cannot obtain it. Further, we prove that on a facility location instance the evolutionary algorithm with CHM operator greatly outperforms the evolutionary algorithm with SBM operator.

The balanced graph partitioning consists in dividing the vertices of an undirected graph into a given number of subsets of approximately equal size, such that the number of edges crossing the subsets is minimized. In this work, we present a multilevel memetic algorithm for this NP-hard problem that relies on a powerful grouping recombination operator and a dedicated local search procedure. The proposed operator tends to preserve the backbone with respect to a set of parent individuals, i.e. the grouping of vertices which is same throughout each parent individual. Although our approach requires significantly longer computing time compared to some current state-of-art graph partitioning algorithms such as SCOTCH, METIS, CHACO, JOSTLE, etc., it competes very favorably with these approaches in terms of solution quality. Moreover, it easily reaches or improves on the best partitions ever reported in the literature.

Genetic algorithm for the personnel assignment problem with multiple objectives

A significant part of the data produced every day by online services is structured as a graph. Therefore, there is the need for efficient processing and analysis solutions for large scale graphs. Among the others, the balanced graph partitioning is a well known NP-complete problem with a wide range of applications. Several solutions have been proposed so far, however most of the existing state-of-the-art algorithms are not directly applicable in very large-scale distributed scenarios. A recently proposed promising alternative exploits a vertex-center heuristics to solve the balance graph partitioning problem. Their algorithm is massively parallel: there is no central coordination, and each node is processed independently. Unfortunately, we found such algorithm to be not directly exploitable in current BSP-like distributed programming frameworks. In this paper we present the adaptations we applied to the original algorithm while implementing it on Spark, a state-of-the-art distributed framework for data processing.

We propose a heuristic for parallel partitioning of graphs into equi-sized components. In particular, we identify a relationship between the graph partitioning problem (GPP) and the traveling saleman problem (TSP), and use that to reduce partitioning to TSP. Given that better performing heuristics are known for TSP than are for GPP, this reduction also leads to improved GPP heuristics. What is more, a good GPP solution can also be used to speed up computation of TSP.We first derive a good bi-partition from a cut of the TSP cycle in time proportional to the number of edges in the graph. We then continue this bi-partitioning recursively until the required number of partitions are left. Further, in order to speed up the computation of TSP, which we use as a subroutine, we perform an initial rough partitioning of the graph into K parts, compute TSP tours in each of these smaller partitions and then merge these local tours to solve the full TSP.We then use this full TSP solution to obtain the final partitioning in parallel. Our empirical analysis shows that for partition count k ≥ 32, our parallel algorithm gives a cut better in size than that of algorithms known for low cut-size (e.g., KaBaPE), and when time is of concern, it finishes in significantly less time with comparable cuts. We also show that our algorithm gives much smaller cuts in comparable time than those known for fast computation (e.g., PT-Scotch).

Approximation algorithm for squared metric facility location problem with nonuniform capacities

Randomized decision making refers to the process of making decisions randomly according to the outcome of an independent randomization device, such as a dice roll or a coin flip. The concept is unconventional, and somehow counterintuitive, in the domain of mathematical programming, in which deterministic decisions are usually sought even when the problem parameters are uncertain. However, it has recently been shown that using a randomized, rather than a deterministic, strategy in nonconvex distributionally robust optimization (DRO) problems can lead to improvements in their objective values. It is still unknown, though, what is the magnitude of improvement that can be attained through randomization or how to numerically find the optimal randomized strategy. In this paper, we study the value of randomization in mixed-integer DRO problems and show that it is bounded by the improvement achievable through its continuous relaxation. Furthermore, we identify conditions under which the bound is tight. We then develop algorithmic procedures, based on column generation, for solving both single- and two-stage linear DRO problems with randomization that can be used with both moment-based and Wasserstein ambiguity sets. Finally, we apply the proposed algorithm to solve three classical discrete DRO problems: the assignment problem, the uncapacitated facility location problem, and the capacitated facility location problem and report numerical results that show the quality of our bounds, the computational efficiency of the proposed solution method, and the magnitude of performance improvement achieved by randomized decisions. Summary of Contribution: In this paper, we present both theoretical results and algorithmic tools to identify optimal randomized strategies for discrete distributionally robust optimization (DRO) problems and evaluate the performance improvements that can be achieved when using them rather than classical deterministic strategies. On the theory side, we provide improvement bounds based on continuous relaxation and identify the conditions under which these bound are tight. On the algorithmic side, we propose a finitely convergent, two-layer, column-generation algorithm that iterates between identifying feasible solutions and finding extreme realizations of the uncertain parameter. The proposed algorithm was implemented to solve distributionally robust stochastic versions of three classical optimization problems and extensive numerical results are reported. The paper extends a previous, purely theoretical work of the first author on the idea of randomized strategies in nonconvex DRO problems by providing useful bounds and algorithms to solve this kind of problems.

Special Issue on Parallel and Distributed Data Mining

Graphs are suitable data structures for expressing the relationship between different types of data. With a continuous increase in the graph size, using suitable methods to divide graphs and parallelize the processing load becomes crucial. Balanced graph partitioning has been extensively studied for static and streaming graphs. However, for a time-evolving graph (TEG), whose size and structure are periodically updated, related partitioning methods are lacking. A straightforward approach is to capture snapshots of a TEG and adopt the partitioning methods designed for static or streaming graphs. Although feasible partitioning quality can be expected, the time overhead is high due to frequent repartitioning. This paper proposes two TEG partitioning methods, namely seed and similarity, to decrease the partitioning time. According to the experimental results, on average, seed and similarity require 29–39% of the partitioning time required by snapshot. Moreover, the proposed methods maintain reasonable partitioning quality.

Facility location selection is a vital decision for companies that affects both cost and delivery time over the years. However, determination of the facility location is a NP-hard problem. A hybrid algorithm that combines revised weighted fuzzy c-means with Nelder Mead (RWFCM-NM) performs well when compared with well-known algorithms for the facility location problem (FLP) with deterministic customer demands and positions. The motivation of the study is both analyzing performance of the RWFCM-NM algorithm with probabilistic customer demands and positions and proposing a new approach for this problem. This paper develops two new algorithms for FLP when customer demands and positions are probabilistic. The proposed algorithms are a probabilistic fuzzy c-means algorithm and Nelder-Mead (Probabilistic FCM-NM), a probabilistic revised weighted fuzzy c-means algorithm and Nelder Mead (Probabilistic RWFCM-NM) for the un-capacitated planar multi-facility location problem when customer positions and customer demands are probabilistic with predetermined service level. Proposed algorithms performances were tested with 13 data sets and comparisons were made with four well known algorithms. According to the experimental results, probabilistic RWFCM-NM algorithm demonstrates superiority on compared algorithms in terms of total transportation costs.

Learning-based methods have been proved to perform well in a variety of areas in the biomedical field, such as biomedical image segmentation, and histopathological image analysis. Deep learning, as the most recently presented approach of learning-based methods, has attracted more and more attention. For instance, massive researches of deep learning methods for image reconstructions of computed tomography (CT) and magnetic resonance imaging (MRI) have been reported, indicating the great potential of deep learning for inverse problems. Optical technology-related medical imaging modalities including diffuse optical tomography (DOT), fluorescence molecular tomography (FMT), bioluminescence tomography (BLT), and photoacoustic tomography (PAT) are also dramatically innovated by introducing learning-based methods, in particular deep learning methods, to obtain better reconstruction results. This review depicts the latest researches on learning-based optical tomography of DOT, FMT, BLT, and PAT. According to the most recent studies, learning-based methods applied in the field of optical tomography are categorized as kernel-based methods and deep learning methods. In this review, the former are regarded as a sort of conventional learning-based methods and the latter are subdivided into model-based methods, post-processing methods, and end-to-end methods. Algorithm as well as data acquisition strategy are discussed in this review. The evaluations of these methods are summarized to illustrate the performance of deep learning-based reconstruction.

Recent hardware advances in quantum and quantum-inspired annealers promise substantial speedup for solving NP-hard combinatorial optimization problems compared to general-purpose computers. These special-purpose hardware are built for solving hard instances of Quadratic Unconstrained Binary Optimization (QUBO) problems. In terms of number of variables and precision of these hardware are usually resource-constrained and they work either in Ising space {-1,1} or in Boolean space {0,1}. Many naturally occurring problem instances are higher-order in nature. The known method to reduce the degree of a higher-order optimization problem uses Rosenberg's polynomial. The method works in Boolean space by reducing the degree of one term by introducing one extra variable. In this work, we prove that in Ising space the degree reduction of one term requires the introduction of two variables. Our proposed method of degree reduction works directly in Ising space, as opposed to converting an Ising polynomial to Boolean space and applying previously known Rosenberg's polynomial. For sparse higher-order Ising problems, this results in a more compact representation of the resultant QUBO problem, which is crucial for utilizing resource-constrained QUBO solvers.

Deep learning (DL) algorithms are considered as a methodology of choice for remote-sensing image analysis over the past few years. Due to its effective applications, deep learning has also been introduced for automatic change detection and achieved great success. The present study attempts to provide a comprehensive review and a meta-analysis of the recent progress in this subfield. Specifically, we first introduce the fundamentals of deep learning methods which are frequently adopted for change detection. Secondly, we present the details of the meta-analysis conducted to examine the status of change detection DL studies. Then, we focus on deep learning-based change detection methodologies for remote sensing images by giving a general overview of the existing methods. Specifically, these deep learning-based methods were classified into three groups; fully supervised learning-based methods, fully unsupervised learning-based methods and transfer learning-based techniques. As a result of these investigations, promising new directions were identified for future research. This study will contribute in several ways to our understanding of deep learning for change detection and will provide a basis for further research. Some source codes of the methods discussed in this paper are available from: https://github.com/lazharkhelifi/deeplearning_changedetection_remotesensing_review.