Metaheuristic Optimization

The one-dimensional bin packing problem (1D-BPP) is a canonical NP-hard combinatorial optimization problem with broad industrial applications. We propose RL-HGGA, a hybrid algorithm that integrates Falkenauer's Hybrid Grouping Genetic Algorithm (HGGA) with a tabular Q-learning controller. Rather than applying genetic operators at fixed probabilities, a Q-learning agent dynamically selects among eight macro-actions -- including BPCX crossover, light and heavy mutation, Martello-Toth local search, and population restart -- based on an eight-dimensional state representation encoding generation progress, stagnation level, optimality gap, average fitness, population variance, and average bin fill rate. The agent is trained with an epsilon-greedy policy over 400 episodes, with epsilon decaying to 0.05. Experiments on standard benchmark families (Falkenauer T/U, Scholl 1-3, Hard28) show that RL-HGGA achieves an average optimality gap of 0.95% -- competitive with HGGA (0.75%) and well below FFD (2.47%) -- while reducing mean computation time from 64.22 s to 1.29 s, a 50x speedup. These results demonstrate that learned adaptive operator selection can achieve near-HGGA solution quality at a fraction of the computational cost.

This paper studies the Metabolic Multi-Agent Optimizer (MMAO) at the framework level rather than at the implementation or benchmark level. The central question is whether the metabolic resource loop of private energy, communal budget, role drift, and lifecycle turnover has a framework-level interpretation beyond narrative metaphor. We introduce a generic MMAO state model that abstracts away domain-specific move operators while retaining the resource bookkeeping that defines the framework. Under mild bounded-gain and bounded-spending assumptions, we establish boundedness and nonnegativity properties for private energy, communal budget, role state, and active population size. We then characterize three endogenous behavioral regimes of the loop: contraction under sustained resource deficit, reinvestment under surplus communal accumulation, and search redistribution under heterogeneous marginal returns across agents or subgroups. The analysis is intentionally conservative. It does not claim global convergence of the full adaptive system, universal superiority over specialist optimizers, or a complete stationary characterization of the resulting process. Instead, it identifies which internal regulation properties are generic consequences of the loop and which remain implementation specific. A compact mechanism-validation package on representative continuous and discrete MMAO realizations provides supporting empirical evidence for this reading, but is not intended to replace a full benchmark study. The resulting contribution is therefore a bounded, regenerative, resource-regulated interpretation of MMAO, rather than a complete proof of all adaptive behaviors of the full algorithm family.

This paper studies whether the Metabolic Multi-Agent Optimizer (MMAO) can be credibly derived into a dynamic-optimization method without replacing its core metabolic control loop by external adaptation modules. The proposed MMAO-Dyn maps private energy, communal budget, role drift, success feedback, and lifecycle turnover to a nonstationary setting in which environmental changes repeatedly invalidate previously useful local structure. We evaluate MMAO-Dyn on an 18-scenario synthetic dynamic continuous benchmark matrix covering shifted sphere, shifted Ackley, and shifted Rastrigin landscapes at $10D$, $20D$, and $30D$, with two change severities and 12 seeds per scenario. The comparison layer includes a generic MMAO variant without dynamic derivation, dynamic random search, dynamic PSO-lite, dynamic DE-lite, and three endogenous ablations. Across the full 216-run matrix, MMAO-Dyn attains mean offline error $28.07$, improving over Generic-MMAO ($29.36$), Dynamic-PSO-lite ($34.65$), Dynamic-DE-lite ($67.09$), and Dynamic-RandomSearch ($111.37$). The gains are clearest in aggregate robustness on sphere and Rastrigin families and in 10-step post-change recovery relative to the generic backbone, whereas the seed-aligned comparison with Dynamic-PSO-lite remains unfavorable in win-loss count and the \texttt{NoMemoryRefresh} ablation stays very close to the full method. We therefore position MMAO-Dyn as a credible family-expansion result for MMAO: the metabolic loop can generate meaningful dynamic behavior, but the strongest current value lies in recovery-oriented resource redistribution rather than in universal dominance or in a fully optimized submechanism design.

This paper evaluates the Metabolic Multi-Agent Optimizer (MMAO) under a stricter empirical protocol rather than reintroducing the framework itself. The study asks whether MMAO's closed-loop resource-allocation principle remains credible under broader, more standard, and more explicitly budget-controlled continuous and discrete benchmarks. The main completed matrix covers eight CEC2017 functions at 10D and 30D with 20 seeds each, and five TSPLIB instances with 20 seeds each, together with stronger reproducible baselines including PSO-lite, ES-lite, and an iterated-greedy 2-opt route baseline. We further add trajectory-level diagnostics for communal budget, success rate, role evolution, and population turnover, plus an auxiliary OR-Library multiple-knapsack slice to extend the discrete evidence beyond routing. Under this protocol, MMAO clearly outperforms the external baseline set on the continuous side and on the TSPLIB side, while the ablation variants remain much closer to the full method than the external baselines are. We therefore position MMAO as a benchmark-backed cross-domain adaptive framework whose most clearly validated value is endogenous resource redistribution under evidence pressure, while also noting that the strongest remaining gap is not basic workability but sharper mechanism isolation and broader competition-grade comparison.

This paper presents the Metabolic Multi-Agent Optimizer (MMAO) as an adaptive metaheuristic built around endogenous resource circulation. The central premise is that search intensity, exploration--exploitation balance, and lifecycle turnover should be induced by a shared metabolic controller rather than by separately attached schedules. We formulate MMAO through bounded private energy, a communal budget, normalized reward, continuous role adaptation, and resource-financed branching and pruning. The method is then instantiated in both continuous and discrete domains and evaluated on a matched small-scale suite including Sphere, Rastrigin, a synthetic Euclidean TSP, and two TSPLIB instances. The results show a consistent pattern: the same metabolic loop remains workable across domains, the discrete realization remains relatively stable under a compact design, and continuous refinement quality is the main cost of keeping the method lean. Taken together, these findings position MMAO as a coherent framework for adaptive heuristic design rather than a loose collection of operators.

Parameter settings in evolutionary algorithms and metaheuristics are important because such parameter values can influence the performance of algorithms under evaluation. For a given algorithm, there are many different numerical experiments to show that the algorithm can work well in practice; however, in most cases there is no theoretical analysis of parameter settings. In this work, we show that theoretical analysis using the theory of dynamical systems and evolution of population variance can give some good results in terms of parameter ranges for the bat algorithm. We also show that results from numerical experiments are consistent with theoretical bounds. Such analyses can provide good insights from different perspectives about the algorithmic characteristics such as variance evolution, transition between exploration and exploitation as well as convergence behaviour.

Traditional meta-heuristics often rely on fixed population sizes, manually chosen search scales, and externally attached parameter-control modules. This paper presents the \textit{Metabolic Multi-Agent Optimizer} (MMAO), a cross-domain optimization framework in which adaptation is derived endogenously from a private-public metabolic resource loop. Each agent carries internal energy, a continuous role state, motion or structural memory, and local search history, while the population shares a communal resource pool. Fitness improvements are converted into normalized metabolic gains through a robust progress scale and a recent success statistic; the same closed loop then regulates sensing intensity, search amplitude, role drift, branching, pruning, respawning, and elite reinvestment. In the continuous setting, MMAO uses energy-regulated symmetric zero-order probing and role-interpolated motion. In the discrete setting, the same control law is instantiated through structural sensing, local route improvement, guided perturbation, and energy-weighted edge reuse. The paper combines an implementation-faithful formulation with a reproducible experimental study on a CEC2017 subset (10D/30D, 20 seeds) and five TSPLIB instances (100 discrete runs in total). The current evidence supports MMAO primarily as a parameter-light, self-calibrating optimization framework whose main validated originality lies in metabolically endogenous resource allocation across heterogeneous search behaviors, rather than as a universally superior optimizer.

Balancing exploration and exploitation remains a central challenge in metaheuristic optimization. To address this issue, this paper proposes Bézier Walk Evolution (BWE), a geometry-driven optimization framework that reformulates evolutionary search as adaptive trajectory construction in the decision space. BWE integrates Bézier curve modeling with a distance-aware random walk mechanism to generate topology-guided search trajectories. By adaptively varying the curve order during evolution, the proposed method enables a smooth transition from diversified global exploration to refined local exploitation. Higher-order Bézier curves leverage multiple population-derived control points to enhance search diversity, while lower-order curves generate near-linear trajectories to improve convergence efficiency. This adaptive geometric search mechanism provides an interpretable alternative to conventional nature-inspired designs. Extensive experiments on 41 benchmark functions from the CEC2017 and CEC2022 suites, spanning dimensions from 10 to 100, show that BWE achieves strong overall performance and favorable scalability compared with 7 classical and 6 state-of-the-art optimizers, including L-SHADE and CMA-ES. Additional evaluations on five constrained engineering design problems further demonstrate the practical applicability and robustness of BWE.

Finding all modes of a multimodal black-box function is a fundamental challenge in optimization, Bayesian inference, and scientific computing. Existing approaches -- basin-hopping, CMA-ES, multistart gradient descent -- operate sequentially and cannot exploit the massive parallelism of modern GPU hardware. We introduce \chisao{} (\textbf{C}onvergence-\textbf{H}alt-\textbf{I}nvert-\textbf{S}tick-\textbf{A}nd-\textbf{O}scillate), a GPU-native population optimizer that runs an entire sample batch simultaneously and exploits a deliberate convergence-anticonvergence oscillation cycle to escape local traps while freezing confirmed modes. The structural move is asymmetric: samples that reach true peaks are frozen (``stuck'') and preserved, while the rest keep exploring via momentum-based anti-convergence and stochastically smoothed gradients. Adaptive reseeding via two complementary strategies (Repulse Monkey and Golden Rooster) maintains population diversity throughout. On all 42 functions of the Simon Fraser University optimization benchmark suite across dimensions $d \in \{2, 4, 8, 16, 32, 64\}$, \chisao{} achieves \textbf{100%} mode recovery where all CPU baselines collapse at $d \geq 8$ on the hardest multimodal functions, at up to \textbf{$34\times$} speedup over basin-hopping on functions where all methods succeed (Michalewicz $d=64$) and up to \textbf{$39\times$} on unimodal functions (Rotated Hyper-Ellipsoid $d=64$, pure GPU dividend). All benchmarks evaluate the objective by value alone -- gradients come from finite differences -- so the reported speedups are a derivative-free worst case. Under substantial likelihood noise ($σ_{\mathrm{noise}}$ up to 1.0), mode detection remains 100% reliable. The algorithm is available as a standalone open-source Python package on PyPI.

This paper introduces RACL, a Reasoning-Agent Control Layer for metaheuristics. RACL places a reasoning agent above an existing optimizer. The agent does not replace the optimizer and does not modify business constraints. Instead, it controls the optimizer's internal search behavior by observing operational memory, reasoning over past behavior, formulating bounded hypotheses, testing interventions, evaluating outcomes, applying guardrails, consolidating useful policies and explaining its decisions. The experiment uses vehicle routing as a testbed, but the contribution is not a new routing solver, a particular ALNS configuration or a specific set of routing rules. The contribution is the RACL method: a way for a reasoning agent to discover, validate, consolidate and explain algorithmic control rules for a metaheuristic. In the current experimental setting, RACL improves or ties the Operational Memory Policy in 21 of 21 feasible cases and improves or ties a non-reasoning Stagnation-Triggered Policy in 18 of 21 feasible cases, with an average RACL vs STP cost delta of -0.641%. In the Sevilla-9/10 runtime sample, RACL improves average cost by -8.337% versus Fixed and -1.605% versus STP without showing material computational overhead. During the proof-of-concept, Codex was used as an in-the-loop reasoning agent observing executions, interpreting logs and proposing live bounded interventions. The policy proxy was later used only to make quantitative evaluation reproducible.

This work presents a tool for the synthesis and simulation of probabilistic architectures for solving combinatorial optimization problems by mapping them to the Ising model. The proposed approach automatically constructs the Ising Hamiltonian and determines the number of probabilistic elements (p-bits) based on problem characteristics such as size and topology. Furthermore, the tool introduces an adaptive strategy for selecting the most suitable update algorithm among Gibbs Sampling, Simulated Annealing (SA), Simulated Quantum Annealing (SQA), and cluster-based methods. Experimental results using benchmark problems demonstrate improved convergence behavior and flexibility compared to fixed approaches. The proposed framework enables systematic evaluation of probabilistic computing strategies and supports the development of future hardware implementations based on MTJs and p-bits.

The permutation flow shop scheduling problem (PFSP) is a classical NP-hard combinatorial optimization problem in intelligent manufacturing. In practice, PFSP is commonly addressed using metaheuristic algorithms, among which the iterated greedy (IG) algorithm is widely adopted due to its simplicity and strong empirical performance. However, classical IG relies on a single fixed destruction operator, which often limits exploration and leads to search stagnation on large and complex problem instances. To address this issue, this work proposes a multi-operator IG algorithm, termed IG-DOE, which enhances exploration by switching among heterogeneous destruction operators along a single search trajectory. The core mechanism, called stagnation-triggered sequential switching, activates the next destruction operator in an ordered destruction operator ensemble (DOE) when stagnation is detected, thereby enriching the perturbation behavior of classical IG. Moreover, to reduce reliance on expert-crafted operators, a large language model (LLM)-assisted framework, termed SCOE, is introduced to automatically construct a high-quality DOE through stagewise evolution, state-awareness, and cooperative evaluation. Experiments on the challenging VRF-hard-large benchmark show that the DOE evolved from smaller problem instances generalizes well to larger unseen instances. Under the same CPU-time limit, IG-DOE obtained much better average performance than QIG, a state-of-the-art IG algorithm. Additional experiments on real-world industrial-data-derived instances further show that the evolved DOE can generalize effectively to different data distributions without additional adaptation.

ZIVARI-TLBO is a grouped Teaching-Learning-Based Optimization (TLBO) method that augments an existing population-state controller with a fixed inter-group evaluated-elite relay. At each scheduled event, every group offers its already evaluated elite to the next group in a fixed ring; the elite replaces the receiver's worst eligible learner only when its stored objective value is better. Because the exact relay copies an already evaluated solution and its stored fitness, it requires no additional objective-function calls. The frozen gts-v4-cm-fixed implementation is evaluated under equal 10,000-evaluation budgets on eight classical functions at dimensions 10, 30, 50, and 100, with 30 matched seeds, and on five constrained engineering problems. A direct ablation against the same grouped landscape-aware controller without relay records 728/11/221 wins/ties/losses and a rank-biserial effect size of 0.624 across dimensions. In an eight-method multidimensional comparison, WOA obtains the best average rank (2.914) and ZIVARI-TLBO ranks second (3.382); ZIVARI-TLBO significantly outperforms TLBO, MCTLBO, DE, PSO, and GWO, loses significantly to WOA, and is not significantly different from HHO after Holm adjustment. Feasibility-aware engineering results are mixed and sensitive to the current static-penalty formulation. The evidence supports a scoped relay contribution and budget-consistent information-sharing mechanism, but not universal state-of-the-art, global-convergence, engineering-dominance, or CEC superiority claims.

Population-based optimizers combine update rules such as mutation, selection, and recombination. When one rule changes, it is often unclear which convergence guarantees survive or how the new combination should be assessed. We develop an operator calculus: an operator is a population-update rule, and the calculus specifies how separately checked effects can be combined. Under explicit regularity and small-step conditions, the leading changes caused by the updates add, yielding reusable building blocks for convergence analysis. The framework distinguishes finding and retaining a good solution, reducing the population's mean objective, and concentrating candidates near an optimizer, and identifies the extra approximation conditions needed for finite evaluation-budget guarantees. Applications include distribution adaptation, recombinative evolution, and consensus dynamics, with verified nonconvex cases. Controlled experiments on a common nonconvex problem collection show how component effects change with population geometry and the performance measure: a rule can worsen the mean objective yet produce better candidates.

The Traveling Salesman Problem (TSP) is a classical NP-hard combinatorial optimization problem that aims to find the shortest Hamiltonian cycle visiting each city exactly once and returning to the starting point. This paper proposes a hybrid metaheuristic for the TSP by combining the Dragonfly Algorithm (DA), a swarm-intelligence-based global search method, with Tabu Search (TS), a memory-based local search technique. The proposed method follows a High-Level Relay Hybridization (HRH) scheme, in which DA is first used to explore the solution space and generate a promising initial tour, while TS subsequently refines this solution through neighbourhood-based improvement and tabu memory. The hybrid approach is evaluated on standard TSPLIB benchmark instances, including burma14, att48, and ch150, and compared with standalone DA, standalone TS, and several classical metaheuristics such as Genetic Algorithm, Ant Colony Optimization, Particle Swarm Optimization, and Random Search. A systematic grid-search procedure is also conducted to study the influence of the main hyperparameters on solution quality and execution time. The experimental results indicate that the proposed hybrid can improve tour quality compared with the standalone DA and TS on the tested instances, highlighting the benefit of combining global exploration with local exploitation. However, the results also suggest that performance remains sensitive to parameter settings and problem size, motivating further validation on larger benchmarks and stronger TSP-specific baselines.

Bearing-only target localization is a fundamental problem in optical measurement and finds extensive applications in unmanned aerial vehicle (UAV) technology. Effective trajectory planning establishes favorable observation geometries, thereby enhancing the target localization accuracy of bearing-only UAV systems. This paper proposes an trajectory optimization method for unmanned aerial vehicles (UAVs) in bearing-only target localization scenarios. By leveraging the Fisher Information Matrix (FIM), the proposed approach dynamically integrates the geometric configuration and vehicle maneuverability into the optimization framework. Specifically, we introduce a spectrally-weighted FIM objective function that provides better gradient dynamics near degenerate configurations, enabling the planner to rapidly escape from poor observation conditions. For dual-UAV scenarios, an intersection angle sine term is introduced to optimize triangulation geometry by improving the sight-line intersection angle, thereby preventing trajectory aggregation. Furthermore, we propose an improved Particle Swarm Optimization (PSO) algorithm with motion model constraints and particle normalization to ensure the physical feasibility of the trajectory and enhance the compatibility with the objective functions. Simulation results demonstrate that the proposed method reduces the median localization error by 99.21% compared to conventional FIM-based approaches in single-UAV scenarios, and achieves a 69.70% improvement for dual-UAV configurations, exhibits superior performance in long-duration bearing-only target localization of maneuverability targets at extended ranges.

Gray-box optimization is an approach for making some problem-specific information available to the algorithm while still relying on fitness information as the main guide to an optimum. This approach was shown to be beneficial in various combinatorial optimization tasks and neatly captures the continuum between fully black-box algorithms and tailored algorithms. In this work, we discuss different flavors of gray-box algorithms. We show that RLS can find a proper $2$-coloring in a bipartite graph starting from a random $2$-coloring, in an expected time of $\mathcal{O}(n \log n)$. In contrast, when starting from a proper $n$-coloring, the (1+1) EA cannot find such a coloring except when offered additional guiding on plateaus of the search space. Finally, we show the run time for this setting can be much improved by using gray-box operators.

Reservoir computing exploits the fixed dynamics of a recurrent network for temporal processing, requiring only a trained linear readout. Biological neural connectomes, shaped by millions of years of evolution, may encode computational structure beyond what random reservoirs provide, yet whether that structure can be further enhanced by principled optimisation remains an open question. We address it by applying four gradient-free, bio-inspired optimisers (Particle Swarm Optimisation, Differential Evolution, Grey Wolf Optimiser, and Whale Optimisation Algorithm) to the edge weights of connectome-based echo-state networks across six species spanning six orders of magnitude in neural complexity: C. elegans (279 neurons), Drosophila (49 nodes), mouse (112), rat (73), macaque (29 regions, continuous FLNe synaptic strengths), and human structural MRI connectivity (83 parcels). Each connectome is evaluated on four canonical reservoir computing benchmarks: Memory Capacity (MC), Lorenz attractor prediction, NARMA-10 system identification, and Mackey-Glass chaotic time-series prediction. All four optimisers consistently outperform unoptimised biological baselines across every task and species when initialised from biological weights. WOA achieves the largest gains on every task: up to a 17x MC improvement (C. elegans: 1.39 to 23.91) and up to 89% NRMSE reduction (Mackey-Glass, human), corresponding to an average 214% improvement across all species and tasks. Crucially, random initialisation on the same topology reliably underperforms biology, establishing biological weight values as an essential inductive bias that topology alone cannot recover. These results position bio-inspired, biologically-initialised optimisation as a principled and broadly effective strategy for connectome reservoir computing across the animal kingdom.

We study parallel Continuous Local Search (CLS) as a solution approach for Boolean satisfiability problems with symmetric pseudo-Boolean (PB) constraints. Here, the $n$-variable PB-satisfiability problem is relaxed to a continuous optimisation problem with a differentiable objective function on an $n$-dimensional hypercube. For satisfiable instances, the global minimisers of this optimisation problem correspond to satisfying assignments of the SAT problem at hand. We present several novel findings via empirical experiments: (i) redundant constraints can inhibit rather than accelerate convergence; (ii) CLS shows promise as a sub-solver in hybridised settings, quickly completing partial assignments; and (iii) local search rapidly converges to a stable distribution of solution quality (i.e., degree of satisfaction), due to saddle-dense objectives where additional solver steps yield diminishing returns. Our findings inform practical uses of CLS for SAT on modern accelerator hardware.

Finding manifold structures in noisy and high-dimensional point clouds is a challenging but important problem. In astronomical observation survey and simulation data the detection of filaments, streams (1D), walls (2D) and clusters (3D) gives rise to deeper understanding of the evolution of our universe. The Locally Aligned Ant Technique (LAAT) uses biologically inspired agents to efficiently recover faint and multidimensional structures. However, very dense hubs (e.g. nodes or globular clusters) dominate the ants' activity, creating unnecessary computational overheads. In this paper we propose a two-stage solution. First a fast preprocessing step locates the hubs and replaces them with a tailored likelihood model. Subsequently, a mixed likelihood-pheromone strategy guides the ants to efficiently bridge the dense regions. We demonstrate improvements in detection efficiency and robustness of LAAT with synthetic and a large-scale astronomical N-body simulation of the cosmic web.

The radial basis function neural network (RBFN) trained with a gradient descending algorithm provides an effective fully connected structure in both shallow and deep networks. The error correction (ErrCor), a state-of-the-art gradient-based training method, selects optimal hidden units to improve accuracy. Alternatively, as a population-based algorithm, the particle swarm optimization algorithm (PSO) uses the swarm experience to optimize RBFN parameters, offering global search and robustness to local minima. Adaptive PSO (APSO) has emerged as an improved variant of PSO. APSO algorithm improves convergence speed by dynamically adjusting swarm parameters during optimization. Both ErrCor and PSO demonstrate improved results and competitive convergence. However, with large datasets, these methods face scalability challenges such as excessive kernel computations and large hidden layer structures. A recent multi-column RBFN approach (MCRN) improves ErrCor performance by deploying small RBFNs in a parallel system. Inspired by MCRN's success, we propose two novel approaches to improve PSO performance: the multi-column RBFN with PSO (MC-PSO) and the multi-column RBFN with APSO (MC-APSO). These methods introduce parallel RBFN structures trained using evolutionary swarm methods. Each RBFN is independently trained on a specific spatial subset of the dataset using either PSO or APSO algorithms. These resulting specialist-trained RBFNs are tailored to their respective subsets. During testing, only selected RBFNs, where the test instance neighbors are located, contribute to the multi-column output. This specialization improves accuracy, while parallelism enhances speed. We evaluate the proposed methods on various benchmark datasets. The MC-PSO and MC-APSO outperform ErrCor, PSO, APSO, and MCRN in terms of accuracy and recall. They also demonstrate faster training and testing times in most experiments.

Neural-guided Ant Colony Optimization (ACO) suffers from a fundamental training-inference misalignment: policies are typically trained to generate static priors (e.g., heatmaps), yet deployed to guide iterative, long-horizon search processes. In this paper, we present DyNACO, a novel framework that achieves dynamic neural guidance by periodically observing the pheromone distribution and the incumbent solution. To make DyNACO tractable at scale, we pair the policy with a perturbation-based ACO backend and a scope-restricted refinement mechanism that jointly ensure efficacy and stable credit assignment. On TSP, DyNACO scales to 100,000-node instances and outperforms neural baselines while often reducing total runtime compared to the unguided solver. We extend DyNACO to CVRP via a capacity-aware backend, consistently improving the unguided baseline with less than 1% neural overhead. We further provide in-depth analysis validating the model's generalization capabilities and elucidating why dynamic guidance outperforms static priors. Our work underscores the necessity of aligning neural training with iterative search dynamics in learning-guided optimization. The code is available at https://github.com/shoraaa/DyNACO.

Operations research practitioners typically tackle NP-hard combinatorial problems using large neighborhood search (LNS), a scalable heuristic that iteratively refines a current solution by locally re-optimizing subsets of its variables. In contrast, most existing approaches for integrating combinatorial optimization layers into neural networks still assume access to an exact global solution, which is computationally intractable. We bridge this gap by introducing regularized LNS (RLNS). By regularizing or perturbing local subproblems, we turn the LNS heuristic into an efficient MCMC sampler over the combinatorial set of feasible solutions, with associated Fenchel-Young losses. Under entropic regularization, we prove that RLNS performs exact block Gibbs sampling. Furthermore, adjusting the number of RLNS iterations allows us to interpolate between pseudolikelihood and exact maximum likelihood estimation, for end-to-end learning without global solvers. We demonstrate our approach on $k$-subset selection, generalized assignment, and stochastic vehicle scheduling problems.

While Large Language Models (LLMs) have recently shown promise in Automated Heuristic Design (AHD), existing methods typically generate and evolve heuristics as a single operator or search strategy, limiting their ability to model strong coupling among multiple decision substructures in problems such as the Traveling Thief Problem (TTP) and the Traveling Purchaser Problem (TPP). In this work, we propose CoEvo-AHD, an LLM-driven dual-population co-evolutionary framework for automated heuristic design in coupled combinatorial optimization. Unlike prior methods that evolve individual heuristics in isolation, CoEvo-AHD leverages LLMs to co-evolve two closely related operator populations. A cooperative evaluation mechanism explicitly captures interactions between route and selection operators, while pairwise scoring and synergistic joint crossover help discover complementary operator logic for joint improvement across coupled decision subspaces. We further design a tool-invocation environment library that encapsulates frequently used core operations, such as local-search delta computation, into callable functions, enabling LLM-generated operators to use standardized interfaces instead of reimplementing inefficient and error-prone problem-specific loops. Experiments on TTP and TPP show that CoEvo-AHD automatically discovers cooperative heuristic combinations and achieves competitive solution quality against traditional heuristics.

The Charlson Comorbidities Index (CCI) is a weighted additive index widely used to estimate ten-year mortality risk, but its original weights may not reflect contemporary prognoses. This limitation is critical in Prostate Cancer (PCa), where radical treatment is recommended only for patients with a life expectancy of at least ten years. For candidates eligible for Radical Prostatectomy (RP), accurate estimation of ten-year other-cause mortality is essential to balance oncological benefit against competing risks and avoid overtreatment. We propose a data-driven framework to derive a comorbidity index tailored to PCa patients considered for RP. Using a retrospective single-institution cohort, we apply Population-Based Bio-Inspired Algorithms (PBBIAs) to recalibrate comorbidity weights and evolve alternative symbolic formulations optimized for ten-year survival discrimination. We compared six optimization strategies, including symbolic regression approaches based on Genetic Programming (GP), population-based metaheuristics, clinically validated baselines, and survival prediction models. Results show that GA, FST-PSO, and SLIM outperform both the original CCI and the PCCI, particularly when PCa-specific variables are included, improving the Concordance Index by up to 0.1. GPLearn yields compact and interpretable models with competitive performance. Overall, the proposed approach provides an updated and interpretable tool to improve patient selection for RP.

The Random Gradient hyper-heuristic was recently shown to be able to learn the optimal neighbourhood size when optimizing the LeadingOnes benchmark via the Randomised Local Search (RLS) meta-heuristic. However, for this to happen, a learning period of a certain length $τ$ had to be used, differently from classic hyper-heuristics, which change their behaviour based on the success of only the previous iteration. In this paper, we show how to automatically set this new parameter value, relieving the user from the non-trivial task of controlling this novel algorithm parameter. We prove that the resulting hyper-heuristic selects the optimal neighbourhood size in a $1-o(1)$ fraction of the iterations and, consequently, optimises the LeadingOnes benchmark in the best possible time (apart from lower-order terms) achievable with these neighborhood sizes.

Active tether-net systems are a promising solution for capturing large non-cooperative targets, such as space debris, by deploying a flexible net manipulated by maneuverable units (MUs). However, concurrent systematic explorations of design and control choices of the tether-net system to understand its full potential remain limited, partly due to the complex, constrained, nonlinear optimization problem that it presents -- one that involves a mixture of continuous, integer and categorical variables, with the latter two arising from net connectivity and component choices, respectively. Classical binary encoding methods are often ineffective for solving highly nonlinear and multimodal Mixed Combinatorial Nonlinear Programmings (MCNLPs) in engineering design, while integer coding approaches can introduce spurious relations among combinations. Given the graph-structured characteristics of the combinatorial space, this paper adopts and extends a new graph-learning-aided optimization approach to solve this MCNLP problem. Here, a Graph Neural Network (GNN) is trained to score (as output) and thereof recommend candidate combinations represented as nodes in a graph, with the continuous variable vector portion of a candidate design given as input. As a result, the MCNLP optimization reduces to an NLP, which can be solved using standard solvers. While this reduction approach is agnostic to the choice of the NLP solver, here a state-of-the-art Particle Swarm Optimization (PSO) algorithm with gradient-based fine-tuning is used as the solver. Demonstrated on the problem of concurrently designing the morphology of the net, choice of mass and thrusters in the MUs and aiming points used by the controller of the tether-net system, the GNN-based recommender is shown to provide significantly faster convergence to similar optimal solutions, compared to direct solution of the MCNLP problem.

A new variant of the classic capacitated facility location problem, which considers incompatibilities between customers, has recently been introduced in the literature. This problem captures the situation where given pairs of customers cannot be served by the same facility. Such a feature is crucial for many practical cases of location problems, such as the presence of hazardous or polluting materials and contention between competing costumers. In this paper, we propose a Large Neighborhood Search (LNS) method to solve this problem. Within the framework of LNS, we introduce three different destroy operators, which are combined in a hybrid manner, and we use an exact solver in the repair phase. Different algorithmic components are investigated for the design of LNS. The experimental analysis shows that our new method outperforms existing state-of-the-art metaheuristics, providing new best solutions for all available benchmark instances.

Particle Swarm Optimization (PSO) frequently suffers from premature convergence. This paper introduces a family of problem-informed diversity-enhancing strategies that manipulate the swarm's social and cognitive components. These include opposing-best strategies that repel particles from optimal regions, negative learning strategies that guide exploration toward poor solutions, and reverse learning strategies that push particles away from inferior regions. These socio-cognitive mechanisms are evaluated against an analogous suite of problem-unaware, explicit randomization strategies that inject randomness either into velocity update components or directly into position updates. The results reveal that the effectiveness of diversity enhancement is determined primarily by how it is embedded within the swarm dynamics, rather than by the mere presence of extraneous problem-informed guidance. Particularly, random perturbations introduced at the velocity-update level consistently outperform those applied directly to particle positions.

Spatial photonic Ising machines (SPIMs) based on spatial light modulators (SLMs) have emerged as highly effective solvers for many tasks, including combinatorial optimization problems and spin-glass simulations. However, traditional SPIMs relying solely on the simulated annealing algorithm require a large number of measurement-feedback iterations to find a relatively optimal solution in complex energy landscapes, suffering from slow convergence and high time cost. Here, we propose an optical genetic-simulated annealing hybrid algorithm to accelerate the ground-state search of SPIMs. GA conducts a global coarse-grained search in the early iteration stage, while SA performs fine-grained local refinement in the late stage. Numerical simulations show that our method enables a higher solution quality of full-rank Max-Cut problems than pure GA or SA at different scales. We also experimentally demonstrate its superiority over conventional algorithms on a gauge-transformation time-division multiplexing SPIM for high-rank optimization problems under the same iteration budget. Our approach can be further developed with other advanced metaheuristic algorithms toward intelligent optical Ising computing systems.