Heuristic Approximation Research Articles

Metagenome comparison (MC): A new framework for detecting unique/enriched OMUs (operational metagenomic units) derived from whole-genome sequencing reads

BackgroundCurrent methods for comparing metagenomes, derived from whole-genome sequencing reads, include top-down metrics or parametric models such as metagenome-diversity, and bottom-up, non-parametric, model-free machine learning approaches like Naïve Bayes for k-mer-profiling. However, both types are limited in their ability to effectively and comprehensively identify and catalogue unique or enriched metagenomic genes, a critical task in comparative metagenomics. This challenge is significant and complex due to its NP-hard nature, which means computational time grows exponentially, or even faster, with the problem size, rendering it impractical for even the fastest supercomputers without heuristic approximation algorithms. MethodIn this study, we introduce a new framework, MC (Metagenome-Comparison), designed to exhaustively detect and catalogue unique or enriched metagenomic genes (MGs) and their derivatives, including metagenome functional gene clusters (MFGC), or more generally, the operational metagenomic unit (OMU) that can be considered the counterpart of the OTU (operational taxonomic unit) from amplicon sequencing reads. The MC is essentially a heuristic search algorithm guided by pairs of new metrics (termed MG-specificity or OMU-specificity, MG-specificity diversity or OMU-specificity diversity). It is further constrained by statistical significance (P-value) implemented as a pair of statistical tests. ResultsWe evaluated the MC using large metagenomic datasets related to obesity, diabetes, and IBD, and found that the proportions of unique and enriched metagenomic genes ranged from 0.001% to 0.08 % and 0.08%–0.82 % respectively, and less than 10 % for the MFGC. ConclusionThe MC provides a robust method for comparing metagenomes at various scales, from baseline MGs to various function/pathway clusters of metagenomes, collectively termed OMUs.

Emin: A First-Principles Thermochemical Descriptor for Predicting Molecular Synthesizability.

Predicting the synthesizability of a new molecule remains an unsolved challenge that chemists have long tackled with heuristic approaches. Here, we report a new method for predicting synthesizability using a simple yet accurate thermochemical descriptor. We introduce Emin, the energy difference between a molecule and its lowest energy constitutional isomer, as a synthesizability predictor that is accurate, physically meaningful, and first-principles based. We apply Emin to 134,000 molecules in the QM9 data set and find that Emin is accurate when used alone and reduces incorrect predictions of "synthesizable" by up to 52% when used to augment commonly used prediction methods. Our work illustrates how first-principles thermochemistry and heuristic approximations for molecular stability are complementary, opening a new direction for synthesizability prediction methods.

Stability analysis of the bias compensated LMS algorithm

The presence of noise is a pervasive issue that significantly impacts the performance of adaptive filtering algorithms. To address this challenge, the bias compensation technique has recently emerged, involving the incorporation of an additional term into the update equation. Despite the apparent simplicity of the bias-compensated least-mean-squares algorithm, conducting a comprehensive theoretical analysis of its performance is a complex task. In this paper, we undertake an exact expectation analysis to demonstrate the asymptotic unbiasedness of the algorithm, even when disregarding the commonly assumed theory of independence between adaptive coefficients and input data. Furthermore, to improve the understanding of the algorithm's stability, we employ a stochastic model that assumes independence between the radial and angular distributions of the input vector. The resulting model is intricate, necessitating heuristic approximations to derive practical insights. Notably, our analysis reveals that the upper bound on the step size of the bias-compensated least-mean-squares algorithm consistently remains smaller than that of the least-mean-squares algorithm. These findings gain robust support from extensive simulations.

Two-layer reconstruction of Raman spectra in diffusive media based on an analytical model in the time domain.

We derive and validate an analytical model that describes the migration of Raman scattered photons in two-layer diffusive media, based on the diffusion equation in the time domain. The model is derived under a heuristic approximation that background optical properties are identical on the excitation and Raman emission wavelengths. Methods for the reconstruction of two-layer Raman spectra have been developed, tested in computer simulations and validated on tissue-mimicking phantom measurements data. Effects of different parameters were studied in simulations, showing that the thickness of the top layer and number of detected photon counts have the most significant impact on the reconstruction. The concept of quantitative, mathematically rigorous reconstruction using the proposed model was finally proven on experimental measurements, by successfully separating the spectra of silicone and calcium carbonate (calcite) layers, showing the potential for further development and eventual application in clinical diagnostics.

Decentralized Optimization for Multicast Adaptive Video Streaming in Edge Cache-Assisted Networks

Adaptive streaming based on DASH offers personalized video experience and smooth playback by allowing dynamical adjustments of the video bitrate to the variations of network conditions. This is especially important for current and future Internet video streaming applications, including emerging ones such as virtual reality-based, as adaptive streaming plays a key role in providing high quality viewing experience, especially in limited bandwidth delivery environments. To enable this promising avenue in a 5G context, efforts are made to consider it alongside multicast and edge caching, as part of the next generation communication technology. In this paper, we model the adaptive streaming transmission problem in a mobile scenario as a multi-source multicast multi-rate problem (MMMP) whose linear relaxation is concave. We decompose the problem in terms of clients and propose the distributed delivery algorithm (DDA). The computation complexity, convergence and time-varying adaptation of DDA are theoretically analyzed. Additionally, to further reduce the computation complexity of the solution, a heuristic approximation method (H-DDA) based on the physical meaning of the problem is proposed and it is also shown how H-DDA converges to the optimal value by numerical means. Finally, we conduct a series of simulation tests to demonstrate the superiority of the proposed HDDA in comparison with other state-of-art solutions.

A Survey on Influence Maximization: From an ML-Based Combinatorial Optimization

Influence Maximization (IM) is a classical combinatorial optimization problem, which can be widely used in mobile networks, social computing, and recommendation systems. It aims at selecting a small number of users such that maximizing the influence spread across the online social network. Because of its potential commercial and academic value, there are a lot of researchers focusing on studying the IM problem from different perspectives. The main challenge comes from the NP-hardness of the IM problem and #P-hardness of estimating the influence spread, thus traditional algorithms for overcoming them can be categorized into two classes: heuristic algorithms and approximation algorithms. However, there is no theoretical guarantee for heuristic algorithms, and the theoretical design is close to the limit. Therefore, it is almost impossible to further optimize and improve their performance. With the rapid development of artificial intelligence, technologies based on Machine Learning (ML) have achieved remarkable achievements in many fields. In view of this, in recent years, a number of new methods have emerged to solve combinatorial optimization problems by using ML-based techniques. These methods have the advantages of fast solving speed and strong generalization ability to unknown graphs, which provide a brand-new direction for solving combinatorial optimization problems. Therefore, we abandon the traditional algorithms based on iterative search and review the recent development of ML-based methods, especially Deep Reinforcement Learning, to solve the IM problem and other variants in social networks. We focus on summarizing the relevant background knowledge, basic principles, common methods, and applied research. Finally, the challenges that need to be solved urgently in future IM research are pointed out.

Bi-sided facility location problems: an efficient algorithm for k-centre, k-median, and travelling salesman problems

This study introduces a general framework, called Bi-sided facility location, for a wide range of problems in the area of combined facility location and routing problems such as locating test centres and designing the network of supermarkets. It is based on a multi-objective optimisation model to enhance the service quality which the clients received, called client-side, and enhance the interconnection quality and eligibility among the centres, called center-side. Well-known problems such as k-median and k-centre for the client-side and the travelling salesman problem for the centre-side are taken into account in this paper. After discussing the complexity of this kind of combination, we propose a heuristic approximation algorithm to find approximation Pareto-optimal solutions for the problem. The algorithm is an efficient local search utilising geometric objects such as the Voronoi diagram and Delaunay triangulation as well as algorithms for computing approximation travelling salesman tour. In addition to the comprehensive theoretical analysis of the proposed models and algorithm, we apply the algorithm to different instances and benchmarks, and compare it with NSGA-II based on set coverage and spacing metrics. The results confirm the efficiency of the algorithm in terms of running time and providing a diverse set of efficient trade-off solutions. Highlights Introducing a general bi-side location model considering centres and clients’ utilities Discussing and proving the NP-hardness of the model in the general framework Considering two instances; k-centre and k-median for client-side and TSP for centre-side Proposing an efficient geometric-based algorithm for solving the problems Implementing, testing, and comparing the proposed algorithm on several benchmarks

Towards a Better Tradeoff between Quality and Efficiency of Community Detection: An Inductive Embedding Method across Graphs

Many network applications can be formulated as NP-hard combinatorial optimization problems of community detection (CD) that partitions nodes of a graph into several groups with dense linkage. Most existing CD methods are transductive , which independently optimized their models for each single graph, and can only ensure either high quality or efficiency of CD by respectively using advanced machine learning techniques or fast heuristic approximation. In this study, we consider the CD task and aims to alleviate its NP-hard challenge. Motivated by the efficient inductive inference of graph neural networks (GNNs), we explore the possibility to achieve a better tradeoff between the quality and efficiency of CD via an inductive embedding scheme across multiple graphs of a system and propose a novel inductive community detection (ICD) method. Concretely, ICD first conducts the offline training of an adversarial dual GNN structure on historical graphs to capture key properties of a system. The trained model is then directly generalized to new graphs of the same system for online CD without additional optimization, where a better tradeoff between quality and efficiency can be achieved. Compared with existing inductive approaches, we develop a novel feature extraction module based on graph coarsening, which can efficiently extract informative feature inputs for GNNs. Moreover, our original designs of adversarial dual GNN and clustering regularization loss further enable ICD to capture permutation-invariant community labels in the offline training and help derive community-preserved embedding to support the high-quality online CD. Experiments on a set of benchmarks demonstrate that ICD can achieve a significant tradeoff between quality and efficiency over various baselines.

Nonlinear canonical correspondence analysis and its application

The canonical correspondence analysis (CCA) is a multivariate direct gradient analysis method performing well in many fields, however, when it comes to approximating the unimodal response of species to an environmental gradient, which still assumes that the relationship between the environment and the weighted species score is linear. In this work, we propose a nonlinear canonical correspondence analysis method (NCCA), which first determines the most appropriate nonlinear explanatory factor through two screenings by correlation and LASSO regression, and successively uses the linear regression method and the improved heuristic optimal quadratic approximation method to fit the chi-square transformation values of the response variables. Thus, our method effectively reflects the nonlinear relationship between the species and the environment factors, and a biplot is employed to visualize the effects of the later on the distribution of species. The results from applying this method over a real dataset show that the NCCA method not only maintains the advantages of the polynomial canonical correspondence analysis (PCCA) proposed by Makarenkov (2002), but also outperforms Makarenkov’s method in explaining the variance of response variables.

Abstract 5370: New oncology target identification and validation platform combining artificial intelligence and preclinical pharmacology

Abstract Despite major advances in cancer therapy in the last decades, treatment resistance can develop over time. Precision medicine allows for the successful implementation of targeted therapies and stratification of patients, but treatment resistance remains a major obstacle in patient management. The identification and validation of new targets associated with cancer resistance remains a major challenge. The great diversity of molecular mechanisms involved in treatment resistance phenomena, whether intrinsic (de novo or primary) or acquired (secondary), constitutes a real therapeutic challenge for patient care. A better understanding of resistance mechanisms would allow to explore new therapeutic strategies to circumvent these phenomena in different types of cancer. The OncoSNIPE® project was developed in this context as part of a multicenter and collaborative clinical study (NCT04548960) in more than 800 chemo-naive adult patients. The objective of this project was to identify early and/or late markers of treatment resistance in three different pathologies for which resistance problems are encountered: triple negative breast cancer (TNBC) or luminal B, locally advanced or metastatic non-small cell lung cancer (NSCLC) and pancreatic ductal adenocarcinoma (PDAC). The program included traditional clinical and whole exome sequencing (WES) monitoring of patient biopsies (Exom-seq and RNA-seq) at diagnosis and relapse, monitoring of blood markers (RNA-seq and Proteomics – Cytokine) at diagnosis, and the evaluation of best therapeutic responses and relapse. The program used bioinformatics, artificial intelligence, statistical learning and semantic enrichment approaches to discover the diversity of mechanisms involved in these resistances and to identify new therapeutic targets, through hetero-modal data including clinical, genomic, transcriptomic, immunological and radiomic dimensions. Subsequently, a specific flowchart for target validation was applied to the resulting list, considering the target's developmental potential, its essentiality, prior knowledge (database mining) and home-made score of the link between the target and the disease. Finally, new targets were prioritized using weighting parameter and heuristic approximation based on the Crank algorithm. Experimental work on multiple targets began in the laboratory, initially in vitro, using 2D and 3D cell culture (including cells from patient-derived xenografts) and molecular interference. A wide variety of intrinsic or acquired molecular mechanisms involved in treatment resistance are being evaluated as candidates for diagnostic and therapeutic development. Citation Format: Sebastien Vachenc, Nicolas Ancellin, Didier Grillot, Kenji Shoji, Joanna Giemza, Nathalie Jeanray, Leila Outemzabet, Salvatore Raieli, Lamine Toure, Olivier Duchamp, Fabrice Viviani, Philippe Genne, Jan Hoflack, Stéphane Gerart. New oncology target identification and validation platform combining artificial intelligence and preclinical pharmacology. [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 5370.

Decomposition Strategies for Vehicle Routing Heuristics

Decomposition techniques are an important component of modern heuristics for large instances of vehicle routing problems. The current literature lacks a characterization of decomposition strategies and a systematic investigation of their impact when integrated into state-of-the-art heuristics. This paper fills this gap: We discuss the main characteristics of decomposition techniques in vehicle routing heuristics, highlight their strengths and weaknesses, and derive a set of desirable properties. Through an extensive numerical campaign, we investigate the impact of decompositions within two algorithms for the capacitated vehicle routing problem: the Adaptive Large Neighborhood Search of Pisinger and Ropke (2007 ) and the Hybrid Genetic Search of Vidal et al. (2012 ). We evaluate the quality of popular decomposition techniques from the literature and propose new strategies. We find that route-based decomposition methods, which define subproblems by means of the customers contained in selected subsets of the routes of a given solution, generally appear superior to path-based methods, which merge groups of customers to obtain smaller subproblems. The newly proposed decomposition barycenter clustering achieves the overall best performance and leads to significant gains compared with using the algorithms without decomposition. History: Erwin Pesch, Area Editor for Heuristic Search and Approximation Algorithms. Funding: This work was supported by the U.S. Air Force [Grant FA9550-17-1-0234], the Ministerio de Ciencia e Innovación (Juan de la Cierva Formación), H2020 Marie Skłodowska-Curie Actions [Grant 945380], the Ministero dell’Università e della Ricerca [Grant 2015JJLC3E_002], the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grant 308528/2018-2], and the Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro [Grant E-26/202.790/2019]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.1288 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0048 ) at ( http://dx.doi.org/10.5281/zenodo.7613129 ).

Input node placement restricting the longest control chain in controllability of complex networks

The minimum number of inputs needed to control a network is frequently used to quantify its controllability. Control of linear dynamics through a minimum set of inputs, however, often has prohibitively large energy requirements and there is an inherent trade-off between minimizing the number of inputs and control energy. To better understand this trade-off, we study the problem of identifying a minimum set of input nodes such that controllabililty is ensured while restricting the length of the longest control chain. The longest control chain is the maximum distance from input nodes to any network node, and recent work found that reducing its length significantly reduces control energy. We map the longest control chain-constraint minimum input problem to finding a joint maximum matching and minimum dominating set. We show that this graph combinatorial problem is NP-complete, and we introduce and validate a heuristic approximation. Applying this algorithm to a collection of real and model networks, we investigate how network structure affects the minimum number of inputs, revealing, for example, that for many real networks reducing the longest control chain requires only few or no additional inputs, only the rearrangement of the input nodes.

Performance Evaluation of Decision-Making Units Through Boosting Methods in the Context of Free Disposal Hull: Some Exact and Heuristic Algorithms

This paper aims to show how to calculate different efficiency measures using a technology estimator defined through the adaptation of the Gradient Tree Boosting algorithm. This adaptation shares some features with the standard nonparametric Free Disposal Hull (FDH) approach, but it overcomes data overfitting problems. Nevertheless, from a computational point of view, the new approach presents thousands of decision variables, making it difficult to solve. To tackle this problem, we also propose and check a heuristic approximation to the exact measures. To demonstrate the applicability of the proposed method, the exact and the heuristic approaches are compared through two empirical applications. The main contributions of this paper are as follows: we build a new bridge between machine learning techniques and technical efficiency measurement. In this framework, we show how to determine the output-oriented and input-oriented radial models, the Russell measure of output efficiency and the Russell measure of input efficiency, as well as the directional distance function and the Enhanced Russell Graph measure. We also prove that the new technique is better, in terms of bias and squared mean error, than the standard FDH technique. Furthermore, we show that the new approach may be seen as a possible remedy for solving the curse of dimensionality problem.

Stochastic crowd shipping last-mile delivery with correlated marginals and probabilistic constraints

In this work, we study last-mile delivery with the option of crowd shipping. A company uses occasional drivers to complement its fleet in the activity of delivering products to its customers. We model it as a variant of the stochastic capacitated vehicle routing problem. Our approach is data-driven, where not only customer orders but also the availability of occasional drivers are uncertain. It is assumed that marginal distributions of the uncertainty vector are known, but the joint distribution is difficult to estimate. We optimize considering a worst-case joint distribution and model with a strategic planning perspective, where we calculate an optimal a priori solution before the uncertainty is revealed. A limit on the infeasibility of the routes due to the capacity is imposed using probabilistic constraints.We propose an extended formulation for the problem using column-dependent rows and implement a branch-price-and-cut algorithm to solve it. We also develop a heuristic approximation to cope with larger instances of the problem. Through computational experiments, we analyze the solution and performance of the implemented algorithms.

Searching for a source without gradients: how good is infotaxis and how to beat it

Infotaxis is a popular search algorithm designed to track a source of odour in a turbulent environment using information provided by odour detections. To exemplify its capabilities, the source-tracking task was framed as a partially observable Markov decision process consisting in finding, as fast as possible, a stationary target hidden in a two-dimensional grid using stochastic partial observations of the target location. Here, we provide an extended review of infotaxis, together with a toolkit for devising better strategies. We first characterize the performance of infotaxis in domains from one dimension to four dimensions. Our results show that, while being suboptimal, infotaxis is reliable (the probability of not reaching the source approaches zero), efficient (the mean search time scales as expected for the optimal strategy) and safe (the tail of the distribution of search times decays faster than any power law, though subexponentially). We then present three possible ways of beating infotaxis, all inspired by methods used in artificial intelligence: tree search, heuristic approximation of the value function, and deep reinforcement learning. The latter is able to find, without any prior human knowledge, the (near) optimal strategy. Altogether, our results provide evidence that the margin of improvement of infotaxis towards the optimal strategy gets smaller as the dimensionality increases.

Multisample Online Learning for Probabilistic Spiking Neural Networks.

Spiking neural networks (SNNs) capture some of the efficiency of biological brains for inference and learning via the dynamic, online, and event-driven processing of binary time series. Most existing learning algorithms for SNNs are based on deterministic neuronal models, such as leaky integrate-and-fire, and rely on heuristic approximations of backpropagation through time that enforces constraints such as locality. In contrast, probabilistic SNN models can be trained directly via principled online, local, and update rules that have proven to be particularly effective for resource-constrained systems. This article investigates another advantage of probabilistic SNNs, namely, their capacity to generate independent outputs when queried over the same input. It is shown that the multiple generated output samples can be used during inference to robustify decisions and to quantify uncertainty-a feature that deterministic SNN models cannot provide. Furthermore, they can be leveraged for training in order to obtain more accurate statistical estimates of the log-loss training criterion and its gradient. Specifically, this article introduces an online learning rule based on generalized expectation-maximization (GEM) that follows a three-factor form with global learning signals and is referred to as GEM-SNN. Experimental results on structured output memorization and classification on a standard neuromorphic dataset demonstrate significant improvements in terms of log-likelihood, accuracy, and calibration when increasing the number of samples used for inference and training.

A heuristic approximation algorithm of minimum dominating set based on rough set theory

A heuristic approximation algorithm of minimum dominating set based on rough set theory

Distance approximation to support customer selection in vehicle routing problems

AbstractEstimating the solution value of transportation problems can be useful to assign customers to days for multi-period vehicle routing problems, or to make customer selection decisions very fast (e.g., within an online environment). In this paper, we apply several regression methods to predict the total distance of the traveling salesman problem (TSP) and vehicle routing problem (VRP). We show that distance can be estimated fairly accurate using simple regression models and only a limited number of features. Besides using features found in the scientific literature, we also introduce new classes of spatial features. The model is validated on a fictional case with different spatial instances considering both a backordering and lost sales configuration, and on a realistic case that involves dynamic waste collection in the city of Amsterdam, The Netherlands. For the fictional case, we show differences in performance per instance type and configuration, and we show that our model can save up to $$25.3\%$$ 25.3 % in distance compared with a heuristic approximation. For the waste collection case, we introduce a cost function that combines the travel distance and service level, and show that our model can reduce distances up to 17% compared to a well-known heuristic approximation while maintaining the same service level. Furthermore, we show the benefits of using approximations for combining offline learning with online or frequent optimization.

Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers

The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.

Stocking Under Random Demand and Product Variety: Exact Models and Heuristics

Efficient inventory management in the face of product variety is an important part of retail operations management. In this study, we analyze the optimal stocking policy for a retailer, in a setup with a single horizontally differentiated product with an arbitrary number of product variants, stochastic demand, and two‐level consumer choice. The demands for individual product variants are negatively correlated conditional on the total demand. We assume that each customer will purchase one unit of a preferred product variant, if it is in stock, and will seek to buy a second choice product, if the former is not in stock. We formulate an exact model, with Poisson customer arrivals. In order to maintain tractability and characterize an optimal policy analytically, we develop a benchmark model which does not explicitly account for the stochastic nature of customer arrival times. In this model, which is a heuristic approximation of the exact model, we find simple conditions under which the objective of maximizing expected profit is jointly concave in the stocking levels of the product variants; under these conditions we prove that the optimal stocking levels are simply scaled versions of the optimal newsvendor quantities. We then analytically establish a connection between the exact and benchmark models. We develop a dynamic Monte Carlo simulation experiment to gain further insights on the impact of different performance measures on the effectiveness of the optimal policy in the benchmark model and its performance in reference to the exact optimal policy.