This study addresses supplier selection and order allocation problems under the risk of supplier disruption. Motivated by real-world supply chains characterized by supplier concentration, this study introduces the concept of a dominant supplier market into the supplier selection and order allocation framework. Conditional Value-at-Risk (CVaR) is incorporated to capture risk-averse procurement decisions. Single-level optimization models are developed, including a risk-neutral model, a CVaR-based risk-averse model, and a bi-objective model that balances risk-neutral and risk-averse objectives. The framework is then extended to a bi-level optimization model in which a dominant supplier strategically sets prices while anticipating the retailer's response. Computational experiments demonstrate the impact of disruption risk and supplier dominance on procurement decisions. While existing managerial insights in the literature have primarily focused on retailers' procurement strategies, this study provides decision support for both the dominant supplier and the retailer in selecting appropriate strategies in a dominant supplier market.
Motivated by the Amazon returns at Kohl's programme, the article analyzes under what conditions buy-online-and-return-in-store (BORS) improves the profit of an e-tailer and a store when they offer substitute products. Firstly, BORS enhances the e-tailer's profit if the unit BORS handling cost is below a threshold, and continues to do so even when the cost exceeds another threshold under a duopoly with multichannel returns. BORS boosts the store's profit if the unit BORS handling cost exceeds a threshold. Secondly, when BORS leads to a monopoly market, BORS is a win-in strategy if the unit BORS handling cost is below a threshold. But when competition still exists with BORS, the unit BORS handling cost should exceed a threshold. Finally, without BORS, a higher consumers' hassle cost of returning online benefits the store but hurts the e-tailer, while with BORS, it benefits both retailers or exerts no impacts under certain conditions.
To ensure supply-demand balance in natural gas networks under uncertainty, a distributionally robust optimization (DRO) model is formulated that jointly optimizes supply allocation, pipeline expansion and storage scheduling. A satisfaction index, defined as the probability of meeting the demand, quantifies the network's reliability. Ambiguity sets can capture uncertainty in demand and storage costs; the model is equivalently reformulated as mixed-integer second-order cone programming (MISOCP). A tailored branch-and-cut algorithm is developed for efficient solutions. An anonymized case adapted from a real network is used to demonstrate the validity of the proposed DRO model: annual supply planning improves long-term returns, and tuning parameters enable a quantifiable risk-return trade-off to match operator's preferences. Relative to a baseline model, the proposed method can reduce the total cost while maintaining feasibility and provide practical and risk-aware decisions for a natural gas network. Supplemental data for this article can be accessed online at http://dx.doi.org/10.1080/0305215X.2026.2655339.
This article proposes FDB-AEO-OD, an enhanced artificial ecosystem optimization (AEO) algorithm for minimum-weight seismic design of steel frames. This method integrates the fitness-distance balance (FDB) guidance strategy with a new orthogonal decomposition (OD) operator constructed via singular value decomposition of elite solutions. By generating mutually orthogonal search directions, OD preserves population diversity, enhances exploration in multimodal and high-dimensional spaces, and mitigates mid-to-late-stage stagnation while maintaining effective exploitation. The performance of FDB-AEO-OD is evaluated on two benchmark asymmetrical steel-frame optimization problems designed under AISC-LRFD requirements with displacement and geometric constraints: a four-story 132-member and a four-story 428-member frame. Comparisons with PSO, AOA, COA, QIO, NSM-TLABC, NSM-SFS, NSM-LSHADE-SPACMA and FDB-AEO show that FDB-AEO-OD consistently delivers the lightest feasible designs and the most reliable performance across multiple independent runs. The results confirm the effectiveness and robustness of the proposed approach for seismic design optimization.
Floating dock gates are large-scale marine structures whose performance and stability are closely related to structural weight and stability. This study addresses the multi-objective optimization of floating dock gates. First, a marine component library is established to discretize optimization variables. An improved particle swarm optimization-simulated annealing (IPSO-SA) algorithm is proposed to resolve issues in the existing particle swarm optimization-simulated annealing algorithm. For multi-objective optimization, a multi-objective particle swarm optimization-simulated annealing (MOPSO-SA) algorithm is introduced, and its performance is validated through numerical simulations and comparisons with existing methods. Finally, the proposed methods are applied to a typical floating dock gate structure optimization. Using the developed component library, a parametric model is created and optimized. The multi-objective optimization reduces the weight by 11.303% and lowers the centre of gravity height by 2.5%. These improvements enhance both the economic performance and structural reliability of the original design.
To address difficulties in relaxation factor selection, local optimality and uncertainty sensitivity in multidisciplinary collaborative optimization (CO), this article proposes a multidisciplinary collaborative robust optimiza-tion method based on weighted allocation of discrepancy information, called stability collaborative optimization-maximum variation analysis (SCO-MVA). The method adaptively adjusts relaxation factors by weighting interdisciplinary and system-discipline discrepancies, and achieves stable coordination through a two-level optimization strategy. Comparative stud-ies with static and dynamic relaxation CO methods show that the proposed approach significantly improves convergence efficiency while maintain-ing optimization accuracy, reducing the average number of iterations by approximately 60-85%. Furthermore, maximum variation analysis is incor-porated to model interval uncertainty and construct a robust optimization framework. Validation using multiple examples demonstrates that robust solutions maintain full constraint feasibility under worst-case uncertainty, with only a 5-15% increase in objective function value, indicating a reason-able trade-off between robustness and optimality.
This article addresses a two-stage flow-shop scheduling problem (FSSP) considering uncertain job processing and release time. To minimize the worst-case expected makespan, a distributionally robust optimization (DRO) approach is designed. By introducing effective bounds and valid inequalities, the problem is transformed into a mixed integer linear program (MlLP), which is solvable via off-the-shelf commercial solvers. To verify the performance of the model, the DRO model is compared with the stochastic linear program (SLP) and its deterministic counterpart under various parameter settings, where the DRO model exhibits greater robustness and computational efficiency in handling almost all the scenarios. Besides, the DRO model demonstrates a prominent advantage when the uncertain interval of the mean is larger, the release time is less scattered and more jobs are scheduled. It is discovered that the proposed DRO model is capable of providing robust schedules in a highly volatile environment, thereby enhancing the resilience and robustness of manufacturing operations.
Optical computed tomography scanners are powerful imaging tools used in three-dimensional radiation dosimetry to reconstruct dose distributions in gel dosimeters. Solid-tank scanners embed the gel in an acrylic block, replacing large fluid baths and simplifying setup. The solid-tank, fan-beam design is formulated as a multiobjective problem that balances imaging extent, uniformity and ray-crossover artifacts. A ray-tracing simulator is developed with new, objective-specific performance measures and a multifidelity setting controlled by ray count. To enable efficient search, the non-dominated sorting genetic algorithm (NSGA-II) is employed within a multifidelity framework that incrementally escalates simulation fidelity and uses the Pareto-optimal survivors from one fidelity stage to initialize the next stage. The authors' method illustrates the advantages of a multiobjective framework to reveal deeper insights into design trade-offs, avoid biased outcomes and support robust lens selection. Moreover, performance comparison indicates that the authors method achieves higher-quality solutions within a comparable runtime to the standard NSGA-II approach.
The hyperplane approximation in the first-order reliability method facilitates computation but restricts its applicability to linear problems. While the second-order reliability method extends to nonlinear scenarios through hyperparaboloid approximation, its approximation formula introduce inherent errors and may fail to yield solutions in certain cases. The direct probability integral method maintains high accuracy by deriving the probability density function directly, although its computational efficiency diminishes when requiring additional limit state function evaluations to enhance precision. To address these limitations, a paraboloid-based direct probability integral method is proposed. The method constructs a curvature-informed paraboloid to approximate the limit state function, eliminating further function evaluations. Probability density integral equations are solved directly through generalized F-discrepancy point selection and the properties of the Dirac delta function and Heaviside function. Failure probability is then obtained by Heaviside value and probability mass of representative points. The method's accuracy and efficiency are validated using five distinct cases.
This article investigates an unrelated parallel machine scheduling problem in which jobs possess fuzzy processing and fuzzy release times, while each machine incurs a unit-time rental cost. The objective is to minimize the total weighted fuzzy completion time. To solve this problem, a reasonable total cost threshold is first established, and a fuzzy mixed-integer programming (FMIP) model is formulated. Subsequently, an improved fuzzy genetic algorithm (IFGA) is designed by integrating an elite genetic algorithm with variable neighbourhood search (VNS). The algorithm incorporates an elitism mechanism, a population perturbation operator, a local enhancement procedure, two infeasible solution repair strategies, and four effective neighbourhood structures. Experimental results demonstrate that IFGA generates solutions closest to the optimal ones on 270 small-scale numerical instances, with the maximum relative deviation within 5%. On 360 large-scale numerical instances, it significantly outperforms other metaheuristic algorithms, and its computational time remains stable within 90 seconds.
This study proposes a novel hybrid hyper-heuristic approach based on the memetic algorithm and artificial rabbits optimization (ARO) algorithm for the no-wait flowshop group scheduling problem with sequence-dependent setup times. The ARO algorithm is used to generate the initial population, which is then evolved implementing a memetic-algorithm-based hyper-heuristic framework incorporating multiple crossover, mutation and hill climbing operators. Each operator and its parameters are regarded as low-level heuristics and are dynamically selected based on scores derived from a reinforcement learning mechanism. The performance of the proposed algorithm is rigorously evaluated on 270 benchmark instances widely used in the literature. Comparative analyses against two state-of-the-art simulated annealing approaches demonstrate the clear superiority of the proposed method, which achieves better results in 73% and 57% of the instances. These results not only highlight the robustness and effectiveness of the developed approach but also establish a strong foundation for its potential in solving complex scheduling problems. Notably, this study represents the first successful application of the ARO algorithm in the domain of discrete optimization, and its integration with a hyper-heuristic framework further amplifies its performance, setting a new benchmark for future research.
Energy-absorbing structures operate under impact and dissipate kinetic energy through material failure and structural collapse. One inherent challenge for the topology design of such structures is to solve impact problems and derive sensitivity, which are often associated with a formidable nonlinearity. To remedy this problem, this article views the problem as finding a material configuration that maximizes the specific energy absorption while satisfying both force and deformation constraints, and proposes a decoupling strategy that solves the optimization problem in a nested loop, where the outer loop performs dynamic analysis to evaluate structural performance and ensure the feasibility of the solution, while the inner loop solves the topology optimization problem with the stiffness as the design objective. After the validity of the method had been confirmed by a standard two-dimensional example, it was extended by considering the constant cross-section manufacturing constraints and plastic hinge effects pertaining to thin-walled structures.
Conjugate Gradient (CG) methods have gained more traction for several classes of problem owing to their characteristics such as low memory requirements and simple implementation. It is well known that two characteristics that define CG methods are step-length alpha((k)) and search direction d((k)) (which has in its formulation a beta((k)) parameter-a crucial component of CG methods) and yet, on the other hand, most researchers of CG methods focus only on developing the beta((k)) term with little concern given to innovation on the alpha((k)) front. Thus, they mainly adopt classical monotone Line Search (LS), which has been shown to creep in for problems with a curved narrow valley. To mitigate some of these shortcomings, this article introduces a non-monotone LS approach that is computationally efficient. Thus, it is suitable for large-scale problems. Moreover, two variants of CG directions based on the Hestenes-Stiefel (HSCG) method are coined by incorporating a newly formulated diagonal-based Barzilai-Borwein (BB) spectral method. The diagonal-based BB approach may capture more information about the curvature of the objective function. Consequently, two new non-monotone CG methods are introduced and, under some mild assumptions, the methods are shown to have sufficient descent property and be globally convergent. Moreover, the convergence rate and complexity of the methods is analysed and is shown to achieve O(log(1/epsilon)) iteration complexity for functions satisfying the Polyak-Lojasiewicz condition. Finally, the applicability of the methods is investigated by solving a data-driven model on real-world datasets and signal processing problems.
This study tackles a complex parallel machine scheduling problem with unrelated machines, sequence-dependent setup times and total weighted tardiness minimization. To address the scalability and expertise limitations of exact and heuristic methods, the prompt-tuned large language model (LLM) application for intelligent dispatching (PLAID) is proposed as a framework that uses fine-tuned large language models to make sequential dispatching decisions. PLAID consists of three stages: generating training data with constraint programming, supervised fine-tuning and dispatching based on learned rules. Experiments on diverse instance sizes show that PLAID achieves competitive performance relative to dispatching rules, metaheuristics and exact approaches, while remaining robust and interpretable. Fine-tuned models such as GPT-4.1-Tuned and GPT-4.1-Nano-Tuned consistently reduce total weighted tardiness, demonstrating the benefit of domain-specific adaptation. Overall, PLAID provides both scalability and transparency, positioning fine-tuned LLMs as practical, human-centric tools for complex manufacturing scheduling.
Post-optimality analysis in linear programming is done through either the stability of the optimal solution (discrete decision variables) or the stability of a given optimal basis with respect to perturbations of the input data (continuous decision variables). Both approaches have been well studied in the literature. In this article, a post-optimality analysis technique is presented that is more general than the tolerance approach and less computationally expensive. Namely, this article extends the notion of local quasi-stability radii in order to allow perturbations into the input data. The present result is applied to ore production problems. As the input data might be of different magnitude, the advantage of this extension is to incorporate information provided by the decision maker into the computation of the local quasi-stability radii. Then, better individual tolerances of the input data of linear multi-objective optimization problems are obtained. The extension is based on the introduction of weighted norms in the formulation of the post-optimality analysis. The weighted norms account for the information provided by the decision maker.
This study proposes a graph edge-attention network (GEAN) to include the topological features and physical information of structures using a graphic representation in the model training process. Unlike conventional graph attention network-based models, which compute message-passing weights solely from node features, GEAN introduces an edge-attention mechanism to jointly model structural node and edge features. The message-passing weights are determined based on stiffness information of structures, enabling the model to capture the influence of element stiffness on force transmission and enhancing physical interpretability. Three numerical examples with different dimensions are used to evaluate the performance of the proposed method. The results demonstrate that GEAN achieves significantly competitive prediction results compared to traditional surrogate and graph neural network-based models. As the dimensionality of the problems increases, GEAN with affordable samples consistently keeps the prediction error around 3%, far smaller than that of the other surrogate-based approaches.
Globalized closed-loop supply chains (CLSC) struggle to balance economic efficiency and delivery reliability under uncertainty. Existing research often prioritizes speed over quantity reliability and cannot effectively model capacity uncertainty with partial distribution information. A new distributionally robust optimization (DRO) model for CLSC network design is proposed, featuring simultaneous optimization of upper-level total profit and lower-level on-time delivery, distributionally robust chance constraints with sub-Gaussian ambiguity sets to handle facility capacity uncertainty strictly, providing probabilistic feasibility guarantees, and an accelerated Benders decomposition algorithm for large-scale mixed integer linear programming. Applied to Ontario's mobile phone industry, the model achieves CAD 92.55 million profit and 97.16% on-time delivery under 5% capacity fluctuation. It incurs only 1.6% cost loss versus deterministic models while preventing capacity violations at five facilities. It shows superior robustness to sample average approximation (SAA), maintaining a 2% constraint violation probability across sample sizes.
The distributed permutation flowshop scheduling problem with sequence-dependent set-up times is investigated in this article by minimizing the total flowtime and the total weighted earliness and tardiness from the due window. To solve this problem, first, a novel constructive heuristic is proposed, in which a new rule based on the earliness and tardiness weight values is proposed by exploring the odds and evens of a sequence. Secondly, an effective iterative greedy algorithm based on accelerated judgement strategy (EIGAJS) is presented. To boost the ability of EIGAJS to explore the solution space, an efficient referenced local search is developed, in which the enhanced idle time insertion method and the accelerated judgement strategy are designed to reduce the invalid insertion. Finally, compared with five other algorithms, the results show that the EIGAJS algorithm has good performance.
