Exact Algorithm Research Articles

Sequential use of blocplan, solver, and particle swarm optimization (PSO) to optimize the double row facility layout

Facility layout optimization is used to increase company productivity by minimizing waste on transportation, movement, and waiting time. It was mentioned in several previous studies that optimal facility layout can reduce production costs by up to 40%. Because of this importance, many previous researchers have carried out research in the field of Facility Layout. The differences between each Facility Layout research are in the characteristics and criteria being analyzed and the optimization method used. The several approaches used to optimize the layout are constructed algorithm, exact algorithm, and metaheuristic. These three methods have their respective purposes and to the best of our knowledge have not been used sequentially. So, this study aims to find the best layout for the double-row facility problem with aisle width consideration using three sequential methods. There are BLOCPLAN for the constructed algorithm, solver for the exact algorithm, and Particle Swarm Optimization (PSO) for the metaheuristic. The result shows that the use of BLOCPLAN gives a better result of Total Material Handling Cost (TMHC) in PSO. For more machines, PSO has better results than Gurobi Optimization.

An enhanced exact algorithm for the multi-trip vehicle routing problem with time windows and capacitated unloading station

This paper introduces a vehicle routing problem that simultaneously considers multiple trips, time windows, and a capacitated unloading station. This problem is a generalization of the multi-trip vehicle routing problem with time windows, which determines a set of least-cost vehicle routes to fulfill all customer demands while respecting the constraints of vehicle capacity and time windows. Due to restricted resources (e.g., equipment and labor force) at the depot, vehicles may need to wait in a queue for being unloaded when they arrive. This unloading capacity constraint significantly complicates the problem, as it causes a trip to involve three stages—traveling, waiting, and unloading. We formulate this problem as an arc flow model and a trip-based set partitioning model, where the latter is solved by a branch-price-and-cut (BPC) algorithm. To improve the computational aspect of the BPC framework, a two-phase column generation (CG) algorithm is designed. First, a bidirectional labeling algorithm is tailored to solve the pricing problem, where two accelerating strategies are employed to speed up the resolution process. Meanwhile, k-path inequalities and limited-memory subset row inequalities are utilized to tighten the linear relaxation of the master problem. Computational results based on the instances adapted from the well-known Solomon’s benchmark show that the developed BPC algorithm can solve most instances within 50 customers to optimality in a short time frame and some instances of 100 customers to optimality within a 3-hour time limit. Moreover, our BPC algorithm performs better than exact algorithms in the literature for similar problem variants in both solution quality and computing time.

ESKEMAP: exact sketch-based read mapping

BackgroundGiven a sequencing read, the broad goal of read mapping is to find the location(s) in the reference genome that have a “similar sequence”. Traditionally, “similar sequence” was defined as having a high alignment score and read mappers were viewed as heuristic solutions to this well-defined problem. For sketch-based mappers, however, there has not been a problem formulation to capture what problem an exact sketch-based mapping algorithm should solve. Moreover, there is no sketch-based method that can find all possible mapping positions for a read above a certain score threshold.ResultsIn this paper, we formulate the problem of read mapping at the level of sequence sketches. We give an exact dynamic programming algorithm that finds all hits above a given similarity threshold. It runs in O(|t|+|p|+ℓ2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O} (|t| + |p| + \\ell ^2)$$\\end{document} time and O(ℓlogℓ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O} (\\ell \\log \\ell )$$\\end{document} space, where |t| is the number of k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k$$\\end{document}-mers inside the sketch of the reference, |p| is the number of k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k$$\\end{document}-mers inside the read’s sketch and ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell$$\\end{document} is the number of times that k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k$$\\end{document}-mers from the pattern sketch occur in the sketch of the text. We evaluate our algorithm’s performance in mapping long reads to the T2T assembly of human chromosome Y, where ampliconic regions make it desirable to find all good mapping positions. For an equivalent level of precision as minimap2, the recall of our algorithm is 0.88, compared to only 0.76 of minimap2.

On the approximability and energy-flow modeling of the electric vehicle sharing problem

The electric vehicle sharing problem (EVSP) arises from the planning and operation of one-way electric car-sharing systems. It aims to maximize the total rental time of a fleet of electric vehicles while ensuring that all the demands of the customer are fulfilled. In this paper, we first show that the EVSP is NP-hard to approximate to within a factor of n1−ϵ in polynomial time, for any ϵ>0, where n denotes the number of customers. In addition, we also show that the problem does not have a monotone structure, which can be detrimental to the development of heuristics employing constructive strategies. Moreover, we propose a novel approach for modeling the EVSP based on energy flows. Based on this new model, we propose a relax-and-fix strategy and an exact algorithm. Our computational results show that our formulation outperforms the previous best-performing formulation in the literature in the number of optimal solutions obtained, optimality gaps, and computational times. Previously, 32.7% of the instances remained unsolved (within a time limit of one hour), while our formulation obtained optimal solutions for all instances. To stress our approaches, two more challenging new sets of instances are generated, for which we can solve 49.5% of the instances, with an average optimality gap of 2.91% for those not solved optimally.

Pattern matching algorithms in blockchain for network fees reduction

AbstractBlockchain received a vast amount of attention in recent years and is still growing. The second generation of blockchain, such as Ethereum, allows execution of almost any program in EVM, making it a global protocol for distributed applications. The code deployment and each operation performed in EVM cost the network fee called gas, whose price varies and can be significant. That is why code optimization and well-chosen algorithms are crucial in programming on the blockchain. This paper evaluates the gas usage of several exact pattern matching algorithms on the EVM. We also propose an efficient implementation of the algorithms in the Solidity/YUL language. We evaluate the gas fees of all the algorithms for different parameters (such as pattern length, alphabet size, and text size). We show a significant gas fee and execution time reduction with up to 22-fold lower gas usage and 55-fold speed-up compared to StringUtils (a popular Solidity string library).

Faster classical boson sampling

Abstract Since its introduction boson has been the subject of intense study in the world of quantum computing. In the Fock protocol, the task is to sample independently from the set of all n by n submatrices built from possibly repeated rows of a larger m by n complex matrix according to a probability distribution related to the permanents of the submatrices. Experimental systems exploiting quantum photonic effects can in principle perform the task at high speed. In the framework of classical computing, Aaronson and Arkhipov (2011) showed that exact boson sampling problem cannot be solved in polynomial time unless the polynomial hierarchy collapses to the third level. Indeed for a number of years the fastest known exact classical algorithm ran in O(binomial(m+n-1, n) n 2^n ) time per sample, emphasising the potential speed advantage of quantum computation. The advantage was reduced by Clifford and Clifford (2018) who gave a significantly faster classical solution taking O(n 2^n + poly(m,n)) time and linear space, matching the complexity of computing the permanent of a single matrix when m is polynomial in n.
 
 We continue by presenting an algorithm for Fock boson sampling whose average-case time complexity is much faster when m is proportional to n. In particular, when m = n our algorithm runs in approximately O(n 1.69^n) time on average. This result further increases the problem size required to establish quantum computational advantage via the Fock scheme of boson sampling.

Homomorphic encrypted Yara rules evaluation

Malware signatures represent a powerful tool for malware detection and classification, widely used by security researchers and security solution providers. Yara rules describe malware based on string patterns that are evaluated on targeted files. Generally, the security provider sends signatures to the client endpoints and the rule evaluation is performed locally, such that the scanned files do not leave the client machines. However, if a zero-day vulnerability is discovered and the security provider exposes the corresponding signature, there is a considerable risk to also disclose the unpatched vulnerability. A solution is represented by homomorphic encrypted Yara rules, which can be evaluated on targeted files without being decrypted. In this article, we propose a homomorphic Yara rules evaluation method and do a comparative analysis with the HENFA method (Homomorphic Encryption for Finite Automata (Genise et al., 2019)). For our method, we propose a fully homomorphic exact string matching algorithm based on the TFHE scheme (Fully Homomorphic Encryption over the Torus (Chillotti et al., 2020)). In order to determine how suitable is the exact string matching approach in practice, we analyze a public Yara rules repository and generate various statistics about the patterns used in the Yara rules. For the two homomorphic Yara rules matching methods, both theoretical and experimental comparative evaluations are presented. Our proposed method implies ciphertexts with smaller sizes and has better efficiency in the average testing scenarios compared to the HENFA method.

Combinatorial Benders decomposition for single machine scheduling in additive manufacturing with two-dimensional packing constraints

This paper addresses a single-machine scheduling problem in additive manufacturing (AM). We focus on the direct metal laser sintering (DMLS) technology of an AM process, where parts can be produced simultaneously in a batch. In this problem, we consider simultaneously the assignment of parts to batches and the packing of parts onto two-dimensional surfaces of the build chamber to minimize the makespan objective. To solve this problem, a mixed integer linear programming model is formulated, and an approximation algorithm is proposed, followed by an exact algorithm based on combinatorial Benders decomposition method with various Benders cuts and acceleration strategies (Algorithm CBD). Finally, we conduct a comprehensive computational study to verify the efficiency of our proposed Algorithm CBD. The computational results show that our proposed Algorithm CBD can effectively solve the test instances with different sizes.

Exact and approximation algorithms for covering timeline in temporal graphs

AbstractWe consider a variant of vertex cover on temporal graphs that has been recently defined for summarization of timeline activities in temporal graphs. The problem has been proved to be NP-hard, even for several restrictions of the time domain and vertex degree. We present novel algorithmic contributions for the problem and we give an approximation algorithm of factor $$O(T \log {n})$$ O ( T log n ) , on a temporal graph of T timestamps and n vertices. We focus then on the NP-hard restriction of the problem, where at most one temporal edge is defined in each timestamp. For this restriction we present a $$4(T-1)$$ 4 ( T - 1 ) approximation algorithm and a parameterized algorithm (a reduction to kernel) for parameter the cost, called span, of the solution.

BiGNN: Bipartite graph neural network with attention mechanism for solving multiple traveling salesman problems in urban logistics

The multiple traveling salesman problems (MTSP), which arise from real world problems, are essential in urban logistics. Variations such as MinMax-MTSP and Bounded-MTSP aim to distribute workload evenly among salesmen and impose constraints on visited cities, respectively. Branch-and-bound (B&B) provides an exact algorithm solution for these problems. The Learn to Branch (L2B) approach guides branch node selection through deep learning. In this study, we utilize mathematical modeling of Bipartite Graph Neural Network (BiGNN) and an attention mechanism to support B&B in exploring solution spaces through imitation learning. The problems are framed to formulate mixed integer linear programming, which is different from conventional algorithms. It is proposed that a bipartite graph network approach makes a feature representation by setting a structure of constraints and variables. Experimental results showed that our model can generate more accurate solutions than three benchmark models. The BiGNN model can effectively learn the strong branch strategy, which reduces solution time by replacing complex calculations with fast approximations. Additionally, the small-scale instances model can be applied to larger-scale ones.

Review of Research on Human-Machine Collaboration in Disassembly Line Balancing Problem

This paper aims to explore the research on the human-machine collaboration in the disassembly line balancing problem, in response to the importance of dismantling and reusing waste products. Human-machine collaboration in disassembly, as a method combining human intelligence with machine power, has the potential to enhance disassembly efficiency, reduce resource wastage, and minimize human exposure to hazards. However, due to the NP-hard nature of this problem, traditional exact algorithms perform poorly when facing large-scale and complex problems. Therefore, this paper explores the application of intelligent algorithms such as genetic algorithms, wolf pack algorithms, etc., and proposes novel and efficient solutions to the human-machine collaboration in disassembly line balancing problem. Additionally, to address the challenge of the large-scale problem state space, this paper also discusses the potential application of emerging technologies such as reinforcement learning. Through these studies, this review aims to promote the development of the remanufacturing industry and facilitate resource utilization and environmental protection.

Towards geodesic ridge curve for region-wise linear representation of geodesic distance field

This paper addresses the challenge of representing geodesic distance fields on triangular meshes in a piecewise linear manner. Unlike general scalar fields, which often assume piecewise linear changes within each triangle, geodesic distance fields pose a unique difficulty due to their non-differentiability at ridge points, where multiple shortest paths may exist. An interesting observation is that the geodesic distance field exhibits an approximately linear change if each triangle is further decomposed into sub-regions by the ridge curve. However, computing the geodesic ridge curve is notoriously difficult. Even when using exact algorithms to infer the ridge curve, desirable results may not be achieved, akin to the well-known medial-axis problem. In this paper, we propose a two-stage algorithm. In the first stage, we employ Dijkstra's algorithm to cut the surface open along the dual structure of the shortest path tree. This operation allows us to extend the surface outward (resembling a double cover but with distinctions), enabling the discovery of longer geodesic paths in the extended surface. In the second stage, any mature geodesic solver, whether exact or approximate, can be employed to predict the real ridge curve. Assuming the fast marching method is used as the solver, despite its limitation of having a single marching direction in a triangle, our extended surface contains multiple copies of each triangle, allowing various geodesic paths to enter the triangle and facilitating ridge curve computation. We further introduce a simple yet effective filtering mechanism to rigorously ensure the connectivity of the output ridge curve. Due to its merits, including robustness and compatibility with any geodesic solver, our algorithm holds great potential for a wide range of applications. We demonstrate its utility in accurate geodesic distance querying and high-fidelity visualization of geodesic iso-lines.

An exact algorithm to find a maximum weight clique in a weighted undirected graph

We introduce a new algorithm MaxCliqueWeight for identifying a maximum weight clique in a weighted graph, and its variant MaxCliqueDynWeight with dynamically varying bounds. This algorithm uses an efficient branch-and-bound approach with a new weighted graph coloring algorithm that efficiently determines upper weight bounds for a maximum weighted clique in a graph. We evaluate our algorithm on random weighted graphs with node counts up to 10,000 and on standard DIMACS benchmark graphs used in a variety of research areas. Our findings reveal a remarkable improvement in computational speed when compared to existing algorithms, particularly evident in the case of high-density random graphs and DIMACS graphs, where our newly developed algorithm outperforms existing alternatives by several orders of magnitude. The newly developed algorithm and its variant are freely available to the broader research community at http://insilab.org/maxcliqueweight, paving the way for transformative applications in various research areas, including drug discovery.

Decomposition algorithms for the robust unidirectional quay crane scheduling problems

Our study focuses on a two-stage robust optimization model for the unidirectional quay crane scheduling problem with uncertain handling times at container terminals. We first implement two classical algorithms adopted in Li and Zhang (2021), the Benders decomposition algorithm and the column-and-constraint generation algorithm, to solve the robust model. Based on analytical and numerical comparisons of them, we design an exact hybrid algorithm to leverage capabilities of both algorithms by alternatively adding cuts of both kinds. Extensive experiments validate the effectiveness of this mechanism. Numerical experiments also reveal that the benefit and the cost of robustness fade away as the uncertainty budget increases and highlight the advantage of our robust approach to deal with uncertainty over a two-stage stochastic program under extreme situations.

Fast exact algorithm for neutrino oscillation in constant matter density

A recently published method [1,2] for solving the neutrino evolution equation with constant matter density is further refined and used to lay out an exact algorithm for computing oscillation probabilities, which is moderately faster than previous methods when looping through neutrinos of different energies. In particular, the three examples of ν(−)e survival, ν(−)μ survival and ν(−)e appearance probabilities are written in terms of mixing angles, mass differences and matter electron density. A program based on this new method is found to be roughly twice as fast as, and in agreement with, the leading GLoBES package. Furthermore, the behaviour of all relevant effective parameters is sketched out in terms of a range of neutrino energies, or matter electron densities. For instance, the ν(−)e survival probability in constant matter density is found to have no dependence on the mixing angle θ23 or the CP-violating phase δ13.

The Floor Is Lava: Halving Natural Genomes with Viaducts, Piers, and Pontoons.

Whole Genome Duplications (WGDs) are events that double the content and structure of a genome. In some organisms, multiple WGD events have been observed while loss of genetic material is a typical occurrence following a WGD event. The requirement of classic rearrangement models that every genetic marker has to occur exactly two times in a given problem instance, therefore, poses a serious restriction in this context. The Double-Cut and Join (DCJ) model is a simple and powerful model for the analysis of large structural rearrangements. After being extended to the DCJ-Indel model, capable of handling gains and losses of genetic material, research has shifted in recent years toward enabling it to handle natural genomes, for which no assumption about the distribution of markers has to be made. The traditional theoretical framework for studying WGD events is the Genome Halving Problem (GHP). While the GHP is solved for the DCJ model for genomes without losses, there are currently no exact algorithms utilizing the DCJ-Indel model that are able to handle natural genomes. In this work, we present a general view on the DCJ-Indel model that we apply to derive an exact polynomial time and space solution for the GHP on genomes with at most two genes per family before generalizing the problem to an integer linear program solution for natural genomes.

On Breaking Truss-based and Core-based Communities

We introduce the general problem of identifying a smallest edge subset of a given graph whose deletion makes the graph community-free. We consider this problem under two community notions that have attracted significant attention: k -truss and k -core. We also introduce a problem variant where the identified subset contains edges incident to a given set of nodes and ensures that these nodes are not contained in any community: k -truss or k -core, in our case. These problems are directly applicable in social networks: The identified edges can be hidden by users or sanitized from the output graph; or in communication networks: the identified edges correspond to vital network connections. We present a series of theoretical and practical results. On the theoretical side, we show through non-trivial reductions that the problems we introduce are NP-hard and, in fact, hard to approximate. For the k -truss-based problems, we also show exact exponential-time algorithms, as well as a non-trivial lower bound on the size of an optimal solution. On the practical side, we develop a series of heuristics that are sped up by efficient data structures that we propose for updating the truss or core decomposition under edge deletions. In addition, we develop an algorithm to compute the lower bound. Extensive experiments on 11 real-world and synthetic graphs show that our heuristics are effective, outperforming natural baselines, and also efficient (up to two orders of magnitude faster than a natural baseline), thanks to our data structures. Furthermore, we present a case study on a co-authorship network and experiments showing that the removal of edges identified by our heuristics does not substantially affect the clustering structure of the input graph. This work extends a KDD 2021 paper, providing new theoretical results as well as introducing core-based problems and algorithms.

On Constrained Mixed-Integer DR-Submodular Minimization

Diminishing returns (DR)–submodular functions encompass a broad class of functions that are generally nonconvex and nonconcave. We study the problem of minimizing any DR-submodular function with continuous and general integer variables under box constraints and, possibly, additional monotonicity constraints. We propose valid linear inequalities for the epigraph of any DR-submodular function under the constraints. We further provide the complete convex hull of such an epigraph, which, surprisingly, turns out to be polyhedral. We propose a polynomial-time exact separation algorithm for our proposed valid inequalities with which we first establish the polynomial-time solvability of this class of mixed-integer nonlinear optimization problems. Funding: This work was supported by the Office of Naval Research Global [Grant N00014-22-1-2602].

Optimal routing with road network for scattered farm fields: Computational experiments with the branch-and-cut and 2-opt algorithms and case study on an agricultural corporation in Japan

This study investigates optimal routing with a road network to minimize the total traveling distance among scattered farm fields for smart agriculture. Based on the case of an agricultural corporation in Japan, the shortest paths between all pairs of farm fields and their distances are obtained by utilizing road network data, and the optimal route is searched by addressing the traveling salesman problem (TSP) with an exact algorithm, which is implemented by the COIN-OR branch and cut (CBC) solver. The applicability of the TSP with the exact algorithm is verified by comparing its computational time and solution to those of the TSP with the 2-opt method, an approximation algorithm, through a computational experiment. Moreover, the effectiveness of the proposed approach is demonstrated through a case study on the agricultural corporation considered. The results of the computational experiment and case study show that the proposed approach can provide the optimal route for daily work within 7.5 seconds and can reduce 6.89% of the traveling distance from that of the route a worker creates empirically.

Preliminary Implications of Viscoelastic Ray Theory for Anelastic Seismic Tomography Models

ABSTRACT The recent developments in general viscoelastic ray theory provide a rigorous mathematical framework for anelastic seismic tomography. They provide closed-form solutions of forward ray-tracing and simple inverse problems for anelastic horizontal and spherical layered media with material gradients. They provide ray-tracing computation algorithms valid for all angles of incidence that account for changes in wave speed, attenuation, and trajectory of anelastic P and S body waves induced by anelastic boundaries. They account for theoretical predictions that seismic waves refract as inhomogeneous waves across anelastic boundaries for all angles of incidence, which in turn accounts for energy carried by plane waves along seismic boundaries at head wave critical angles and wide-angle refracted (WAR) ray paths that are not predicted by elastic models. Exact viscoelastic ray-tracing numerical results for various models provide examples that illustrate the effects of anelastic boundaries on the travel times and amplitudes of seismic waves. They show the effects are strongly dependent on angle of incidence. For near-critical and wide angles of incidence the anelastic effects on travel times and amplitudes can be large and are not explained by elastic ray theory, but the effects on travel times can be relatively small and difficult to distinguish from those for elastic media for pre-near-critical angles of incidence. The results for some models indicate that reflected anelastic WAR waves may be observable at the surface and possibly account for some prominent seismic arrivals not explained by elasticity. These preliminary results suggest that the application of exact viscoelastic ray-tracing computation algorithms to exploration and teleseismic data sets can reveal new insights regarding the properties and distribution of anelastic materials in the Earth.