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In this paper, we introduce two powerful graph reductions for the maximum weighted stable set (mwss) in general graphs. We show that these reductions allow to reduce the mwss in claw-free graphs to the mwss in a class of quasi-line graphs, that we call bipolar-free. For this latter class, we provide a new algorithmic decomposition theorem running in polynomial time. We then exploit this decomposition result and our reduction tools again to transform the problem to either a single matching problem or a longest path computation in an acyclic auxiliary graph (in this latter part we use some results of Pulleyblank and Shepherd [10]). Putting all the pieces together, the main contribution of this paper is a new polynomial time algorithm for the mwss in claw-free graphs. A rough analysis of the complexity of this algorithm gives a time bound of O(n6), where n is the number of vertices in the graph, and which we hope can be improved by a finer analysis. Incidentally, we prove that the mwss problem can be solved efficiently for any class of graphs that admits a "suitable" decomposition into pieces where the mwss is easy.

Parameterized runtime analysis seeks to understand the influence of problem structure on algorithmic runtime. In this paper, we contribute to the theoretical understanding of evolutionary algorithms and carry out a parameterized analysis of evolutionary algorithms for the Euclidean traveling salesperson problem (Euclidean TSP). We investigate the structural properties in TSP instances that influence the optimization process of evolutionary algorithms and use this information to bound their runtime. We analyze the runtime in dependence of the number of inner points k. In the first part of the paper, we study a [Formula: see text] EA in a strictly black box setting and show that it can solve the Euclidean TSP in expected time [Formula: see text] where A is a function of the minimum angle [Formula: see text] between any three points. Based on insights provided by the analysis, we improve this upper bound by introducing a mixed mutation strategy that incorporates both 2-opt moves and permutation jumps. This strategy improves the upper bound to [Formula: see text]. In the second part of the paper, we use the information gained in the analysis to incorporate domain knowledge to design two fixed-parameter tractable (FPT) evolutionary algorithms for the planar Euclidean TSP. We first develop a [Formula: see text] EA based on an analysis by M. Theile, 2009, ”Exact solutions to the traveling salesperson problem by a population-based evolutionary algorithm,” Lecture notes in computer science, Vol. 5482 (pp. 145–155), that solves the TSP with k inner points in [Formula: see text] generations with probability [Formula: see text]. We then design a [Formula: see text] EA that incorporates a dynamic programming step into the fitness evaluation. We prove that a variant of this evolutionary algorithm using 2-opt mutation solves the problem after [Formula: see text] steps in expectation with a cost of [Formula: see text] for each fitness evaluation.

The aim of this paper is to study both the theoretical and experimental properties of chaotic neural network (CNN) models for solving combinatorial optimization problems. Previously we have proposed a unifying framework which encompasses the three main model types, namely, Chen and Aihara's chaotic simulated annealing (CSA) with decaying self-coupling, Wang and Smith's CSA with decaying timestep, and the Hopfield network with chaotic noise. Each of these models can be represented as a special case under the framework for certain conditions. This paper combines the framework with experimental results to provide new insights into the effect of the chaotic neurodynamics of each model. By solving the N-queen problem of various sizes with computer simulations, the CNN models are compared in different parameter spaces, with optimization performance measured in terms of feasibility, efficiency, robustness and scalability. Furthermore, characteristic chaotic neurodynamics crucial to effective optimization are identified, together with a guide to choosing the corresponding model parameters.

© 2020 World Scientific Publishing Company. Optimization Spiking Neural P System (OSNPS) is the first membrane computing model to directly derive an approximate solution of combinatorial problems with a specific reference to the 0/1 knapsack problem. OSNPS is composed of a family of parallel Spiking Neural P Systems (SNPS) that generate candidate solutions of the binary combinatorial problem and a Guider algorithm that adjusts the spiking probabilities of the neurons of the P systems. Although OSNPS is a pioneering structure in membrane computing optimization, its performance is competitive with that of modern and sophisticated metaheuristics for the knapsack problem only in low dimensional cases. In order to overcome the limitations of OSNPS, this paper proposes a novel Dynamic Guider algorithm which employs an adaptive learning and a diversity-based adaptation to control its moving operators. The resulting novel membrane computing model for optimization is here named Adaptive Optimization Spiking Neural P System (AOSNPS). Numerical result shows that the proposed approach is effective to solve the 0/1 knapsack problems and outperforms multiple various algorithms proposed in the literature to solve the same class of problems even for a large number of items (high dimensionality). Furthermore, case studies show that a AOSNPS is effective in fault sections estimation of power systems in different types of fault cases: including a single fault, multiple faults and multiple faults with incomplete and uncertain information in the IEEE 39 bus system and IEEE 118 bus system.

This paper aims to tackle the Patient Admission Scheduling Problem (PASP) using the Discrete Flower Pollination Algorithm (DFPA), a new, meta-heuristic optimization method based on plant pollination. PASP is one of the most important problems in the field of health care. It is a highly constrained and combinatorial optimization problem of assigning patients to medical resources in a hospital, subject to predefined constraints, while maximizing patient comfort. While the flower pollination algorithm was designed for continuous optimization domains, a discretization of the algorithm has been carried out for application to the PASP. Various neighborhood structures have been employed to enhance the method, and to explore more solutions in the search space. The proposed method has been tested on six instances of benchmark datasets for comparison against another algorithm using the same dataset. The prospective method is shown to be very efficient in solving any scheduling problem.

Understanding the behaviour of heuristic search methods is a challenge. This even holds for simple local search methods such as 2-OPT for the Traveling Salesperson problem. In this paper, we present a general framework that is able to construct a diverse set of instances that are hard or easy for a given search heuristic. Such a diverse set is obtained by using an evolutionary algorithm for constructing hard or easy instances that are diverse with respect to different features of the underlying problem. Examining the constructed instance sets, we show that many combinations of two or three features give a good classification of the TSP instances in terms of whether they are hard to be solved by 2-OPT., 20 pages, 18 figures

Due to the current limitations of sequencing technologies,de novogenome assembly is typically carried out in two stages, namely contig (sequence) assembly and scaffolding. While scaffolding is computationally easier than sequence assembly, the scaffolding problem can be challenging due to the high repetitive content of eukaryotic genomes, possible mis-joins in assembled contigs and inaccuracies in the linkage information. Genome scaffolding tools either use paired-end/mate-pair/linked/Hi-C reads or genome-wide maps (optical, physical or genetic) as linkage information. Optical maps (in particular Bionano Genomics maps) have been extensively used in many recent large-scale genome assembly projects (e.g., goat, apple, barley, maize, quinoa, sea bass, among others). However, the most commonly used scaffolding tools have a serious limitation: they can only deal with one optical map at a time, forcing users to alternate or iterate over multiple maps. In this paper, we introduce a novel scaffolding algorithm called OMGS that for the first time can take advantages of multiple optical maps. OMGS solves several optimization problems to generate scaffolds with optimal contiguity and correctness. Extensive experimental results demonstrate that our tool outperforms existing methods when multiple optical maps are available, and produces comparable scaffolds using a single optical map. OMGS can be obtained fromhttps://github.com/ucrbioinfo/OMGS

Many natural optimization problems are NP-hard, which implies that they are probably hard to solve exactly in the worst-case. However, it suffices to get reasonably good solutions for all (or even most) instances in practice. This paper presents a new algorithm for computing approximate solutions in Θ(N) for the maximum exact 3-satisfiability (MAX-E-3-SAT) problem by using supervised learning methodology. This methodology allows us to create a learning algorithm able to fix Boolean variables by using local information obtained by the Survey Propagation algorithm. By performing an accurate analysis, on random conjunctive normal form instances of the MAX-E-3-SAT with several Boolean variables, we show that this new algorithm, avoiding any decimation strategy, can build assignments better than a random one, even if the convergence of the messages is not found. Although this algorithm is not competitive with state-of-the-art maximum satisfiability solvers, it can solve substantially larger and more complicated problems than it ever saw during training.

Many real-world optimization problems can be solved by using the data-driven approach only, simply because no analytic objective functions are available for evaluating candidate solutions. In this paper, we address a class of expensive data-driven constrained multiobjective combinatorial optimization problems, where the objectives and constraints can be calculated only on the basis of a large amount of data. To solve this class of problems, we propose using random forests (RFs) and radial basis function networks as surrogates to approximate both objective and constraint functions. In addition, logistic regression models are introduced to rectify the surrogate-assisted fitness evaluations and a stochastic ranking selection is adopted to further reduce the influences of the approximated constraint functions. Three variants of the proposed algorithm are empirically evaluated on multiobjective knapsack benchmark problems and two real-world trauma system design problems. Experimental results demonstrate that the variant using RF models as the surrogates is effective and efficient in solving data-driven constrained multiobjective combinatorial optimization problems.

The ultimate goal of metabolic engineering is to produce desired compounds on an industrial scale in a cost effective manner. To address challenges in metabolic engineering, computational strain optimization algorithms based on genome-scale metabolic models have increasingly been used to aid in overproducing products of interest. However, most of these strain optimization algorithms utilize a metabolic network alone, with few approaches providing strategies that also include transcriptional regulation. Moreover previous integrated approaches generally require a pre-existing regulatory network. In this study, we developed a novel strain design algorithm, named OptRAM (Optimization of Regulatory And Metabolic Networks), which can identify combinatorial optimization strategies including overexpression, knockdown or knockout of both metabolic genes and transcription factors. OptRAM is based on our previous IDREAM integrated network framework, which makes it able to deduce a regulatory network from data. OptRAM uses simulated annealing with a novel objective function, which can ensure a favorable coupling between desired chemical and cell growth. The other advance we propose is a systematic evaluation metric of multiple solutions, by considering the essential genes, flux variation, and engineering manipulation cost. We applied OptRAM to generate strain designs for succinate, 2,3-butanediol, and ethanol overproduction in yeast, which predicted high minimum predicted target production rate compared with other methods and previous literature values. Moreover, most of the genes and TFs proposed to be altered by OptRAM in these scenarios have been validated by modification of the exact genes or the target genes regulated by the TFs, for overproduction of these desired compounds by in vivo experiments cataloged in the LASER database. Particularly, we successfully validated the predicted strain optimization strategy for ethanol production by fermentation experiment. In conclusion, OptRAM can provide a useful approach that leverages an integrated transcriptional regulatory network and metabolic network to guide metabolic engineering applications., Author summary Computational strain design algorithms based on genome-scale metabolic models have increasingly been used to guide rational strain design for metabolic engineering. However, most strain optimization algorithms only utilize a metabolic network alone and cannot provide strategies that also involve transcriptional regulation. In this paper, we developed a novel strain design algorithm, named OptRAM (Optimization of Regulatory And Metabolic Network), which can identify combinatorial optimization strategies including overexpression, knockdown or knockout of both transcription factors and metabolic genes, based on our previous IDREAM integrated network framework. OptRAM uses simulated annealing with a novel objective function, which can ensure a favorable coupling between the production of a desired chemical and cell growth. This strategy can be deployed for strain design of bacteria, archaea or eukaryotes. The other advantage of OptRAM compared with previous heuristic approaches is that we systematically evaluated the implementation cost of different solutions and selected strain designs which are more likely to be achievable in experiments. Through the in-silico strain design case studies for producing succinate, 2,3-butanediol, and ethanol in yeast, we demonstrated that OptRAM can identify strategies that increase production beyond what is seen currently, or found as potential designs using alternative methods. We also validated the modified genes chosen by OptRAM in example cases against previous in vivo experiments in the LASER database. Additionally, we experimentally validated the ethanol strain design by evaluating its performance in fermentation. OptRAM provides a robust approach to strain design across gene regulatory network modification and metabolic engineering.

Flux balance analysis (FBA) is one of the most often applied methods on genome-scale metabolic networks. Although FBA uniquely determines the optimal yield, the pathway that achieves this is usually not unique. The analysis of the optimal-yield flux space has been an open challenge. Flux variability analysis is only capturing some properties of the flux space, while elementary mode analysis is intractable due to the enormous number of elementary modes. However, it has been found by Kelk et al. 2012, that the space of optimal-yield fluxes decomposes into flux modules. These decompositions allow a much easier but still comprehensive analysis of the optimal-yield flux space. Using the mathematical definition of module introduced by M¨uller and Bockmayr 2013, we discovered that flux modularity is rather a local than a global property which opened connections to matroid theory. Specifically, we show that our modules correspond one-to-one to so-called separators of an appropriate matroid. Employing efficient algorithms developed in matroid theory we are now able to compute the decomposition into modules in a few seconds for genome-scale networks. Using that every module can be represented by one reaction that represents its function, in this paper, we also present a method that uses this decomposition to visualize the interplay of modules. We expect the new method to replace flux variability analysis in the pipelines for metabolic networks.

The design of container shipping networks is an important logistics problem, involving assets and operational costs measured in billions of dollars. To guide the optimal deployment of the ships, a single vessel round trip is considered by minimizing operational costs and flowing the best paying demand under commercially driven constraints. This paper introduces the Single Liner Shipping Service Design Problem. Arc-flow and path-flow models are presented using state-of-the-art elements from the wide literature on pickup and delivery problems. A Branch-and-Cut-and-Price algorithm is proposed, and implementation details are discussed. The algorithm can solve instances with up to 25 ports to optimality, a very promising result as real-world vessel roundtrips seldom involve more than 20 ports. © 2013 Elsevier Ltd.

Background Structural alignment of proteins is one of the most challenging problems in molecular biology. The tertiary structure of a protein strictly correlates with its function and computationally predicted structures are nowadays a main premise for understanding the latter. However, computationally derived 3D models often exhibit deviations from the native structure. A way to confirm a model is a comparison with other structures. The structural alignment of a pair of proteins can be defined with the use of a concept of protein descriptors. The protein descriptors are local substructures of protein molecules, which allow us to divide the original problem into a set of subproblems and, consequently, to propose a more efficient algorithmic solution. In the literature, one can find many applications of the descriptors concept that prove its usefulness for insight into protein 3D structures, but the proposed approaches are presented rather from the biological perspective than from the computational or algorithmic point of view. Efficient algorithms for identification and structural comparison of descriptors can become crucial components of methods for structural quality assessment as well as tertiary structure prediction. Results In this paper, we propose a new combinatorial model and new polynomial-time algorithms for the structural alignment of descriptors. The model is based on the maximum-size assignment problem, which we define here and prove that it can be solved in polynomial time. We demonstrate suitability of this approach by comparison with an exact backtracking algorithm. Besides a simplification coming from the combinatorial modeling, both on the conceptual and complexity level, we gain with this approach high quality of obtained results, in terms of 3D alignment accuracy and processing efficiency. Conclusions All the proposed algorithms were developed and integrated in a computationally efficient tool descs-standalone, which allows the user to identify and structurally compare descriptors of biological molecules, such as proteins and RNAs. Both PDB (Protein Data Bank) and mmCIF (macromolecular Crystallographic Information File) formats are supported. The proposed tool is available as an open source project stored on GitHub (https://github.com/mantczak/descs-standalone). Electronic supplementary material The online version of this article (doi:10.1186/s12859-016-1237-9) contains supplementary material, which is available to authorized users.

This paper surveys main principles of feature selection and their recent applications in big data bioinformatics. Instead of the commonly used categorization into filter, wrapper, and embedded approaches to feature selection, we formulate feature selection as a combinatorial optimization or search problem and categorize feature selection methods into exhaustive search, heuristic search, and hybrid methods, where heuristic search methods may further be categorized into those with or without data-distilled feature ranking measures.

Optimization is a powerful paradigm for expressing and solving problems in a wide range of areas, and has been successfully applied to many vision problems. Discrete optimization techniques are especially interesting, since by carefully exploiting problem structure they often provide non-trivial guarantees concerning solution quality. In this paper we briefly review dynamic programming and graph algorithms, and discuss representative examples of how these discrete optimization techniques have been applied to some classical vision problems. We focus on the low-level vision problem of stereo; the mid-level problem of interactive object segmentation; and the high-level problem of model-based recognition.

Ant colony optimization (ACO) has widely been applied to solve combinatorial optimization problems in recent years. There are few studies, however, on its convergence time, which reflects how many iteration times ACO algorithms spend in converging to the optimal solution. Based on the absorbing Markov chain model, we analyze the ACO convergence time in this paper. First, we present a general result for the estimation of convergence time to reveal the relationship between convergence time and pheromone rate. This general result is then extended to a two-step analysis of the convergence time, which includes the following: 1) the iteration time that the pheromone rate spends on reaching the objective value and 2) the convergence time that is calculated with the objective pheromone rate in expectation. Furthermore, four brief ACO algorithms are investigated by using the proposed theoretical results as case studies. Finally, the conclusions of the case studies that the pheromone rate and its deviation determine the expected convergence time are numerically verified with the experiment results of four one-ant ACO algorithms and four ten-ant ACO algorithms.

A new field of research is rapidly expanding at the crossroad between statistical physics, information theory and combinatorial optimization. In particular, the use of cutting edge statistical physics concepts and methods allow one to solve very large constraint satisfaction problems like random satisfiability, coloring, or error correction. Several aspects of these developments should be relevant for the understanding of functional complexity in neural networks. On the one hand the message passing procedures which are used in these new algorithms are based on local exchange of information, and succeed in solving some of the hardest computational problems. On the other hand some crucial inference problems in neurobiology, like those generated in multi-electrode recordings, naturally translate into hard constraint satisfaction problems. This paper gives a non-technical introduction to this field, emphasizing the main ideas at work in message passing strategies and their possible relevance to neural networks modeling. It also introduces a new message passing algorithm for inferring interactions between variables from correlation data, which could be useful in the analysis of multi-electrode recording data., Prepared for the proceedings of the 2007 Tauc Conference on Complexity in Neural Network Dynamics

Results from the application of three nonlinear stiffness reconstruction algorithms to two simple cylindrical geometries are presented in this paper. Finite-element simulated harmonic motion data with added noise were initially used to represent a measured surface displacement dataset for each geometry. This motion was used as input to gradient-descent, combinatorial optimization, and hybrid reconstruction algorithms that aimed to reconstruct two shape-based parameters describing the internal stiffness of the geometry. Both the combinatorial optimization and hybrid algorithms showed significant advantages in reconstructed parameter accuracy when compared with the traditional gradient-descent approach, with success metrics improving by 13-28%. Results from the hybrid algorithm applied to silicone phantom displacements demonstrated for the first time the ability of this type of algorithm to reconstruct internal stiffness using only experimentally measured surface motion data. Improvements in the sophistication of the hybrid approach should lead to improved accuracy in reconstructed solutions, as well as enabling reconstructions where the geometry is less straightforward.

Although genetic factors play an important role in most human diseases, multiple genes or genes and environmental factors may influence individual risk. In order to understand the underlying biological mechanisms of complex diseases, it is important to understand the complex relationships that control the process. In this paper, we consider different perspectives, from each optimization, complexity analysis, and algorithmic design, which allows us to describe a reasonable and applicable computational framework for detecting gene-gene interactions. Accordingly, support vector machine and combinatorial optimization techniques (local search and genetic algorithm) were tailored to fit within this framework. Although the proposed approach is computationally expensive, our results indicate this is a promising tool for the identification and characterization of high order gene-gene and gene-environment interactions. We have demonstrated several advantages of this method, including the strong power for classification, less concern for overfitting, and the ability to handle unbalanced data and achieve more stable models. We would like to make the support vector machine and combinatorial optimization techniques more accessible to genetic epidemiologists, and to promote the use and extension of these powerful approaches.

Accuracy maximization and complexity minimization are the two main goals of a fuzzy expert system based microarray data classification. Our previous Genetic Swarm Algorithm (GSA) approach has improved the classification accuracy of the fuzzy expert system at the cost of their interpretability. The if-then rules produced by the GSA are lengthy and complex which is difficult for the physician to understand. To address this interpretability-accuracy tradeoff, the rule set is represented using integer numbers and the task of rule generation is treated as a combinatorial optimization task. Ant colony optimization (ACO) with local and global pheromone updations are applied to find out the fuzzy partition based on the gene expression values for generating simpler rule set. In order to address the formless and continuous expression values of a gene, this paper employs artificial bee colony (ABC) algorithm to evolve the points of membership function. Mutual Information is used for idenfication of informative genes. The performance of the proposed hybrid Ant Bee Algorithm (ABA) is evaluated using six gene expression data sets. From the simulation study, it is found that the proposed approach generated an accurate fuzzy system with highly interpretable and compact rules for all the data sets when compared with other approaches.

Assortment optimization has received significant attention in recent revenue management and combinatorial optimization literature. In “The Approximability of Assortment Optimization Under Ranking Preferences,” A. Aouad, V. Farias, R. Levi, and D. Segev provide best-possible approximability bounds for this problem under an almost general model specification, where preferences are expressed as a distribution over rankings. This paper shows how this optimization problem relates to the computational task of detecting large independent sets in graphs, allowing the establishment of strong complexity lower bounds with respect to various problem parameters. These findings are complemented by a number of algorithms that attain essentially best-possible approximation factors, proving that the hardness results are tight up to lower-order terms. Surprisingly, their results imply that a simple and widely studied policy, known as revenue-ordered assortments, achieves the best possible performance guarantee with respect to prices.