Search Results (419)

This paper proposes a power-based optimization procedure to identify the optimal number and vertical placement of buckling restrained brace (BRB) outrigger systems for enhancing the seismic performance of core-wall-dominated benchmark model. The proposed method is validated using a nine-zone numerical model subjected to nonlinear time-history analysis implemented in MATLAB R2025.a (25.1.0.2943329). The optimization variables include the number and locations of outriggers as well as the stiffness of the BRBs, while the objective function is defined as the minimization of the maximum inter-story drift response. Outriggers are installed between zones 2 and 9, with each zone subdivided into five potential outrigger levels located 150 mm above the floor level, resulting in 40 potential outrigger placement scenarios. The total number of outriggers is constrained to range from one to eight, with at most one outrigger allowed per zone. Optimal outrigger–BRB configurations are identified by incrementally distributing BRB stiffness at the perimeter column-outrigger connection regions using a power-based allocation strategy. At each optimization step, the proposed framework evaluates only one candidate configuration per eligible story and outrigger level, resulting in several nonlinear time-history analysis grows linearly with the number of candidate locations. This contrasts with the combinatorial growth in computational demand typically associated with exhaustive or evolutionary optimization methods and leads to a significant reduction in overall computational efforts. Full article

The Traveling Salesman Problem (TSP) is a fundamental challenge in combinatorial optimization, with wide-ranging applications in logistics, manufacturing, and network design. In addition to the classical formulation, recent years have witnessed the emergence of complex variants, such as the TSP with Drones (TSP-D), TSP with Time Windows, and Prize-Collecting TSP, that incorporate novel constraints reflecting real-world requirements like last-mile delivery and multimodal logistics. This review presents a comprehensive survey of metaheuristic approaches for solving both the classical TSP and its emerging extensions, with particular emphasis on metaheuristic, hybrid methods, and machine learning-enhanced strategies. Recent algorithmic developments, benchmark datasets, and evaluation metrics are investigated, and critical challenges in addressing drone coordination, synchronization, and uncertainty are identified, as well. Bibliometric analysis is further provided to map research trends and the evolution of the field. By synthesizing foundational techniques and state-of-the-art innovations, this review outlines current progress and proposes future directions for metaheuristic optimization in increasingly dynamic and heterogeneous routing scenarios. Full article

Nature-inspired metaheuristic algorithms are commonly applied to complex combinatorial optimization problems where exact methods are computationally impractical. Tourist route optimization is a representative multi-objective problem characterized by realistic constraints such as travel time, cost, opening hours, and transportation modes. Although Mushroom Reproduction Optimization is computationally efficient, it often experiences premature convergence in complex search spaces. This paper proposes a novel hybrid algorithm, Mushroom–Weed Hybrid Reproduction Optimization (MWHRO), which integrates the colony-based local search of the Mushroom Reproduction algorithm with the fitness-proportional reproduction and competitive elimination mechanisms of Invasive Weed Optimization. Hybridization enhances population diversity and global exploration while preserving fast convergence. The proposed algorithm is evaluated based on a realistic tourist route optimization problem using real-world data from Zagreb, Croatia, across multiple transportation modes and objective-weight scenarios. Performance is compared against Ant Colony Optimization, Invasive Weed Optimization, Particle Swarm Optimization, and standard Mushroom Reproduction Optimization under equal evaluation budgets. Experimental results demonstrate that the proposed MWHRO algorithm consistently achieves high-quality solutions with significantly lower execution times, particularly in constrained and multimodal scenarios. Statistical analysis confirms the robustness and practical suitability of the proposed approach for real-world route optimization. Full article

Although DNA-based data storage theoretically provides an information density of 2 bits per nucleotide, biochemical constraints transform sequence design into a high-dimensional constrained combinatorial optimization problem. The high computational cost and low encoding efficiency of conventional rule-based approaches make metaheuristic methods an effective alternative. This study proposes the TC-HUR hybrid algorithm to simultaneously optimize information density and conflicting biophysical constraints, including homopolymer (HP) length, GC content, melting temperature ($T_m$), and reverse-complement (RC) similarity. The method escapes local optima using Cauchy jump-enhanced Hunger Games Search (HGS), performs high-precision exploitation via Runge–Kutta (RUN) operators, and refines constraint violations at the nucleotide level through an adaptive intensive mutation mechanism. The algorithm is evaluated on a complex dataset of 1853 nucleotides under different noise regimes. TC-HUR outperforms RUN by 2.5% and HGS by 16.7% in average fitness. While maintaining homopolymer length near the ideal threshold, it reduces reverse-complement similarity to 19.10%, ensuring high sequence diversity. Under high-noise conditions, TC-HUR achieves a normalized edit distance of 0.1290, reducing insertion–deletion (indel) errors by approximately 14%. The results demonstrate that the proposed model effectively generates biophysically synthesizable and noise-resilient DNA codes. Full article

The blending process in raw material yards is essential for maintaining precise material proportions in downstream production, directly influencing product quality and energy efficiency in industries such as steel and coal processing. However, stringent operational constraints, including silo capacity limits, discharge rates, equipment movement delays, and a strict no-empty-silo requirement, result in a strongly coupled, high-dimensional combinatorial scheduling problem. In this paper, we develop a mixed-integer nonlinear programming (MINLP) model to capture the complex dynamics of silo weight and equipment operations. The primary scientific contribution of this work lies in the theoretical discovery of a structural decoupling property within the complex MINLP. We analytically prove that by fixing the replenishment sequence, the intractable global problem can be rigorously decomposed into two subproblems: a linear programming (LP) problem for silo-filling cart scheduling and a shortest-path problem solvable via dynamic programming (DP) for reclaimer scheduling. Leveraging this decomposition, a two-stage metaheuristic algorithm is proposed, combining greedy initialization with multi-round simulated annealing enhanced by local search. Experimental validation using real industrial data demonstrates that the proposed method consistently outperforms the greedy algorithm. Crucially, while the commercial solver Gurobi struggles to converge within a practical 1800 s time limit, our approach yields comparable solution quality in mere seconds. Furthermore, robustness analysis under a 20% demand surge confirms the algorithm’s adaptive capability, maintaining the silo weight stability through re-optimization. This research provides a robust, computationally efficient solution for the blending process in raw material yards. Full article

Quantum optimization has recently drawn considerable attention as one of the possible applications of noisy intermediate-scale quantum computation, yet the problem of qubit requirement remains a major bottleneck when combinatorial optimization problems are converted into quantum circuits. This issue becomes especially critical in solving the capacitated vehicle routing problem (CVRP) with the quantum approximate optimization algorithm (QAOA), since the number of required qubits increases polynomially with respect to the number of nodes. This study investigates whether a heuristic divide-and-conquer strategy can be adapted to the quantum setting so as to improve qubit efficiency while preserving the optimization capability to a reasonable extent. The proposed method decomposes a single CVRP into multiple traveling salesman problems (TSPs) by the sweeping-based clustering method, searches for the sector configuration with the smallest angle sum by Grover’s search algorithm, and then solves each sector-wise TSP with the QAOA aided by the gravitational search algorithm. Experiments on five benchmark datasets show that the proposed approach attains feasible solutions within 3.4 to 12.7% of the reinforcement-learning baseline on the main test set. These results suggest that the proposed approach serves as a plausible quantum heuristic framework for constrained routing optimization, with the advantage of reducing the qubit burden by decomposing the original problem into smaller subproblems. Full article

The Traveling Salesman Problem (TSP) remains a central benchmark in combinatorial optimization, with applications in logistics, manufacturing, and network design. While exact solvers and classical heuristics offer strong performance, they rely on handcrafted design and show limited adaptability. Recent advances in deep learning have introduced a new paradigm: learning heuristics directly from data, with Transformers standing out for capturing global dependencies and scaling effectively via parallelism. This survey offers a component-wise analysis of Transformer-based TSP models, serving as both a structured review and a tutorial for new researchers. We classify solution paradigms—including constructive autoregressive and non-autoregressive models, local-search refinement, and hyperheuristics—and examine state representations, architectural variants (pointer networks, efficient attention, hierarchical or dual-aspect designs), and resolution strategies such as decoding heuristics and integrations with classical refiners. We also highlight hybrid models combining Transformers with CNNs, GNNs, or hierarchical decomposition, alongside training methods spanning supervised imitation and reinforcement learning. By organizing the literature around these building blocks, we clarify where Transformers excel, where classical heuristics remain essential, and how hybridization can bridge the gap. Our goal is to provide a critical roadmap and tutorial-style reference connecting classical optimization with modern Transformer-based methods. Full article

Background: Combinatorial optimization problems (COPs) are central to Logistics and Supply Chain decision making, yet their NP-hardness prevents exact optimal solutions in reasonable time. Methods: This work addresses that limitation by developing a novel ternary network flow linear programming (LP) model of the assignment problem (AP) polytope. The model is very large scale (with $\mathsf{\Theta }\left(m^9\right)$ variables and $\mathsf{\Theta }\left(m^8\right)$ constraints, where m is the number of assignments). Although not intended to compete with conventional two-dimensional formulations of the AP with respect to solution procedures, it enables hard COPs to be solved exactly as “strict” (integrality requirements-free) LPs through simple transformations of their cost functions. Illustrations are given for the quadratic assignment problem (QAP) and the traveling salesman problem (TSP). Results: Because the proposed LP model is polynomial-sized and there exist polynomial-time algorithms for solving LPs, it affirms “$P=NP$.” A separable substructure of the model shows promise for practical-scale instances due to its suitability for large-scale optimization techniques such as Dantzig–Wolfe Decomposition, Column Generation, and Lagrangian Relaxation. The formulation also has greater robustness relative to standard network flow models. Conclusions: Overall, the approach provides a systematic, modeling-barrier-free framework for representing NP-complete problems as polynomial-sized LPs, with clear theoretical interest and practical potential for medium to large-scale Logistics and other COP-intensive applications. Full article

We introduce cumulative tic-tac-toe, a novel variant of the classic $3\times 3$ tic-tac-toe game in which play continues until the board is completely filled. Each player’s final score is determined by the total number of three-in-a-row sequences they form. Using combinatorial game theory (CGT), we establish that under optimal play, the game is a draw, and we characterize its theoretical properties. To empirically validate and optimize practical play, we develop a reinforcement learning (RL) framework based on temporal-difference (TD) learning, which is enhanced with a domain-informed evaluation function to accelerate convergence. The experimental results show that our triplet-coverage difference (TCD) evaluation function reduces the average number of training episodes by approximately 23.1% compared with a random-initialization baseline, a statistically significant improvement at the 5% significance level. These results demonstrate the efficiency of our CGT–RL approach for cumulative tic-tac-toe and suggest that similar methods may be useful for analyzing related combinatorial games. We also discuss potential analogies in domains such as competitive resource allocation and coalition formation, illustrating how cumulative-scoring games connect abstract game-theoretic ideas to practical sequential decision problems. Full article

Addressing prevalent challenges in current cooperative task assignment methods for cross-domain unmanned swarm, such as the disconnection between decision-making and execution processes, and the inadequate incorporation of platform kinematic constraints, this study introduces an integrated decision-control cooperative task assignment approach based on a bi-level optimization framework. The proposed framework formulates a bi-level programming model that tightly couples upper-level task assignment with lower-level optimal control. The upper-level model aims to minimize the maximum task completion time by optimizing the assignment and visitation sequences of diverse target types across heterogeneous unmanned platforms. The lower-level model, given the task sequences from the upper level, addresses a minimum-time optimal control problem based on a comprehensive nonlinear kinematic model. This approach enables precise computation of task execution times, which are subsequently fed back to the decision-making layer, thereby establishing a closed-loop optimization mechanism. To solve this complex model efficiently, the lower-level employs differential flatness transformation to eliminate trigonometric functions in the kinematic equations and discretizes the continuous-time optimal control problem into a nonlinear programming problem via the Radau pseudospectral method. For the upper-level combinatorial optimization, an improved genetic algorithm is developed, integrating hybrid encoding, dual-archive elitism preservation, adaptive crossover and mutation strategies, and periodic local search. Simulation results demonstrate that, compared with traditional Euclidean-distance-based assignment methods, the proposed approach generates kinematically feasible and smooth trajectories while thoroughly accounting for the kinematic constraints of heterogeneous platforms, thereby demonstrating its effectiveness and superiority in improving the comprehensive mission performance of cross-domain unmanned swarms. Full article

Column generation is a fundamental technique for solving large-scale combinatorial optimization problems such as unit commitment and vehicle routing, yet its performance is often limited by dual oscillation. This study explores the intrinsic cause of this phenomenon from the perspective of shadow price theory and demonstrates that dual oscillation arises from the lack of marginal interpretability of Lagrange multipliers when multiple dual solutions coexist. To address this issue, an improved column generation framework is proposed in which traditional multipliers are replaced with minimum-norm multipliers that possess clear economic meaning and act as directional shadow prices. A generalized pricing subproblem is formulated, and partial minimum-norm multipliers are obtained through convex quadratic optimization to guide column generation. Numerical experiments on a simplified single-period unit commitment case and large-scale cutting stock problems showed that the proposed approach eliminated invalid column generation and achieved speedy convergence to the optimal solution within only two iterations for the unit commitment case, and the classical column generation exhibited slow convergence with dual oscillation in large-scale scenarios while the improved algorithm achieved fast and stable convergence. The results indicate that the stabilization method enhances the consistency of dual variables and provides a more robust foundation for the theoretical and practical development of column generation algorithms. Full article

Vitamin D is widely recognized for its pivotal role in the prevention and treatment of various cancers. The active compounds derived from plants have garnered significant attention due to their multi-faceted anticancer properties. Given the complexity and heterogeneity of cancer, monotherapies often fall short in effectiveness. As a result, combinatorial pharmacological strategies, which utilize multiple drug agents, are increasingly being employed globally. Notably, emerging evidence highlights the potent synergistic anticancer effects of vitamin D in combination with certain phytochemicals against a variety of cancers. This review explores the cooperative mechanisms through which vitamin D and phytochemicals enhance cancer prevention and therapy. In addition to examining their synergistic effects, this review also discusses recent advancements in nanotechnology-based delivery systems for vitamin D, which hold promise for optimizing its therapeutic potential. Collectively, these findings underscore the potential of combining vitamin D with phytochemicals and innovative delivery methods as a promising strategy in the fight against cancer, paving the way for more effective, multi-targeted therapeutic approaches. Full article

The Set Covering Problem is a fundamental NP-hard problem in combinatorial optimization and plays a central role in a wide range of industrial decision-making processes, including logistics planning, scheduling, facility location, network design, and resource allocation. In many real-world contexts, problems of this type are large in scale and highly constrained, which makes exact solution methods computationally impractical and encourages the use of metaheuristic approaches capable of producing high-quality solutions within limited time budgets. In this work, we propose a discrete adaptation of the Dream Optimization Algorithm, focusing on the challenges that emerge when algorithms originally designed for continuous search spaces are applied to binary and strongly constrained models. The continuous search process is mapped onto the binary decision space through a fixed discretization scheme. As a consequence of this transformation, some constraints may not be met, underscoring the importance of effective feasibility restoration mechanisms. Because the discretization stage may produce infeasible solutions and frequently induces plateaus that hinder further improvement, an explicit repair phase becomes necessary to restore feasibility and promote effective search progression. To strengthen this process, the study introduces an adaptive control mechanism based on bandit driven operator selection, which dynamically chooses among different repair procedures during the search. Experimental results on benchmark instances show that the proposed approach consistently achieves high quality solutions with low relative deviation from known optima and stable behavior across independent runs. Full article

This paper addresses the Distance-Constrained Inventory Routing Problem (DCIRP), a complex problem that combines inventory management and vehicle routing in a logistics context. The problem arises in the context of a specialty gas delivery company that maintains a specialty gas holding facility at each customer’s site and uses several trucks to deliver specialty gas, with the additional constraint that drivers are limited to the number of kilometers they can drive each day. A Mixed Integer Linear Programming (MILP) formulation is proposed to model the DCIRP. The DCIRP is a variant of the Inventory Routing Problem (IRP), and an NP-hard combinatorial optimization problem. The main objective of this research is to improve the efficiency and effectiveness of DCIRP resolution, while accounting for vehicle capacity constraints, customer inventory levels, and delivery route distance constraints. By optimizing routes and inventory management, the company’s operations become more sustainable. To solve the problem, three solution approaches are proposed. The first is an exact method based on the MILP formulation. The second is a matheuristic that uses an inventory-first, route-second (IFRS) approach, including a minimum route cost approximation and a local search procedure. The results show that the proposed matheuristic produces high-quality solutions with a reasonable computational effort. Full article

Motor starter calibration requires long-distance rotation of a setting cam to locate current graduation points, generating substantial non-value-added mechanical travel time on production lines. This paper proposes a cam pre-adjustment angle prediction method that integrates a phenomenological gray-box bimetallic model with a hierarchical combinatorial algorithm framework. A generalized lumped-parameter model incorporating heat dissipation correction and mechanical gap compensation is constructed to describe the electrothermal–mechanical coupling of the bimetallic strip. An improved fuzzy C-means (IFCM) algorithm addresses the cold-start problem for new material batches, and an adaptive particle swarm optimization (APSO) algorithm performs online parameter identification. To handle the process asymmetry arising from the unidirectional cam rotation mechanism, an optimized gray wolf optimizer with one-sided error control (GWO-OSE) based on an asymmetric loss function is employed to inversely determine the optimal pre-adjustment angle while actively suppressing over-prediction. Validation on 1200 production line samples across three material batches demonstrates an over-prediction rate of only 2.8%, a mean absolute angle prediction error of 23.9°, a reduction in single-product calibration time of approximately 12 s, and an improvement in overall production line efficiency of 24.5%. This efficiency gain results from the process-level redesign facilitated by the pre-adjustment strategy rather than from minimizing absolute prediction error, and the proposed method provides an engineering-applicable optimization strategy for reducing non-value-added calibration time in motor starter production lines. Full article