Combinatorial Optimization Research Articles

In silico analysis of Design of Experiment methods for metabolic pathway optimization

Microbial cell factories allow the production of chemicals presenting an alternative to traditional fossil fuel-dependent production. However, finding the optimal expression of production pathway genes is crucial for the development of efficient production strains. Unlike sequential experimentation, combinatorial optimization captures the relationships between pathway genes and production, albeit at the cost of conducting multiple experiments. Fractional factorial designs followed by linear modeling and statistical analysis reduce the experimental workload while maximizing the information gained during experimentation. Although tools to perform and analyze these designs are available, guidelines for selecting appropriate factorial designs for pathway optimization are missing. In this study, we leverage a kinetic model of a seven-genes pathway to simulate the performance of a full factorial strain library. We compare this approach to resolution V, IV, III, and Plackett Burman (PB) designs. Additionally, we evaluate the performance of these designs as training sets for a random forest algorithm aimed at identifying best-producing strains. Evaluating the robustness of these designs to noise and missing data, traits inherent to biological datasets, we find that while resolution V designs capture most information present in full factorial data, they necessitate the construction of a large number of strains. On the other hand, resolution III and PB designs fall short in identifying optimal strains and miss relevant information. Besides, given the small number of experiments required for the optimization of a pathway with seven genes, linear models outperform random forest. Consequently, we propose the use of resolution IV designs followed by linear modeling in Design-Build-Test-Learn (DBTL) cycles targeting the screening of multiple factors. These designs enable the identification of optimal strains and provide valuable guidance for subsequent optimization cycles.

Fuzzy Self-tuning Bees Algorithm for designing optimal product lines

The Product Line Design (PLD) problem is an NP-hard combinatorial optimization problem in marketing that aims at determining an optimal product line through which a firm can optimize a desired objective, like its profits or market share. Since the PLD problem has been proved to have high complexity in real-life applications, high-quality solutions have been detected by researchers who develop various optimization methods and test their performance. The Bees Algorithm (BA) is a successful swarm intelligent optimization algorithm which is based on the behavior of bees. The aim of this research is to develop and assess BA in the optimal PLD problem. In this effort, a set of fuzzy rules has been developed to autonomously compute parameters for each individual solution throughout the optimization process. The performance of two BA variants is compared with those of popular previous approaches, using both real and simulated data of customer preferences. The findings reveal that BA constitutes an enhanced alternative approach for designing optimal product lines.

Deep reinforcement learning for autonomous SideLink radio resource management in platoon-based C-V2X networks: An overview

Dynamic and autonomous SideLink (SL) Radio Resource Management (RRM) is essential for platoon-based cellular vehicular networks. However, this task is challenging due to several factors. These include the limited spectrum below 6 GHz, stringent vehicle-to-everything (V2X) communications requirements, uncertain and dynamic environments, limited vehicle sensing capabilities, and inherent distributed operation. These limitations often lead to resource collisions, data packet loss, and increased latency. Current standardized approaches in Long-Term Evolution-V2X (LTE-V2X) and New Radio-V2X (NR-V2X) rely on random resource selection, limiting their efficiency. Moreover, RRM is inherently a complex combinatorial optimization problem. It may involve conflicting objectives and constraints, making traditional approaches inadequate. Platoon-based communication necessitates careful resource allocation to support a diverse mix of communication types. These include safety-critical control messaging within platoons, less time-sensitive traffic management information between platoons, and even infotainment services like media streaming. Optimizing resource sharing inter- and intra- platoons is crucial to avoid excessive interference and ensure overall network performance. Deep Reinforcement Learning (DRL), combining Deep Learning (DL) and Reinforcement Learning (RL), has recently been investigated for network resource management. It offers a potential solution for these challenges. A DRL agent, represented by deep neural networks, interacts with the environment and learns optimal decision-making through trial and error. This paper overviews proposed DRL-based methods for autonomous SL RRM in single and multi-agent platoon-based C-V2X networks. It considers both intra- and inter-platoon communications with their specific requirements. We discuss the components of Markov Decision Processes (MDP) used to model the sequential decision-making of RRM. We then detail the DRL algorithms, training paradigms, and insights on the achieved results. Finally, we highlight challenges in existing works and suggest strategies for addressing them.

Computing With Residue Numbers in High-Dimensional Representation

Abstract We introduce residue hyperdimensional computing, a computing framework that unifies residue number systems with an algebra defined over random, high-dimensional vectors. We show how residue numbers can be represented as high-dimensional vectors in a manner that allows algebraic operations to be performed with component-wise, parallelizable operations on the vector elements. The resulting framework, when combined with an efficient method for factorizing high-dimensional vectors, can represent and operate on numerical values over a large dynamic range using resources that scale only logarithmically with the range, a vast improvement over previous methods. It also exhibits impressive robustness to noise. We demonstrate the potential for this framework to solve computationally difficult problems in visual perception and combinatorial optimization, showing improvement over baseline methods. More broadly, the framework provides a possible account for the computational operations of grid cells in the brain, and it suggests new machine learning architectures for representing and manipulating numerical data.

Deep reinforcement learning-based spatio-temporal graph neural network for solving job shop scheduling problem

AbstractThe job shop scheduling problem (JSSP) is a well-known NP-hard combinatorial optimization problem that focuses on assigning tasks to limited resources while adhering to certain constraints. Currently, deep reinforcement learning (DRL)-based solutions are being widely used to solve the JSSP by defining the problem structure on disjunctive graphs. Some of the proposed approaches attempt to leverage the structural information of the JSSP to capture the dynamics of the environment without considering the time dependency within the JSSP. However, learning graph representations only from the structural relationship of nodes results in a weak and incomplete representation of these graphs which does not provide an expressive representation of the dynamics in the environment. In this study, unlike existing frameworks, we defined the JSSP as a dynamic graph to explicitly consider the time-varying aspect of the JSSP environment. To this end, we propose a novel DRL framework that captures both the spatial and temporal attributes of the JSSP to construct rich and complete graph representations. Our DRL framework introduces a novel attentive graph isomorphism network (Attentive-GIN)-based spatial block to learn the structural relationship and a temporal block to capture the time dependency. Additionally, we designed a gated fusion block that selectively combines the learned representations from the two blocks. We trained the model using the proximal policy optimization algorithm of reinforcement learning. Experimental results show that our trained model exhibits significant performance enhancement compared to heuristic dispatching rules and learning-based solutions for both randomly generated datasets and public benchmarks.

Efficient Quantum Circuit Simulation by Tensor Network Methods on Modern GPUs

Efficient simulation of quantum circuits has become indispensable with the rapid development of quantum hardware. The primary simulation methods are based on state vectors and tensor networks. As the number of qubits and quantum gates grows larger in current quantum devices, traditional state-vector-based quantum circuit simulation methods prove inadequate due to the overwhelming size of the Hilbert space and extensive entanglement. Consequently, brutal force tensor network simulation algorithms become the only viable solution in such scenarios. The two main challenges faced in tensor network simulation algorithms are optimal contraction path finding and efficient execution on modern computing devices, with the latter determining the actual efficiency. In this study, we investigate the optimization of such tensor network simulations on modern GPUs and propose general optimization strategies from two aspects: computational efficiency and accuracy. First, we propose to transform critical Einstein summation operations into GEMM operations, leveraging the specific features of tensor network simulations to amplify the efficiency of GPUs. Second, by analyzing the data characteristics of quantum circuits, we employ extended precision to ensure the accuracy of simulation results and mixed precision to fully exploit the potential of GPUs, resulting in faster and more precise simulations. Our numerical experiments demonstrate that our approach can achieve a 3.96× reduction in verification time for random quantum circuit samples in the 18-cycle case of Sycamore, with sustained performance exceeding 21 TFLOPS on one A100. This method can be easily extended to the 20-cycle case, maintaining the same performance, accelerating by 12.5× compared to the state-of-the-art CPU-based results and 4.48–6.78× compared to the state-of-the-art GPU-based results reported in the literature. Furthermore, the strategies presented in this article hold general applicability for accelerating problems that can be tackled by contracting tensor networks such as graphical models and combinatorial optimizations.

Collaborative Scheduling of Mass Rescue Operations at Sea

The continued growth of the global cruise market has posed a major challenge to maritime search and rescue, as available rescue resources are limited compared to the scale of passenger ship disasters. To bridge the gap between the number of passengers in distress and the availability of rescue resources, this paper develops a two-stage Mass Rescue Operation (MRO) decision support model (MRO model) to fully utilize the available multiple rescue resources. Based on the combinatorial optimization theory, in the MRO model we consider the rescue capacity of multiple rescue resources and the synergy between them, the accident types and the marine environment conditions to optimize two objectives (rescue time and number of rescue resources dispatched) in two stages. In the first stage, the objective is to minimize the rescue time by Classical Selection Sort Algorithm. In the second stage, the rescue time and the number of rescue resources are simultaneously optimized by Simulated Annealing Arithmetic (SAA) integrated with Genetic Algorithm (GA). Furthermore, considering the actual role of helicopters in MROs, the MRO model is enhanced to schedule helicopters mandatorily or non-mandatorily. Finally, the MRO model was verified by simulating accidents in the Taiwan Strait. The simulation results show that compared with the first stage, the rescue time in the second stage model is saved by up to 16.18% and the number of rescue resources is reduced by up to 45.16%.

Modeling and Solving the Knapsack Problem with a Multi-Objective Equilibrium Optimizer Algorithm Based on Weighted Congestion Distance

The knapsack problem is a typical bi-objective combinatorial optimization issue, wherein maximizing the value of the packed items is achieved concurrently with minimizing the weight of the load. Due to the conflicting objectives of the knapsack problem and the typical discrete property of the items involved, swarm intelligence algorithms are commonly employed. The diversity of optimal combinations in the knapsack problem has become a focal point, which involves finding multiple packing solutions at the same value and weight. For this purpose, this paper proposes a Multi-Objective Equilibrium Optimizer Algorithm based on Weighted Congestion Distance (MOEO_WCD). The algorithm employs a non-dominated sorting method to find a set of Pareto front solutions rather than a single optimal solution, offering multiple decision-making options based on the varying needs of the decision-makers. Additionally, MOEO_WCD improves the balance pool generation mechanism and incorporates a weighted congestion incentive, emphasizing the diversity of packing combination solutions under the objectives of value and weight to explore more Pareto front solutions. Considering the discrete characteristics of the knapsack combination optimization problem, our algorithm also incorporates appropriate discrete constraint handling. This paper designs multiple sets of multi-objective knapsack combinatorial optimization problems based on the number of knapsacks, the number of items, and the weights and values of the items. This article compares five algorithms suitable for solving multi-objective problems: MODE, MO-PSO-MM, MO-Ring-PSO-SCD, NSGA-II, and DN-NSGAII. In order to evaluate the performance of the algorithm, this paper proposes a new solution set coverage index for evaluation. We also used the hypervolume indicator to evaluate the diversity of algorithms. The results show that our MOEO-WCD algorithm achieves optimal coverage of the reference composite Pareto front in the decision space of four knapsack problems. The experimental results indicate that our MOEO_WCD algorithm achieves the optimal coverage of the reference composite Pareto front in the decision space for four sets of knapsack problems. Although our MOEO_WCD algorithm covers less of the composite front in the objective space compared with the MODE algorithm for knapsack problem 1, its coverage of the integrated reference solutions in the decision space is greater than that of the MODE algorithm. The experiments demonstrate the superior performance of the MOEO_WCD algorithm on bi-objective knapsack combinatorial optimization problem instances, which provides an important solution to the search for diversity in multi-objective combinatorial optimization solutions.

Extended formulations for binary optimal control problems

AbstractExtended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by adding artificial variables, one can often find a small linear formulation, i.e., one containing a polynomial number of variables and constraints, such that the projection to the original space of variables yields a perfect linear formulation. Motivated by binary optimal control problems with switching constraints, we show that a similar approach can be useful also for optimization problems in function space, in order to model the closed convex hull of feasible controls in a compact way. More specifically, we present small extended formulations for switches with bounded variation and for dwell-time constraints. For general linear switching point constraints, we devise an extended model linearizing the problem, but show that a small extended formulation that is compatible with discretization cannot exist unless P = NP.

The Logic and Application of Greedy Algorithms

Abstract. Being easy to implement and offering faster solutions, the greedy algorithms have widely been used in solving combinatorial optimization problems in computer science and many practical applications, such as resource allocation and data compression. This paper aims at analyzing the definitions, theory, and application of greedy algorithms in computer science as well as their logic and efficacy in numerous situations. In this analysis, concepts such as the greedy choice property and optimal substructure are examined as essential to understanding how greedy algorithms operate. The provided analysis mainly assumes prior knowledge of concepts and problems like the Fractional Knapsack problem and the Shortest Path problem solution as well as some practical problems, for example, resource allocation and the exact coin change problem. Analytical data and real applications are used to analyze the performance of greedy algorithms vis-a-vis other categories, such as the dynamic programming paradigm. The results reveal that greedy algorithms have the potential for great efficiency while also being restricted by certain parameters. They are ideal in the following aspects pertaining to computational aspects, that is, speed, ease of implementation, and applicability to large datasets. But they do not necessarily promise strong optimality in certain situations. The conclusion notes that greedy algorithms deserve further applications when the specified conditions are met and states that the effectiveness of these conditions needs to be studied.

A hybrid method for delineating homogeneous forest segments from LiDAR data in Catalonia (Spain)

ABSTRACT Laser scanning data are increasingly used to segment forests into homogeneous units, called segments or stand compartments. Region growing and region merging have been traditionally employed for this purpose. Recently, alternative methods such as cellular automata (CA), self-organizing maps (SOM), and combinatorial optimization have emerged, promising more homogeneous stand delineations. However, these newer methods often require fine-tuning due to rugged stand boundaries. To address this, we propose and assess a novel hybrid approach that combines two segmentation algorithms, resulting in smoother boundaries and homogeneous stands. Our hybrid method outperforms traditional fine-tuning techniques, particularly using CA or SOM for initial segmentation and then refining it with another cellular automaton (CA’), adjusted to produce smooth boundaries. The new two-step hybrid method resulted in better segmentation results than the one-step algorithm combined with previously suggested fine-tuning methods. SOM-CA’ showed the highest degree of explained variance (R2) of the LiDAR metrics used in the segmentation. CA-CA’ reached almost the same R2 values with a larger average segment area. When the R2 of the LiDAR metrics was used as the criterion, the segments produced by the hybrid method outperformed the stand delineations of the current Spanish forest map with a clear margin.

Biologically inspired adaptive crack network reconstruction based on slime mould algorithm.

The dynamic crack propagation trajectories play a crucial role in enhancing our understanding of spatial mechanisms involved in crack expansion. However, visualization of internal cracks under complex crack conditions has always been a challenge. Biological networks have been honed by many cycles of evolutionary selection pressure and are likely to yield reasonable solutions to such combinatorial optimization problems. This study applied the slime mould algorithm to improve the accuracy of internal crack localization in rocks and employed Minimum spanning tree and Gaussian mixture model to construct the crack propagation trajectories. By introducing the concept of bond length, the evolution characteristics of crack levels were effectively characterized. Research results showed that this approach effectively preserves essential crack localization information while mitigating the influence of interfering parameters, providing crack characterization results that exhibit high consistency with actual fracture patterns. The curves of cumulative bond length and relative bond length over time conform to the trend of a Growth/Sigmoidal curve. The strength of the bond was correlated with the temporal process of crack propagation. This result could be helpful for analyzing crack trajectories and predicting rock stability.

Data-driven prediction of relevant scenarios for robust combinatorial optimization

We study iterative constraint and variable generation methods for (two-stage) robust combinatorial optimization problems with discrete uncertainty. The goal of this work is to find a set of starting scenarios that provides strong lower bounds early in the process. To this end we define the Relevant Scenario Recognition Problem (RSRP) which finds the optimal choice of scenarios which maximizes the corresponding objective value. We show for classical and two-stage robust optimization that this problem can be solved in polynomial time if the number of selected scenarios is constant and NP-hard if it is part of the input. Furthermore, we derive a linear mixed-integer programming formulation for the problem in both cases.Since solving the RSRP is not possible in reasonable time, we propose a machine-learning-based heuristic to determine a good set of starting scenarios. To this end, we design a set of dimension-independent features, and train a Random Forest Classifier on already solved small-dimensional instances of the problem. Our experiments show that our method is able to improve the solution process even for larger instances than contained in the training set, and that predicting even a small number of good starting scenarios can considerably reduce the optimality gap. Additionally, our method provides a feature importance score which can give new insights into the role of scenario properties in robust optimization.

From coordinate subspaces over finite fields to ideal multipartite uniform clutters

AbstractTake a prime power q, an integer $$n\ge 2$$ n ≥ 2 , and a coordinate subspace $$S\subseteq GF(q)^n$$ S ⊆ G F ( q ) n over the Galois field GF(q). One can associate with S an n-partite n-uniform clutter $$\mathcal {C}$$ C , where every part has size q and there is a bijection between the vectors in S and the members of $$\mathcal {C}$$ C . In this paper, we determine when the clutter $$\mathcal {C}$$ C is ideal, a property developed in connection to Packing and Covering problems in the areas of Integer Programming and Combinatorial Optimization. Interestingly, the characterization differs depending on whether q is 2, 4, a higher power of 2, or otherwise. Each characterization uses crucially that idealness is a minor-closed property: first the list of excluded minors is identified, and only then is the global structure determined. A key insight is that idealness of $$\mathcal {C}$$ C depends solely on the underlying matroid of S. Our theorems also extend from idealness to the stronger max-flow min-cut property. As a consequence, we prove the Replication and $$\tau =2$$ τ = 2 Conjectures for this class of clutters.

Intelligent Generative Models for Quantum Neural Networks

AbstractThe potential of quantum neural networks (QNN) for applications in several fields has been widely demonstrated, but hyperparameter selection remains a technical challenge. The complexity of combinatorial optimization rises dramatically as the dimensionality of the hyperparameter space increases, making hyperparameter selection exceptionally complex. Traditional manual trial‐and‐error methods are both time‐consuming and expensive. To break through this bottleneck, the Ansatz structure set is proposed and the Hyperband algorithm is utilized to combine the structure set with the stacking number and algorithmic hyperparameters to propose the Hyperband‐QNN model. The model can intelligently generate QNN according to the actual data features, and in practical applications in many fields such as medicine and agriculture, it performs well compared with the traditional machine learning algorithms as well as the quantum algorithms QSVM and QKNN, and when it is used to deal with the large‐scale data, the efficiency advantage becomes more obvious with the increase of the number of samples. This not only proves the advantages of Hyperband‐QNN model in practical applications but also provides useful exploration and reference for the integration of traditional algorithms and quantum algorithms in practical problems and the play of their respective advantages.

Point-feature label placement with maximum entropy principle

A map becomes readable and translatable only after the use of labels. High-quality label placement (i.e., labelling) is a combinatorial optimization problem, where one or more objective functions are required. However, such objective functions are still not well achieved in existing methods with commonly used labelling rules (e.g., “avoidance of overlapping labels” and “placement at priority positions”). In this study, we define a new objective function using the maximum entropy principle and employ a modified genetic algorithm in the optimization process. Comparative experiments have been conducted with 29 existing labelling methods in a dataset of 1000 points. Experimental results show that the average percentage of non-overlapping labels by this new method reaches 94.73% (i.e., being ranked second in all 30 methods) and has no statistically significant difference from the best one (i.e., 94.87%). By further analysis, it is found that this new method not only can place more labels in priority positions than the method being ranked first but also has the potential to place labels for line and area features. Such results indicate that the maximum entropy principle may pave the way for further research in cartography.

A Novel k-Means Framework via Constrained Relaxation and Spectral Rotation.

Owing to its simplicity, the traditional k - means (Lloyd heuristic) clustering method plays a vital role in a variety of machine-learning applications. Disappointingly, the Lloyd heuristic is prone to local minima. In this article, we propose k - mRSR, which converts the sum-of-squared error (SSE) (Lloyd) into a combinatorial optimization problem and incorporates a relaxed trace maximization term and an improved spectral rotation term. The main advantage of k - mRSR is that it only needs to solve the membership matrix instead of computing the cluster centers in each iteration. Furthermore, we present a nonredundant coordinate descent method that brings the discrete solution infinitely close to the scaled partition matrix. Two novel findings from the experiments are that k - mRSR can further decrease (increase) the objective function values of the k - means obtained by Lloyd (CD), while Lloyd (CD) cannot decrease (increase) the objective function obtained by k - mRSR. In addition, the results of extensive experiments on 15 datasets indicate that k - mRSR outperforms both Lloyd and CD in terms of the objective function value and outperforms other state-of-the-art methods in terms of clustering performance.

Convergence of Hybrid Grey Wolf Optimization with Heuristic Approaches for Enhanced Job Shop Scheduling

This scholarly inquiry examines the utilization of the Hybrid Grey Wolf Optimization Algorithm (HGWOA) in addressing the Job Shop Scheduling Problem (JSSP), a combinatorial optimization problem commonly encountered within production management. The central aim is to minimize makespan, defined as the cumulative duration necessary to finalize all tasks on a designated set of machines while observing precedence constraints. Conventional Optimization methodologies frequently encounter difficulties with intricate instances of JSSP owing to its NP-hard classification. We introduce a ground-breaking method the Grey Wolf Optimization Algorithm (GWOA) with various meta-heuristic strategies to augment its fruitfulness in resolving JSSP. The multiple findings underscore the usefulness of HGWOA, highlighting its prospective applicability in real-world contexts of production scheduling and management.

Application of hyperspectral band selection method based on deep reinforcement learning to low-value recyclable waste classification

Hyperspectral images (HSIs) have proven effective for classification of Low-value Recyclable Waste (LVRW). However, the high correlation between bands in HSIs introduces redundant information. In this paper, to overcome the challenge of low applicability of existing band selection methods of LVRW HSIs, we propose a Dueling Double Deep Q Network based on Supervised Band Selection method (D3QN-SBS). Specifically, we formulate band selection as a reinforcement learning problem, treating it as a combinatorial optimization task that explores band combinations within a discrete space, using overall accuracy as the reward to tune the policy and optimise the state-action value function. The results of comparative experiments show that D3QN-SBS outperforms other methods when selecting 2–10 bands, where achieves an accuracy of about 99.24 %, 99.10 %, 99.05 %, and 99.16 % in k-NN, SVM-RBF, RF, and MLP based on 10 bands, the precision, recall, and F1-score are nearly 100 % for OTHERS and are more than 99 % for PS. In K-fold cross-validation, the majority of the folds under four classifiers achieves above 98 % for four evaluation metrics and the average F1-scores are 99.25 %, 99.01 %, 99.06 %, and 99.17 %. This approach can be deployed in LVRW sorting equipment, contributing to the advancement of hyperspectral imaging technologies in plastic waste sorting field.

A New Grey Prediction Model and Its Application in Renewable Energy Consumption

Renewable energy is an energy resource that can be used continuously. At present, international oil prices continue to rise, the problem of global climate change is becoming increasingly prominent, and renewable energy and clean energy have ushered in a new round of development opportunities. Based on the new gray prediction model, this paper forecasts the consumption of renewable energy and further analyzes the sustainable development of renewable energy. In this paper, the combinatorial optimization method of cumulative order, background value coefficient, and initial conditions, parameter optimization combination, parameter combinatorial optimization process of the gray prediction model, and parameter optimization mechanism based on the PSO algorithm are proposed, and the reduction error analysis is carried out. The consumption of wind power and photovoltaic renewable energy is forecasted, and three different forecasting methods as exponential smoothing method, time series analysis method, and new gray forecasting method are compared, and the wind speed, irradiation intensity, and load are forecasted by these three different forecasting methods. Compared with the time series analysis method and the exponential smoothing method, the RMSE of the new grey prediction method is reduced by 127.12% and 160.59%, and the error rate is reduced by 3.16% and 4%, respectively. Based on the consumption forecast of renewable energy, this paper analyzes its sustainability from three directions economy, resource supply, and environment, and finally gives energy policy recommendations.