This paper proposes a hierarchical matheuristic for the Helicopter Routing Problem (HRP) with the Greedy Randomized Adaptive Search Procedure (GRASP), mathematical models, and Variable Neighborhood Search (VNS). The HRP focuses on fulfilling transportation requests, defined by embarkation and disembarkation pairs, with helicopters as the transport mode. The proposed method uses constructive heuristics and the Set-Covering Problem (SCP) for routing. SCP utilizes local optima from earlier VNS iterations to form a partial tour, which a constructive heuristic may complete. The solution then undergoes local search via VNS, iteratively applied as the main GRASP loop. Finally, the Set-Partitioning Problem (SPP) provides a superior solution to those found in the GRASP. The hierarchical approach is applied to HRP challenges across varied search spaces. A new operator is introduced to efficiently map between these search spaces. Additionally, a new SPP model for HRP is presented, including constraints focused on secure vehicle landings. This integrated approach aims to optimize HRP processes by navigating different search spaces, enhancing adaptability, and addressing safety in landings. Computational results on two HRP instance sets, HRPS and HRPM, demonstrate the algorithm’s competitiveness in solution quality.
The Family Traveling Salesman Problem (FTSP) seeks a minimum-cost tour from a depot that visits a prescribed number of members of each customer family. This paper studies the Family Capacitated Vehicle Routing Problem (F-CVRP), a generalization of the FTSP in which customers carry demands and are served by a homogeneous fleet of capacitated vehicles, and proposes a hybrid metaheuristic for it. The method, named ILS+SP, couples an Iterated Local Search (ILS), which embeds a Random Variable Neighborhood Descent (RVND) over classical and problem-specific neighborhoods and accepts worsening moves through a Simulated-Annealing criterion, with a Set Partitioning (SP) post-optimization over the pool of routes collected during the search. On 144 large benchmark instances with more than 50 nodes, the metaheuristic wins or ties on every instance against the state-of-the-art heuristic of the literature, reducing the average gap to the best known solution from 1.84 to 0.01 0.47% to the best solutions found across all our runs, within an average total running time of 37 s (a 20-second ILS budget plus the Set Partitioning post-optimization), showing that the method scales to these instance sizes in terms of running time.
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.
