Approximation Algorithm Research Articles

Coordinated risk-averse distributionally robust optimization for maintenance and generation schedules of offshore wind farm cluster

The coordinated optimization of maintenance and generation schedules of multiple offshore wind farms (OWFs) bring great benefits in reducing the maintenance and operation cost of OWF cluster. Firstly, a two-stage coordinated risk-averse distributionally robust optimization (CRDRO) model for maintenance and generation schedules of wind turbines (WTs) in OWF cluster is proposed. This model takes into account uncertainties related to the prediction errors in WTs’ maximum available active power outputs, the travel time of maintenance vessels, and the high operational cost risks associated with these uncertainties. A feasible route generating algorithm is designed to obtain all feasible maintenance combinations for WTs and the corresponding routes of maintenance vessels for the CRDRO model. The risk-averse term, which is a weighted sum of expected operation costs and GlueVaR value, is used to measure the tail risk of the worst probability distribution. To solve the two-stage CRDRO model, the risk-averse term is simplified into the form of expected value calculation, which can be further transformed into the tractable form by using the strong duality theorem. Finally, the two-stage CRDRO model is solved by the column-and-constraint generation algorithm, with the nonconvex sub-problem being addressed by the outer approximation algorithm. Case studies on an real-world cluster comprising three OWFs verify the correctness and efficiency of the proposed method, and demonstrate that the CRDRO model enhances the overall economic efficiency and reduces the high operational cost risk under extreme scenarios.

Multi-Objective Portfolio Optimization Using a Quantum Annealer

In this study, the portfolio optimization problem is explored, using a combination of classical and quantum computing techniques. The portfolio optimization problem with specific objectives or constraints is often a quadratic optimization problem, due to the quadratic nature of, for example, risk measures. Quantum computing is a promising solution for quadratic optimization problems, as it can leverage quantum annealing and quantum approximate optimization algorithms, which are expected to tackle these problems more efficiently. Quantum computing takes advantage of quantum phenomena like superposition and entanglement. In this paper, a specific problem is introduced, where a portfolio of loans need to be optimized for 2030, considering ‘Return on Capital’ and ‘Concentration Risk’ objectives, as well as a carbon footprint constraint. This paper introduces the formulation of the problem and how it can be optimized using quantum computing, using a reformulation of the problem as a quadratic unconstrained binary optimization (QUBO) problem. Two QUBO formulations are presented, each addressing different aspects of the problem. The QUBO formulation succeeded in finding solutions that met the emission constraint, although classical simulated annealing still outperformed quantum annealing in solving this QUBO, in terms of solutions close to the Pareto frontier. Overall, this paper provides insights into how quantum computing can address complex optimization problems in the financial sector. It also highlights the potential of quantum computing for providing more efficient and robust solutions for portfolio management.

Drone-Based Bug Detection in Orchards with Nets: A Novel Orienteering Approach

The use of drones for collecting information and detecting bugs in orchards covered by nets is a challenging problem. The nets help in reducing pest damage, but they also constrain the drone’s flight path, making it longer and more complex. To address this issue, we model the orchard as an aisle-graph, a regular data structure that represents consecutive aisles where trees are arranged in straight lines. The drone flies close to the trees and takes pictures at specific positions for monitoring the presence of bugs, but its energy is limited, so it can only visit a subset of positions. To tackle this challenge, we introduce the Single-drone Orienteering Aisle-graph Problem (SOAP), a variant of the orienteering problem, where likely infested locations are prioritized by assigning them a larger profit. Additionally, the drone’s movements have a cost in terms of energy, and the objective is to plan a drone’s route in the most profitable locations under a given drone’s battery. We show that SOAP can be optimally solved in polynomial time, but for larger orchards/instances, we propose faster approximation and heuristic algorithms. Finally, we evaluate the algorithms on synthetic and real datasets to demonstrate their effectiveness and efficiency.

The third and fourth international competitions on computational models of argumentation: Design, results and analysis

The International Competition on Computational Models of Argumentation (ICCMA) focuses on reasoning tasks in abstract argumentation frameworks. Submitted solvers are tested on a selected collection of benchmark instances, including artificially generated argumentation frameworks and some frameworks formalizing real-world problems. This paper presents the novelties introduced in the organization of the Third (2019) and Fourth (2021) editions of the competition. In particular, we proposed new tracks to competitors, one dedicated to dynamic solvers (i.e., solvers that incrementally compute solutions of frameworks obtained by incrementally modifying original ones) in ICCMA’19 and one dedicated to approximate algorithms in ICCMA’21. From the analysis of the results, we noticed that i) dynamic recomputation of solutions leads to significant performance improvements, ii) approximation provides much faster results with satisfactory accuracy, and iii) classical solvers improved with respect to previous editions, thus revealing advancement in state of the art.

A Steiner-point-based algorithm for approximate shortest paths in weighted equilateral-triangle meshes

Let T be a tessellation composed of equilateral triangular regions, where each region has an associated positive weight. We present two methods that discretize the space based on the placement of Steiner points in the cells of T. Using such a discretization, we can use Dijkstra's algorithm for computing the shortest path in the geometric graph obtained. This will lead us to two approximation algorithms for solving the Weighted Region Problem. For a given parameter ε∈(0,1], the first discretization scheme provides an approximate path that is (1+0.428ε) times better than the approximation given by Aleksandrov et al. (2005) [5]. The other discretization scheme uses at least (ε+2ε+4ε+4)log2⁡e fewer points per segment of the triangulation with the same approximation factor.

Approximation algorithms for maximum weighted target cover problem with distance limitations

Approximation algorithms for maximum weighted target cover problem with distance limitations

MATE: When multi-agent Deep Reinforcement Learning meets Traffic Engineering in multi-domain networks

As the global network evolves into a large-scale interconnection system with multiple distributed domains, scalability and efficiency have become equally important for Traffic Engineering (TE). Traditional centralized TE suffers from significant computational complexity and privacy concerns, while distributed TE results in suboptimal routing decisions due to its lack of a coordination mechanism. This paper proposes MATE, an innovative, scalable, and efficient TE framework for multi-domain networks featuring a hierarchical control plane. MATE designs a three-stage workflow to optimize routing decisions for inter-domain traffic while ensuring their QoS guarantees. First, in the bottom-up topology abstraction stage, MATE aggregates network resources within each domain, creating an abstract view of the global network state while protecting each domain’s internal information. Second, in the top-down decision-making stage, MATE computes a QoS-constrained domain sequence based on the global network state and then converts it into multi-path routing in all related domains. Third, MATE conducts parallel inferences across relevant domains on traffic split ratios for multi-path routing using well-designed multi-agent reinforcement learning. We evaluate MATE on both real-world and synthetic topologies under various traffic patterns. In a large-scale topology encompassing 16 domains, MATE achieves near-optimal link utilization across 97% network scenarios, with an approximation ratio of below 1.3. The experimental results demonstrate MATE’s superiority in fulfilling QoS requirements, minimizing maximum link utilization, and maintaining robustness against traffic pattern variations and random link failures.

Constructing Semantic Summaries Using Embeddings

The increase in the size and complexity of large knowledge graphs now available online has resulted in the emergence of many approaches focusing on enabling the quick exploration of the content of those data sources. Structural non-quotient semantic summaries have been proposed in this direction that involve first selecting the most important nodes and then linking them, trying to extract the most useful subgraph out of the original graph. However, the current state of the art systems use costly centrality measures for identifying the most important nodes, whereas even costlier procedures have been devised for linking the selected nodes. In this paper, we address both those deficiencies by first exploiting embeddings for node selection, and then by meticulously selecting approximate algorithms for node linking. Experiments performed over two real-world big KGs demonstrate that the summaries constructed using our method enjoy better quality. Specifically, the coverage scores obtained were 0.8, 0.81, and 0.81 for DBpedia v3.9 and 0.94 for Wikidata dump 2018, across 20%, 25%, and 30% summary sizes, respectively. Additionally, our method can compute orders of magnitude faster than the state of the art.

A research on an improved fuzzy approximate entropy algorithm for EMG-based shoulder and neck muscle fatigue detection

A robust muscle fatigue algorithm plays a pivotal role in depicting the degree of muscle fatigue in both time-series EMG signal graphs and spectral graphs, aligning with human perception. While the fuzzy approximate entropy (fApEn) algorithm has been enhanced from the foundation of approximate entropy (ApEn) through the incorporation of fuzzy affiliation, concerns persist regarding the threshold value and the algorithm’s application range. This study extracts EMG signals across varied time durations and head-down angles, employing enhanced signal preprocessing techniques and optimizing the fApEn algorithm. Furthermore, real-time fatigue perceptions of subjects were recorded using the rating of perceived exertion. Experimental outcomes reveal that the EMG signal, post-wavelet analysis preprocessing, demonstrates promising noise reduction capabilities. Notably, the fApEn algorithm exhibits considerable enhancements through the identification of an optimal threshold using the gradient descent algorithm and a machine learning strategy.

Tight Lieb–Robinson Bound for approximation ratio in quantum annealing

Quantum annealing (QA) holds promise for optimization problems in quantum computing, especially for combinatorial optimization. This analog framework attracts attention for its potential to address complex problems. Its gate-based homologous, QAOA with proven performance, has attracted a lot of attention to the NISQ era. Several numerical benchmarks try to compare these two metaheuristics, however, classical computational power highly limits the performance insights. In this work, we introduce a parametrized version of QA enabling a precise 1-local analysis of the algorithm. We develop a tight Lieb–Robinson bound for regular graphs, achieving the best-known numerical value to analyze QA locally. Studying MaxCut over cubic graph as a benchmark optimization problem, we show that a linear-schedule QA with a 1-local analysis achieves an approximation ratio over 0.7020, outperforming any known 1-local algorithms.

An approximation algorithm for the -prize-collecting multicut problem in trees with submodular penalties

An approximation algorithm for the -prize-collecting multicut problem in trees with submodular penalties

Finite-Time High-Probability Bounds for Polyak–Ruppert Averaged Iterates of Linear Stochastic Approximation

This paper provides a finite-time analysis of linear stochastic approximation (LSA) algorithms with fixed step size, a core method in statistics and machine learning. LSA is used to compute approximate solutions of a d-dimensional linear system [Formula: see text] for which [Formula: see text] can only be estimated by (asymptotically) unbiased observations [Formula: see text]. We consider here the case where [Formula: see text] is an a sequence of independent and identically distributed random variables sequence or a uniformly geometrically ergodic Markov chain. We derive pth moment and high-probability deviation bounds for the iterates defined by LSA and its Polyak–Ruppert-averaged version. Our finite-time instance-dependent bounds for the averaged LSA iterates are sharp in the sense that the leading term we obtain coincides with the local asymptotic minimax limit. Moreover, the remainder terms of our bounds admit a tight dependence on the mixing time [Formula: see text] of the underlying chain and the norm of the noise variables. We emphasize that our result requires the LSA step size to scale only with logarithm of the problem dimension d. Funding: The work of A. Durmus and E. Moulines was partly supported by [Grant ANR-19-CHIA-0002]. This project received funding from the European Research Council [ERC-SyG OCEAN Grant 101071601]. The research of A. Naumov and S. Samsonov was prepared within the framework of the HSE University Basic Research Program.

Explicit machine learning-based model predictive control of nonlinear processes via multi-parametric programming

Machine learning-based model predictive control (ML-MPC) has been developed to control nonlinear processes with unknown first-principles models. While ML models can capture nonlinear dynamics of complex systems, the complexity of ML models leads to increased computation time for real-time implementation of ML-MPC. To address this issue, in this work, we propose an explicit ML-MPC framework for nonlinear processes using multi-parametric programming. Specifically, a self-adaptive approximation algorithm is first developed to obtain a piecewise linear affine function that approximates the behaviors of ML models. Then, multi-parametric quadratic programming (mpQP) problems are formulated to generate the solution map for states in discretized state–space. Furthermore, to accelerate the implementation of explicit ML-MPC, a neighbor-first search algorithm is developed. Finally, an example of a chemical reactor is used to demonstrate the effectiveness of the explicit ML-MPC.

On the Two-Dimensional Knapsack Problem for Convex Polygons

We study the two-dimensional geometric knapsack problem for convex polygons. Given a set of weighted convex polygons and a square knapsack, the goal is to select the most profitable subset of the given polygons that fits non-overlappingly into the knapsack. We allow to rotate the polygons by arbitrary angles. We present a quasi-polynomial time O (1)-approximation algorithm for the general case and a pseudopolynomial time O (1)-approximation algorithm if all input polygons are triangles, both assuming polynomially bounded integral input data. Additionally, we give a quasi-polynomial time algorithm that computes a solution of optimal weight under resource augmentation—that is, we allow to increase the size of the knapsack by a factor of 1+δ for some δ > 0 but compare ourselves with the optimal solution for the original knapsack. To the best of our knowledge, these are the first results for two-dimensional geometric knapsack in which the input objects are more general than axis-parallel rectangles or circles and in which the input polygons can be rotated by arbitrary angles.

Pseudo-model-based iterative learning control for nonlinear multi-phase batch processes

In this article, a pseudo-model-based iterative learning control (ILC) is exploited for multi-phase batch processes which can be described as a nonlinear switched system with unknown functions and identical states in different phases. The nonlinear switched system is converted into a linear model whose system parameter matrix is approximated by minimizing the discrepancy from the real system output increment to the approximated system output increment. A data-driven ILC is constructed in an interactive form with system parameter matrix approximate algorithm. Meanwhile, the signs of the diagonal elements of system lower triangular parameter matrix are introduced into the construction of control input law. Theoretical analysis shows that the pseudo-model-based ILC (PM-ILC) concept can be extended to multi-phase batch processes with non-identical states in different phases. Furthermore, the approximation error of the system parameters matrix is bounded and the proposed PM-ILC is robust if the parameter is appropriately chosen. Simulation results illustrate the effectiveness and practicability of the proposed PM-ILC.

Sketching Approximability of All Finite CSPs

A constraint satisfaction problem (CSP), \(\textsf {Max-CSP}(\mathcal {F})\) , is specified by a finite set of constraints \(\mathcal {F}\subseteq \lbrace [q]^k \rightarrow \lbrace 0,1\rbrace \rbrace\) for positive integers q and k . An instance of the problem on n variables is given by m applications of constraints from \(\mathcal {F}\) to subsequences of the n variables, and the goal is to find an assignment to the variables that satisfies the maximum number of constraints. In the (γ ,β)-approximation version of the problem for parameters 0 ≤ β ≤ γ ≤ 1, the goal is to distinguish instances where at least γ fraction of the constraints can be satisfied from instances where at most β fraction of the constraints can be satisfied. In this work, we consider the approximability of this problem in the context of sketching algorithms and give a dichotomy result. Specifically, for every family \(\mathcal {F}\) and every β < γ, we show that either a linear sketching algorithm solves the problem in polylogarithmic space or the problem is not solvable by any sketching algorithm in \(o(\sqrt {n})\) space. In particular, we give non-trivial approximation algorithms using polylogarithmic space for infinitely many constraint satisfaction problems. We also extend previously known lower bounds for general streaming algorithms to a wide variety of problems, and in particular the case of q = k =2, where we get a dichotomy, and the case when the satisfying assignments of the constraints of \(\mathcal {F}\) support a distribution on \([q]^k\) with uniform marginals. Prior to this work, other than sporadic examples, the only systematic classes of CSPs that were analyzed considered the setting of Boolean variables q = 2, binary constraints k =2, and singleton families \(|\mathcal {F}|=1\) and only considered the setting where constraints are placed on literals rather than variables. Our positive results show wide applicability of bias-based algorithms used previously by [ 47 ] and [ 41 ], which we extend to include richer norm estimation algorithms, by giving a systematic way to discover biases. Our negative results combine the Fourier analytic methods of [ 56 ], which we extend to a wider class of CSPs, with a rich collection of reductions among communication complexity problems that lie at the heart of the negative results. In particular, previous works used Fourier analysis over the Boolean cube to initiate their results and the results seemed particularly tailored to functions on Boolean literals (i.e., with negations). Our techniques surprisingly allow us to get to general q -ary CSPs without negations by appealing to the same Fourier analytic starting point over Boolean hypercubes.

Cost Minimization of Digital Twin Placements in Mobile Edge Computing

In the past decades, explosive numbers of Internet of Things (IoT) devices (objects) have been connected to the Internet, which enable users to access, control, and monitor their surrounding phenomenons at anytime and anywhere. To provide seamless interactions between the cyber world and the real world, Digital twins (DTs) of objects (IoT devices) are key enablers for real time monitoring, behavior simulations and predictive decisions on objects. Compared to centralized cloud computing, mobile edge computing (MEC) has been envisioning as a promising paradigm for low latency IoT applications. Accelerating the usage of DTs in MEC networks will bring unprecedented benefits to diverse services, through the co-evolution between physical objects and their virtual DTs, and DT-assisted service provisioning has attracted increasing attention recently. In this paper, we consider novel DT placement and migration problems in an MEC network with the mobility assumption of objects and users, by jointly considering the freshness of DT data and the service cost of users requesting for DT data. To this end, we first propose an algorithm for the DT placement problem with the aim to minimize the sum of the DT update cost of objects and the total service cost of users requesting for DT data, through efficient DT placements and resource allocation to process user requests. We then devise an approximation algorithm with a provable approximation ratio for a special case of the DT placement problem when each user requests the DT data of only one object. Meanwhile, considering the mobility of users and objects, we devise an online, two-layer scheduling algorithm for DT migrations to further reduce the total service cost of users within a given finite time horizon. We finally evaluate the performance of the proposed algorithms through experimental simulations. The simulation results show that the proposed algorithms are promising.

A novel and effective method for solving the router nodes placement in wireless mesh networks using reinforcement learning.

Router nodes placement (RNP) is an important issue in the design and implementation of wireless mesh networks (WMN). This is known as an P-hard problem, which cannot be solved using conventional algorithms. Consequently, approximate optimization strategies are commonly used to solve this problem. With heavy node density and wide-area WMNs, solving the RNP problem using approximation algorithms often faces many difficulties, therefore, a more effective solution is necessary. This motivated us to conduct this work. We propose a new method for solving the RNP problem using reinforcement learning (RL). The RNP problem is modeled as an RL model with environment, agent, action, and reward are equivalent to the network system, routers, coordinate adjustment, and connectivity of the RNP problem, respectively. To the best of our knowledge, this is the first study that applies RL to solve the RNP problem. The experimental results showed that the proposed method increased the network connectivity by up to 22.73% compared to the most recent methods.

System capacity model and algorithm for urban multimodal transport network with transfer

ABSTRACT This paper proposes a method for calculating transport networks capacity in dealing with multimodal transfers. Multimodal networks are represented by a modified ‘supernetwork’, while the passenger’s travels are defined as ‘superpaths’. Within this framework, the relation between the travel demand from O-D matrices and the resulting link flows in the supernetwork is modelled as a relationship matrix to describe urban mobility by using a logit-based stochastic user equilibrium. Based on this relationship matrix, an approximate iteration algorithm (AIA) is developed. Our numerical results show that the AIA performs better than the sensitivity analysis-based algorithm (SAB) and genetic algorithm (GA) regarding the execution-time, and that the capacity of multimodal transport networks can be underestimated if the combined travels are neglected.

Practical Algorithms with Guaranteed Approximation Ratio for Traveling Tournament Problem with Maximum Tour Length 2

The traveling tournament problem (TTP) is a hard but interesting sports scheduling problem inspired by Major League Baseball, which is to design a double round-robin schedule such that each pair of teams plays one game in each other’s home venue, minimizing the total distance traveled by all n teams (n is even). In this paper, we consider TTP-2 (i.e., TTP under the constraint that at most two consecutive home games or away games are allowed for each team). In this paper, we propose practical algorithms for TTP-2 with improved approximation ratios. Because of the different structural properties of the problem, all known algorithms for TTP-2 are different for n/2 being odd and even, and our algorithms are also different for these two cases. For even n/2, our approximation ratio is [Formula: see text], improving the previous result of [Formula: see text]. For odd n/2, our approximation ratio is [Formula: see text], improving the previous result of [Formula: see text]. In practice, our algorithms are easy to implement. Experiments on well-known benchmark sets show that our algorithms beat previously known solutions for all instances with an average improvement of 5.66%. Funding: This work was supported by the National Natural Science Foundation of China [Grants 62372095 and 62172077] and the Sichuan Natural Science Foundation [Grant 2023NSFSC0059].