This paper addresses the minimum linear arrangement problem, a classical graph layout problem in which the objective is to minimize the sum of absolute differences between the labels assigned to adjacent vertices in undirected graphs. The paper introduces small boundary (SB(k)), a family of linear-time greedy heuristics that guide vertex labeling through a prioritization scheme based on the structure of labeled and k levels of unlabeled vertex neighborhoods. An extensive experimental evaluation on 26 large-scale real-world graphs demonstrates that the proposed heuristic with k=2 consistently outperforms 19 established low-cost graph-theoretic reordering algorithms, including the leading constructive method used within a high-performing metaheuristic algorithm for the problem. Additionally, the SB(2) heuristic outperforms this high-performing metaheuristic algorithm while requiring up to 800 times less computational effort. The paper further shows that integrating SB(2) as the initialization procedure within this metaheuristic yields improved solution quality, highlighting its effectiveness as both a standalone heuristic and a high-quality initializer. Overall, the proposed approach provides a fast, scalable, and practical solution for tackling MinLA on large-scale graphs.
We address the problem of achieving convergence and diversity in many-objective problems, focusing on continuous and unconstrained functions. It is known that with increasing numbers of objectives (say from 4 to 20) even modern many-objective Evolutionary Algorithms (EAs) may struggle to converge to, and fully distribute across the Pareto front. This paper presents a general and modular hybrid approach that integrates local search into reference-vector-based Many-Objective Evolutionary Algorithms (MaOEAs), addressing issues such as weakened selection pressure and the increasing complexity of exploring high-dimensional objective spaces. The hybrid approach employs Sequential Quadratic Programming (SQP) guided by achievement scalarizing directions, derived from either the Weighted Achievement Scalarizing Function (W-ASF) or the Penalty-based Boundary Intersection (PBI) schemes, depending on the decomposition strategy of the underlying MaOEA. It is designed to be broadly applicable with limited parameter tuning, facilitating integration with algorithms from the NSGA-III and MOEA-DD families. The effectiveness of the proposed approach is demonstrated through extensive experiments on standard continuous-variable many-objective benchmark problems as well as on representative real-world case studies. Results show that integrating local search significantly enhances performance, while a principled method for setting hybrid parameters ensures robustness and reproducibility. Although limited to an empirical study over a (large) test function suite, these findings highlight the potential of combining mathematical programming techniques with evolutionary algorithms for high-dimensional many-objective optimization problems.
This paper introduces and solves the mixed fleet optimization problem with electric and fuel vehicles for distribution planning, when periodically repeating a given set of routes. This integrated problem determines fleet sizing and scheduling with the objective of minimizing the total cost of fleet, transportation, energy, carbon emissions, and inventory. We use comprehensive calculations of energy consumption and carbon emissions and formulate the mixed fleet optimization problem as a non-linear mixed integer program. Subsequently, analytical results for optimal route cycle time and vehicle type and insights on their effect on scheduling are derived. These findings inform our development of novel scheduling strategies within a powerful multi-start solution framework that effectively links cycle time adjustment and vehicle type optimization. Computational experiments demonstrate the strong performance of our approach and yield valuable insights into the complex cost trade-offs involved. Finally, we evaluate the economic benefits of adopting a m3ixed fleet and investigate the influence of various factors on overall performance.
This paper presents a hybrid metaheuristic framework for portfolio optimization with cardinality constraints, a computationally challenging problem in constrained asset allocation. The model minimizes downside risk relative to a predefined target return while incorporating realistic investment restrictions such as allocation bounds and a maximum number of selected assets. The proposed method integrates Simulated Annealing (SA) and Tabu Search (TS) within a coordinated hybrid optimization framework for mixed continuous–discrete portfolio optimization. SA performs stochastic exploration over continuous portfolio weights, while TS refines the discrete asset-selection layer through add–drop–swap neighborhood moves supported by tabu-based memory structures. The algorithm iteratively enforces feasibility, diversification, and local intensification through projection and neighborhood refinement procedures. A comprehensive computational analysis is conducted using historical data from the S P 500 index over the period 2020–2024, including sensitivity analysis with respect to portfolio cardinality, comparative evaluation against DE, PSO, and GA metaheuristics, validation against exact mixed-integer programming benchmarks, statistical robustness analysis, and out-of-sample testing under high-volatility market conditions. The computational results indicate that the proposed SA–TS framework provides a robust and computationally effective approach for downside-risk portfolio optimization under cardinality constraints.
The cumulative capacitated vehicle routing problem (CCVRP), which is widely implemented in humanitarian relief and emergency supply scenarios, aims to minimize the total cumulative customer arrival time. This paper investigates a new variant of CCVRP, namely the multi-depot cumulative capacitated vehicle routing problem with prioritized customers (MDCCVRP-Pr), where each customer has a specific priority. A mathematical model is formulated to minimize the sum of total customers arrival times and penalty costs from priority violations. A local search-based heuristic (LS-AM) with an adaptive mechanism is developed under the framework of iterated local search, adopting an adaptive parameter to dynamically determine the execution of exploitation and exploration procedures. The algorithm integrates variable neighborhood descent, dynamic perturbation and multi-depot adjustment strategies, and a parameter adaptively updating mechanism. Computational results demonstrate that the proposed adaptive mechanism is effective, and the proposed algorithm is highly competitive in obtaining high-quality solutions compared with existing approaches.
This study presents a competitive algorithm in which the particle swarm optimization algorithm is combined with a simulated annealing procedure and a Lin-Kernighan-Helsgaun heuristic to provide high-quality solutions to the clustered orienteering problem. In this problem, the customers are grouped into clusters, each of which is associated with a profit, and this profit is collected if and only if all the customers in the cluster are served. A single vehicle is available to visit the customers, and each customer can belong to multiple clusters. The goal is to maximize the total collected profit within a maximum limit on the travel time. This study proposes the first swarm-based algorithm with certain innovations to deal with the clustered orienteering problem, which is an NP-hard problem. The salient features of the proposed algorithm are a ‘partial move’ strategy with a new equation for calculating the next position of a particle, periodic restarting of particles, and a mutation operator to increase the search diversification. The experimental results show that the proposed algorithm is competitive with the state-of-the-art algorithms from the literature. The proposed algorithm achieved the best result on one of the 924 less challenging benchmark instances and on 18 of the 72 highly challenging instances. Moreover, it consistently outperformed all methods in the literature except for the evolutionary algorithm (EA), with no statistically significant difference observed between EA and the proposed algorithm. Nevertheless, the proposed algorithm outperformed EA on the challenging benchmark instances at a confidence level of 91
In this paper, we address the integrated Berth Allocation Problem (BAP) and Quay Crane Assignment Problem (QCAP) with ship-to-ship (STS) transshipment integral operations, namely BACAP-STS, a complex optimization challenge in container terminal operations. We formulate the BACAP-STS as a bi-objective mathematical model that simultaneously minimizes (1) total ship dwell time and delay penalties, and (2) the total number of quay cranes (QC) assigned. To solve this NP-hard problem, we develop an adapted version of the Non-Dominated Sorting Genetic Algorithm III (NSGA-III), comprising a problem-specific repair mechanism for constraint handling, tailored chromosome encoding for mixed continuous and binary variables, and adapted operators. The algorithm’s performance is evaluated using real-world data from the Port of Le Havre, and we implemented baseline versions of Simulated Annealing (SA) and Tabu Search (TS) following established protocols for a fair comparison under identical experimental conditions. Results demonstrate that our adapted NSGA-III outperforms the benchmark methods in terms of feasibility rate, error metrics (Mean Squared Error (MSE), Root Mean Squared Error (RMSE)), and Pareto front quality (Hypervolume (HV)). Solution quality is further evaluated using the Generational Distance (GD) metric to quantify the proximity of the obtained Pareto fronts to the reference front. Finally, the proposed approach provides port operators with a practical decision-support tool for balancing service efficiency with resource utilization in transshipment operations.
The use of unmanned aerial vehicles (UAVs) for transmission tower inspection has gained increasing attention given their potential to enhance operational efficiency, reduce costs, and improve safety. This paper explores a novel UAV location-routing problem that arises in transmission tower inspection. Specifically, the problem involves determining the station locations, UAV routes between transmission towers, and inspection paths around each transmission tower. We first propose a mixed-integer linear programming model to formulate this problem. As the problem is computationally challenging, we introduce a hybrid evolutionary algorithm based on a memetic computing framework. The proposed algorithm includes a pre-processing procedure to accelerate search efficiency, an inherit-repair crossover operator to generate high-quality offspring solutions, a mixed tabu strategy for intensified local improvement, and a quality-and-distance-based population updating mechanism to preserve solution diversity. Extensive computational experiments based on 70 real-world instances demonstrate the effectiveness of the proposed algorithm. The results show that our algorithm exhibits competitive performance against an exact solver on small instances, and it significantly outperforms other algorithms being compared on large instances. These findings provide a valuable benchmark for future research on UAV-based infrastructure inspection optimization.
Community healthcare has become a considerable portion of a country’s economy due to its significant impact. One of the most important fields in community healthcare is the delivery of emergency medical services (EMS), which are provided to patients outside the hospital before their transfer to the nearest medical center. There is an increasing need to deliver the most effective care to individuals using limited resources. In this context, optimization methods have been successfully applied to manage various problems in healthcare environments. However, there are a limited number of research papers that consider community EMS as an optimization problem. To address this gap, this paper considers the staff scheduling problem in the Community EMS (SSP-CEMS) field, which is modeled as the vehicle routing problem with time windows (VRP-TW). Therefore, a self-learning genetic algorithm (SLGA) is proposed based on reinforcement learning. This strategy is used to automatically update the GA parameters to detect the next promising search direction. Then, computational experiments are performed using Solomon’s benchmark instances. The obtained results demonstrate the competitive performance of the proposed SLGA relative to the classical GA across standard VRP-TW benchmarks, supporting its potential applicability to community EMS scheduling contexts.
We study the Job Shop Scheduling Problem with machine Availability Constraints (JSSP-AC) within a quantum-annealing framework. Using a dummy-job transformation, both fixed and variable machine unavailability periods are incorporated into a standard time-indexed quadratic unconstrained binary optimization (QUBO) model. We then introduce a constructive heuristic ℋ , its preemptive variant ℋ^* , and three annealing-based methods: ℳ_1 , based on a naive time horizon; ℳ_2 , using the tighter bound returned by ℋ ; and ℳ_3 , which additionally uses the heuristic solution as a warm start in a reverse-annealing setting. A proof-of-concept experiment on D-Wave hardware confirms that the proposed formulation can be embedded and solved on small instances. On a broader benchmark, ℋ outperforms repaired dispatching heuristics, while the tighter horizon reduces QUBO size by 29.9 ℳ_1 to 5.0 ℳ_2 and 3.3 ℳ_3 , highlighting the value of classical bounds and warm starts in quantum annealing for scheduling under machine unavailability.
The Positive Influence Dominating Set Problem (PIDS) is a variant of the well-known Dominating Set Problem. It involves selecting a subset of vertices that positively dominate the remaining vertices in a given graph G=(V,E) . More formally, a vertex v_i ∈ V is said to be positively dominated if at least a portion of ρ deg_G(v_i) of its neighbors belongs to the selected set, where deg_G(v_i) is the degree of v_i , and 0<ρ <1 is the influence factor. The objective is to identify the smallest subset of positive influence dominants. This problem is NP-hard on general graphs and remains computationally challenging even for particular classes of graphs. In this paper, we propose an efficient algorithm for solving PIDS, based on the Local Branching approach combined with the CPLEX mathematical programming solver, especially to enhance intensification and provide a good partial solution. Also, to ensure solution diversification, we develop a destructive-reconstructive greedy heuristic to explore previously unvisited subspaces. We conduct extensive experiments to evaluate our method on real-world benchmark instances of varying sizes, including large-scale graphs, and compare it with five existing state-of-the-art solving approaches. The experimental results demonstrate that the proposed approach yields high-quality solutions within reasonable computational times, highlighting its performance for efficiently solving PIDS.
Green scheduling systems are attracting increasing attention due to their environmental impacts. This paper addresses the Green Flexible Job-Shop Scheduling Problem with variable processing speeds, aiming to minimize both the makespan and total energy consumption. To solve this problem, we propose a self-learning Variable Neighborhood Search with Q-learning (SL_VNS) algorithm, which integrates three key mechanisms: (1) four initialization strategies designed to generate high-quality initial solutions; (2) A parameter adaptation strategy based on reinforcement learning to select optimal parameters dynamically; and (3) an elite archive to save historical solutions for improved performance. Computational experiments demonstrate that the proposed algorithm is more effective and robust compared to other algorithms.
This paper introduces an extended version of the min-Knapsack Problem with Compactness Constraints (mKPC), referred to as the min-Knapsack Problem with Compactness Constraints and Penalty Values (mKPCP). In this extension, penalty values are assigned to specific items that incur additional cost when excluded from the knapsack. Alongside the cost, weight, and compactness constraints of the original mKPC, which enforce proximity among selected items, the mKPCP integrates these penalties as soft constraints to reflect the importance of certain items. To solve the mKPCP, we propose a matheuristic method that combines the learning mechanism of the Fixed Set Search (FSS) metaheuristic with integer programming (IP) to improve partial solutions throughout the search process. A greedy randomized algorithm is employed to generate the initial population, promoting both diversity and solution quality. New instances are generated to evaluate the performance of the proposed method on the mKPCP. In addition, the method is tested on the mKPC and compared with existing mixed-integer programming (MIP) based techniques, such as compact MIP and branch-and-cut algorithms. Experimental results demonstrate that the proposed approach yields competitive performance across a wide range of instances. Furthermore, the method is problem-independent in nature and can be adapted to other binary optimization problems, such as the minimum vertex cover and facility location problems, with very little modifications.
This paper introduces a metaheuristic approach for solving the Maximum Disjoint Dominating Sets Problem (MDDSP). The problem is initially addressed using a Greedy Randomized Adaptive Search Procedure (GRASP), which incorporates two distinct local search strategies. The first employs a standard swap neighborhood, while the second utilizes a novel neighborhood structure designed to complement and enhance the effectiveness of the swap-based approach. To further improve performance, the GRASP is extended into the Fixed Set Search (FSS) metaheuristic, which integrates a learning mechanism to guide the search process. Computational experiments are conducted on various graph types, including random, Watts–Strogatz, and Barabási–Albert graphs, with up to 1,000 vertices and differing densities. The results show that the FSS significantly outperforms state-of-the-art methods, such as the multi-constructor Construct, Merge, Solve, and Adapt (CMSA) algorithm, delivering superior solution quality across nearly all test instances. The enhanced local search techniques proved particularly effective on dense graphs. Furthermore, the results confirm that the FSS consistently improves the performance of the underlying GRASP, highlighting its robustness and efficiency for solving the MDDSP.
Support Vector Machines (SVM) have been widely used in supervised learning due to their strong generalization capabilities. SVM + extends this framework under the Learning Using Privileged Information (LUPI) paradigm, incorporating additional training-stage information unavailable during inference. However, SVM + involves the tuning of four hyperparameters, doubling the dimensionality of the optimization problem compared to standard SVM, and thereby increasing computational cost substantially. To address this challenge, this work introduces GAGS (Genetic Algorithm-Based Grid Search), a methodological hybridization framework tailored for SVM + model selection that integrates grid-based structured search, adaptive precision through logarithmic mapping, and advanced parallelization strategies. The term 'Grid Search' in GAGS refers to the grid-based structural partitioning used for initial exploration and parallel computation, and not to a traditional exhaustive search. By distributing computations across independent processing units, GAGS enables structured exploration of the hyperparameter space and reduces the likelihood of premature convergence and local optima entrapment, while substantially reducing execution time under the evaluated settings. The proposed GAGS-SVM + framework is evaluated on a binary classification task using the MNIST and CWRU datasets under a rigorous protocol of 20 independent runs. Experimental results show that the GAGS methodology achieves statistically higher mean accuracy than the tested baselines under a fixed evaluation budget, reducing error rates in the vision domain test (MNIST) to below 4.5
Efficient and robust charging infrastructure plays a key role in accelerating the adoption of electric buses (eBuses) in urban transit systems. Unlike diesel buses, eBuses depend on strategically placed fast-charging stations to maintain continuous operation while ensuring high service quality. Planners must balance infrastructure investment, network reliability, and operational feasibility when determining optimal charging locations. Providing redundant charging access prevents disruptions from station failures, energy consumption fluctuations, and scheduling uncertainties. This work introduces an Iterated Local Search (ILS) algorithm that optimises the number and placement of charging stations. The approach improves robustness by incorporating backup charging stations and flexible energy redistribution techniques. We evaluate performance using real-world public transportation data from Cork and Dublin, comparing results against the state-of-the-art Large Neighborhood Search (LNS) method. Our experiments show that ILS outperforms LNS in 81.2
Many variants of the vehicle routing problem (VRP) pose significant computational challenges in logistics optimization, and improvement heuristics have emerged as effective tools for refining solutions found by local search methods and meta-heuristics. This paper introduces exact route-modifying improvement models (RMIMs). They are improvement models that aim to assemble high-quality solutions by selecting routes from a pool while allowing modifications to be made to the selected routes. These models can be embedded in a complete heuristic or used to post-optimize solutions produced by other methods. We evaluate our proposed models on vehicle routing problems with intra-route constraints, including the multi-trip VRP (MTVRP), the pickup and delivery problem with time windows (PDPTW), and the VRP with time windows (VRPTW). For the MTVRP, we propose a full matheuristic that uses a RMIM to achieve best known solutions for most benchmark instances for the MTVRP. By warm-starting with the current best known solutions from the literature the RMIMs improve many existing solutions for both the PDPTW and the VRPTW. These findings showcase the value of using RMIMs to enhance solutions to different types of VRPs.
The Distributor’s Pallet Loading Problem aims to optimize the loading of different 3D boxes on the minimum number of pallets. We consider an Integer Linear Programming (ILP) model for the problem that includes constraints deriving from real applications, such as stability and compression limits. In order to solve the ILP problem efficiently, we propose a method that exploits Machine Learning algorithms to classify predetermined layers of boxes, based on their “importance” of being used for an ILP solution. This classification is used to heuristically limit the number of layers taken into account by the ILP solver. We demonstrate the effectiveness of our approach by comparing the ILP solution with and without the Machine Learning component. The numerical results show that the proposed Machine Learning matheuristic approach achieves optimized pallet loading solutions in significantly reduced computational time.
This work introduces the Single Source Capacitated Partial Set Covering Location Problem (SSCPSCLP). Given a set of potential capacitated facilities and a set of customers with their demands, this problem consists of determining the facilities to be opened and the customers to be served to minimize the total cost of opening facilities, ensuring that at least a minimum amount of the total demand is served, only covered customers can be served, the capacity of the facilities is not exceeded, and each customer can be served by at most one facility. This work introduces a mathematical model for the problem and, since it is NP-hard, develops an algorithm based on the Tabu Search (TS) metaheuristic to handle large-scale instances. The TS algorithm explores the problem’s solution space through two neighborhoods, one of which is incorporated into a local search procedure that is periodically applied. The initial solution is generated either by a constructive greedy heuristic or by solving the linear relaxation of the SSCPSCLP. Four TS variants were proposed, differing in the method for generating the initial solution and in the use of local search. The results of computational experiments on instances from the literature show that the TS algorithm finds high-quality solutions in a shorter runtime than a mathematical programming-based solver and that the version using initial solutions from the linear relaxation of the problem and local search performs best.
The vertex connectivity of a graph is the minimum number of vertices whose removal disconnects the graph, and it is a fundamental notion that measures the level of interconnectedness of vertices. Mining subgraphs with high vertex connectivity has wide applications in robust and efficient communication networks and the organization of task groups. However, existing approaches often neglect size constraints, leading to subgraphs that are either too large or too small for practical use. Therefore, in this paper, we introduce the size constraint and formulate the graph downsizing problem: Given a graph G with n vertices and a positive integer τ
