Search Results (94)

Flight Schedule Problem optimization is a typical NP-hard combinatorial optimization problem that is challenging to solve using traditional algorithms, so metaheuristic algorithms are commonly adopted for such problems. This paper proposes a Discrete Memory-Enhanced Restructured Particle Swarm Optimization algorithm (DMERPSO) to address Flight Scheduling Problem optimization. Firstly, this paper designs a hybrid particle encoding scheme capable of simultaneously handling flight time adjustments (integer variables) and route selections (categorical variables) for the Flight Schedule Problem. Secondly, a new update equation of particle positions is provided based on probability selection within the three terms of the Memory-Enhanced Restructured Particle Swarm Optimization (MERPSO) algorithm, and the calculation of the selection probability is designed. Thirdly, the two strategies and perturbation terms of MERPSO are improved in order to be adapted to optimize the discrete Flight Schedule Problem. Finally, simulation experiments are conducted using DMERPSO based on real flight data from multiple Chinese airports with the objective of minimizing total flight delays, leading to better solutions that are faster than various benchmark algorithms. The DMERPSO algorithm exhibits significant advantages in reducing total delays, improving solution stability, and enhancing robustness, which validates that DMERPSO provides an effective new approach for solving Flight Schedule Problem optimization problems. Full article

In the field of structural health monitoring systems, sensors serve as the fundamental components for assessing infrastructure integrity. The rationality of their spatial configuration significantly influences the precision of structural performance assessment, the efficacy of damage detection algorithms, and the operational reliability of the system throughout its designated lifecycle. A robust optimization methodology for the placement of multi-type sensors is proposed in this study, explicitly formulated to mitigate the negative impact of sensor malfunctions during long-term operation. First, a rigorous evaluation framework for sensor placement schemes is established based on Bayesian inference and the minimization of information entropy, thereby quantifying the uncertainty inherent in parameter identification. Then, a probabilistic model of sensor failure is developed utilizing the Weibull distribution to capture time-dependent reliability characteristics, combined with a modified information entropy calculation method that mathematically assimilates these failure probabilities into the optimization objective. Finally, a heuristic search strategy is employed to achieve the robust optimal placement of multi-type sensors, efficiently navigating the complex combinatorial search space. In contrast to deterministic information entropy (DIE) methodologies, which assume ideal sensor functionality, the robust information entropy (RIE) approach comprehensively accounts for the stochastic nature of sensor failures and their impact on the information content of the monitoring network, thereby significantly augmenting the robustness and redundancy of the sensor configuration. Validations utilizing a numerical frame structure and a finite element bridge model demonstrate that the RIE method effectively integrates the sensor failure probability model to yield robust optimal placement schemes, minimizing the risk of information loss and ensuring reliable structural health monitoring throughout the engineering lifecycle. Full article

Many problems in physics and computer science can be framed in terms of combinatorial optimization. Due to this, it is interesting and important to study theoretical aspects of such optimization. Here, we study connections between Kolmogorov complexity, optima, and optimization. We argue that (1) optima and complexity are connected, with extrema being more likely to have low complexity (under certain circumstances); (2) optimization by sampling candidate solutions according to algorithmic probability may be an effective optimization method; and (3) coincidences in extrema to optimization problems are a priori more likely as compared to a purely random null model. Full article

Deep reinforcement learning (DRL)-based algorithms for solving the Traveling Salesman Problem (TSP) have demonstrated competitive potential compared to traditional heuristic algorithms on small-scale TSP instances. However, as the problem size increases, the NP-hard nature of the TSP leads to exponential growth in the combinatorial search space, state–action space explosion, and sharply increased sample complexity, which together cause significant performance degradation for most existing DRL-based models when directly applied to large-scale instances. This research proposes a two-stage reinforcement learning framework, termed GCRL-TSP (Graph Convolutional Reinforcement Learning for the TSP), which consists of a heatmap generation stage based on a graph convolutional neural network, and a heatmap-assisted Proximal Policy Optimization (PPO) training stage, where the generated heatmaps are used as auxiliary guidance for policy optimization. First, we design a divide-and-conquer heatmap generation strategy: a graph convolutional network infers m-node sub-heatmaps, which are then merged into a global edge-probability heatmap. Second, we integrate the heatmap into PPO by augmenting the state representation and restricting the action space toward high-probability edges, improving training efficiency. On standard instances with 200/500/1000 nodes, GCRL-TSP achieves a Gap% of 4.81/4.36/13.20 (relative to Concorde) with runtimes of 36 s/1.12 min/4.65 min. Experimental results show that GCRL-TSP achieves more than twice the solving speed compared to other TSP solving algorithms, while obtaining solution quality comparable to other algorithms on TSPs ranging from 200 to 1000 nodes. Full article

The computational tractability of Integrated Information Theory (IIT) is fundamentally constrained by the exponential cost of identifying the Minimum Information Partition (MIP), which is required to quantify integrated information (Φ). Existing approaches become impractical beyond ~15–20 variables, limiting IIT analyses on realistic neural and complex systems. We introduce GeoMIP, a geometric–topological framework that recasts the MIP search as a graph-based optimization problem on the n-dimensional hypercube graph: discrete system states are modeled as graph vertices, and Hamming distance adjacency defines edges and shortest-path structures. Building on a tensor-decomposed representation of the transition probabilities, GeoMIP constructs a transition-cost (ground cost) structure by dynamic programming over graph neighborhoods and BFS-like exploration by Hamming levels, exploiting hypercube symmetries to reduce redundant evaluations. We validate GeoMIP against PyPhi, ensuring reliability of MIP identification and Φ computation. Across multiple implementations, GeoMIP achieves 165–326× speedups over PyPhi while maintaining 98–100% agreement in partition identification. Heuristic extensions further enable analyses up to ~25 variables, substantially expanding the practical IIT regime. Overall, by leveraging the hypercube’s explicit graph structure (vertices, edges, shortest paths, and automorphisms), GeoMIP turns an intractable combinatorial search into a scalable graph-based procedure for IIT partitioning. Full article

Background/Objective: Neuroimmune and metabolic dysregulation have been increasingly implicated in the cognitive heterogeneity of autism spectrum disorder (ASD). However, it remains unclear whether anti-inflammatory diets engage distinct biological and cognitive pathways in autistic and neurotypical children. This study examined whether a 12-week anti-inflammatory dietary protocol produces group-specific neuroimmune–metabolic signatures and cognitive responses in autistic children, neurotypical children receiving the same diet, and untreated neurotypical controls. Methods: Twenty-two children (11 with ASD, six a on neurotypical diet [NT-diet], and five neurotypical controls [NT-control]) completed pre–post assessments of plasma IFN-γ, CXCL1, RANTES (CCL5), trimethylamine-N-oxide (TMAO), and an extensive ENI-2/WISC-IV neuropsychological battery. Linear mixed-effects models were used to test the Time × Group effects on biomarkers and cognitive domains, adjusting for age, sex, and baseline TMAO. Bayesian estimation quantified individual changes (posterior means, 95% credible intervals, and posterior probabilities). Immune–cognitive coupling was explored using Δ–Δ correlation matrices, network metrics (node strength, degree centrality), exploratory mediation models, and responder (≥0.5 SD domain improvement) versus non-responder analyses. Results: In ASD, the diet induced robust reductions in IFN-γ, RANTES, CXCL1, and TMAO, with decisive Bayesian evidence for IFN-γ and RANTES suppression (posterior P(δ < 0) > 0.99). These shifts were selectively associated with gains in verbal learning, semantic fluency, verbal reasoning, attention, and visuoconstructive abilities, whereas working memory and executive flexibility changes were heterogeneous, revealing executive vulnerability in individuals with smaller TMAO reductions. NT-diet children showed modest but consistent improvements in visuospatial processing, attention, and processing speed, with minimal biomarker changes; NT controls remained biologically and cognitively stable. Network analyses in ASD revealed a dense chemokine-anchored architecture with CXCL1 and RANTES as central hubs linking biomarker reductions to improvements in fluency, memory, attention, and executive flexibility. ΔTMAO predicted changes in executive flexibility only in ASD (explaining >50% of the variance), functioning as a metabolic node of executive susceptibility. Responders displayed larger coordinated decreases in all biomarkers and broader cognitive gains compared to non-responders. Conclusions: A structured anti-inflammatory diet elicits an ASD-specific, coordinated neuroimmune–metabolic response in which suppression of CXCL1 and RANTES and modulation of TMAO are tightly coupled with selective improvements in verbal, attentional, and executive domains. Neurotypical children exhibit modest metabolism-linked cognitive benefits and minimal immune modulation. These findings support a precision-nutrition framework in ASD, emphasizing baseline immunometabolic profiling and network-level biomarkers (CXCL1, RANTES, TMAO) to stratify responders and design combinatorial interventions targeting neuroimmune–metabolic pathways. Full article

Pascal’s triangle is a classical mathematical construct, historically studied for centuries, that organises binomial coefficients in a triangular array and serves as a cornerstone in combinatorics, algebra, and number theory. Herein, we propose to model it with Petri nets, a formal specification technique derived from discrete event systems. A minimal Petri net is created that generates Pascal’s triangle under a simple arithmetic rule. Token counts in each place coincide with binomial coefficients, providing a direct combinatorial interpretation. Two other classical structures emerge from this model: by colouring tokens depending on their parity, the Sierpiński triangle appears; by routing tokens randomly at each branching, the binomial distribution arises, converging to a Gaussian limit as depth increases. As a result, a single Petri construction unifies three mathematical objects: Pascal’s Triangle, Sierpiński’s Triangle, and the Gaussian distribution. This connection illustrates the invaluable potential of Petri nets as unifying tools for modelling discrete mathematical structures and beyond. Full article

The mathematical universe of the quantum topos, which is formulated on the basis of classical Boolean snapshots, delivers a neo-realist description of quantum mechanics that preserves realism. The main contribution of this article is developing formal objectivity in physical theories beyond quantum mechanics in the topos-theory approach. It will be shown that neo-realist responses to non-perturbative structures of quantum field theory do not preserve realism. In this regard, the method of Feynman graphons is applied to reframe the task of describing objectivity in quantum field theory in terms of replacing the standard Hilbert-space/operator-algebra ontology with a new context category built from a certain family of topological Hopf subalgebras of the topological Hopf algebra of renormalization as algebraic/combinatorial data tied to non-perturbative structures. This topological-Hopf-algebra ontology, which is independent of instrumentalist probabilities, enables us to reconstruct gauge field theories on the basis of the mathematical universe of the non-perturbative topos. The non-Boolean logic of the non-perturbative topos cannot be recovered by classical Boolean snapshots, which is in contrast to the quantum-topos reformulation of quantum mechanics. The article formulates a universal version of the non-perturbative topos to show that quantum field theory is a globally and locally neo-realist theory which can be reconstructed independent of the standard Hilbert-space/operator-algebra ontology. Formal objectivity of the universal non-perturbative topos offers a new route to build objective semantics for non-perturbative structures. Full article

This paper expands the Mallows model for use in combinatorial domains. The Mallows model is a popular distribution used to sample permutations around a central tendency but requires a unique normalizing constant for each distance metric used in order to be computationally efficient. In this paper, closed-form expressions for the Mallows model normalizing constant are derived for the Hamming distance, symmetric difference, and the similarity coefficient in combinatorial domains. Additionally, closed-form expressions are derived for the normalizing constant of the weighted Mallows model in combinatorial domains. The weighted Mallows model increases the versatility of the Mallows model by allowing granular control over likelihoods of individual components in the domain. The derivation of the closed-form expression results in a reduction of the order of calculations required to calculate probabilities from exponential to constant. Full article

Cellular organisms store heritable information in two forms, genetic and epigenetic, the latter being largely dependent on cytosine methylation (5mC). Chargaff’s Second Parity Rule (CSPR) describes the nucleotide composition of cellular genomes in terms of intra-strand DNA symmetry. However, it remains unknown whether DNA methylation patterns display intra-strand DNA symmetry. Computational analysis was conducted of the DNA methylation patterns observed in human cell lines and in tissue samples from healthy donors. Analysis of 5mC marks in mutually reverse-complementary pairs of short oligomers, containing CpG dinucleotide in the middle, revealed deviations from CSPR and methylation asymmetry that can be observed for two non-overlapping mirror groups defined by CpG methylation values. Deviations from CSPR, together with combinatorial probabilities of pattern distributions and computer simulations, highlight the non-random nature of methylation processes and enabled us to identify specific cell types as outliers. Further analysis revealed a compensatory methylation asymmetry that reduces deviations from intra-strand symmetry and implies the existence of strand-specific methylation during cell differentiation. Among six pairs of reverse-complementary tetranucleotides, four pairs with specific sequence motifs display pronounced methylation asymmetry. This mirror asymmetry may be associated with chromosome folding and the formation of a complex three-dimensional landscape. Full article

Scenario-based testing is a mainstream approach for evaluating the safety of automated driving systems (ADS). However, logical scenarios are defined through parameter spaces, and performance differences among systems under test make it difficult to ensure fairness and coverage using the same concrete parameters. Accordingly, an automated driving system testing method is proposed. Guided by the established full-coverage testing framework, a quantitative evaluation method for scenario representativeness is first proposed by jointly analyzing naturalistic driving probability distributions and hazard-related characteristics. Furthermore, a hybrid algorithm integrating heat-guided hierarchical search and genetic optimization is developed to address the non-uniform full-coverage problem, enabling efficient selection of representative parameters that ensure complete coverage of the logical scenario space. The proposed method is validated through empirical studies in representative use cases, including lead vehicle braking and cut-in scenarios. Experimental results show that the proposed method achieves 100% coverage of the logical scenario parameter space with an 8% boundary fitting error, outperforming mainstream baselines including monte carlo (84.3%, 19%), combinatorial testing (86.5%, 14%) and importance sampling (72.0%, 7%). The approach achieves exhaustive coverage of the logical scenario space with limited concrete scenarios, and effectively supports the development of consistent, reproducible and efficient scenario generation frameworks for testing organizations. Full article

This paper addresses the cooperative task assignment problem for heterogeneous unmanned aerial vehicles with time windows considering uncertain fuel consumption. In the scenario where probabilistic fuel consumption exists and its distribution needs to be estimated from historical data samples, we first formulate the problem as a chance-constrained combinatorial optimization problem and utilize the sample average approximation method to solve it. Further, to address the issue of ambiguous distribution, we introduce distributionally robust chance constraints, which consider a set of probability distributions that are contained within a 1-Wasserstein ball centered around the empirical distribution of field data. We approximate the distributionally robust chance-constrained cooperative task assignment problem by applying a CVaR-based tractable approximation such that the problem can be transformed into a deterministic mixed-integer linear programming problem, which can be efficiently solved by state-of-the-art optimization solvers. Finally, we conduct a series of numerical experiments, which not only verify the computational efficiency of the distributionally robust chance-constrainted models but also reduce the degree of constraint violation in out-of-sample tests compared with a sample average approximation method. Full article

Chart reasoning, a critical task for automating data interpretation in domains such as aiding scientific data analysis and medical diagnostics, leverages large-scale vision language models (VLMs) to interpret chart images and answer natural language questions, enabling semantic understanding that enhances knowledge accessibility and supports data-driven decision making across diverse domains. In this work, we formalize chart reasoning as a sequential decision-making problem governed by a Markov Decision Process (MDP), thereby providing a mathematically grounded framework for analyzing visual question answering tasks. While recent advances such as multi-step reasoning with Monte Carlo tree search (MCTS) offer interpretable and stochastic planning capabilities, these methods often suffer from redundant path exploration and inefficient reward propagation. To address these challenges, we propose a novel algorithmic framework that integrates a pheromone-guided search strategy inspired by Ant Colony Optimization (ACO). In our approach, chart reasoning is cast as a combinatorial optimization problem over a dynamically evolving search tree, where path desirability is governed by pheromone concentration functions that capture global phenomena across search episodes and are reinforced through trajectory-level rewards. Transition probabilities are further modulated by local signals, which are evaluations derived from the immediate linguistic feedback of large language models. This enables fine grained decision making at each step while preserving long-term planning efficacy. Extensive experiments across four benchmark datasets, ChartQA, MathVista, GRAB, and ChartX, demonstrate the effectiveness of our approach, with multi-agent reasoning and pheromone guidance yielding success rate improvements of +18.4% and +7.6%, respectively. Full article

Piano fingering estimation remains a complex problem due to the combinatorial nature of hand movements and no best solution for any situation. A recent model-free reinforcement learning framework for piano fingering modeled each monophonic piece as an environment and demonstrated that value-based methods outperform probability-based approaches. Building on their finding, this paper addresses the more complex polyphonic fingering problem by formulating it as an online model-free reinforcement learning task with a novel training strategy. Thus, we introduce a novel Elite Episode Replay (EER) method to improve learning efficiency by prioritizing high-quality episodes during training. This strategy accelerates early reward acquisition and improves convergence without sacrificing fingering quality. The proposed architecture produces multiple-action outputs for polyphonic settings and is trained using both elite-guided and uniform sampling. Experimental results show that the EER strategy reduces training time per step by 21% and speeds up convergence by 18% while preserving the difficulty level and result of the generated fingerings. An empirical study of elite memory size further highlights its impact on training performance in solving piano fingering estimation. Full article

Unmanned aerial vehicles (UAVs) have emerged as a promising solution for collaborative search missions in complex environments. However, in the presence of interference, communication disruptions between UAVs and ground control stations can severely degrade coordination efficiency, leading to prolonged search times and reduced mission success rates. To address these challenges, this paper proposes a novel multi-agent deep reinforcement learning (MADRL) framework for joint spectrum and search collaboration in multi-UAV systems. The core problem is formulated as a combinatorial optimization task that simultaneously optimizes channel selection and heading angles to minimize the total search time under dynamic interference conditions. Due to the NP-hard nature of this problem, we decompose it into two interconnected Markov decision processes (MDPs): a spectrum collaboration subproblem solved using a received signal strength indicator (RSSI)-aware multi-agent proximal policy optimization (MAPPO) algorithm and a search collaboration subproblem addressed through a target probability map (TPM)-guided MAPPO approach with an innovative action-masking mechanism. Extensive simulations demonstrate superior performance compared to baseline methods (IPPO, QMIX, and IQL). Extensive experimental results demonstrate significant performance advantages, including 68.7% and 146.2% higher throughput compared to QMIX and IQL, respectively, along with 16.7–48.3% reduction in search completion steps versus baseline methods, while maintaining robust operations under dynamic interference conditions. The framework exhibits strong resilience to communication disruptions while maintaining stable search performance, validating its practical applicability in real-world interference scenarios. Full article