Large-scale Benchmark Instances Research Articles

Comparison of New and Old Optimization Algorithms for Traveling Salesman Problem on Small, Medium, and Large-scale Benchmark Instances

The Traveling Salesman Problem (TSP), a prominent combinatorial optimization issue, is the subject of this study's evaluation of the performance of new and old optimization techniques. This paper seeks to expand knowledge of optimization techniques and how they might be applied to solve TSP challenges. The goal of the research is to compare various algorithms' scalability, convergence, and computation times on benchmark instances of several sizes. To achieve this goal, this paper carried out extensive testing using the Artificial Bee Colony (ABC), Grey Wolf Optimization (GWO), and Salp Swarm Algorithm (SSA) as new optimization algorithms and the Genetic Algorithm (GA), Ant Colony Optimization (ACO), and Simulated Annealing (SA) as old optimization algorithms. On small, medium, and large-scale benchmark cases, these algorithms were examined. The findings of this investigation show that the new optimization techniques are more convergent and scalable than the old ones, especially for medium-scale scenarios. They perform better performance in terms of solution quality by applying objective function values. The new methods also exhibit improved scalability, successfully adjusting to medium-scale instances. However, there were no discernible changes between the smaller and larger instances. This study makes an impact by offering insightful information about how well optimization methods perform while solving the TSP. Each algorithm's strengths and downsides have been reported, and these details offer useful guidance for choosing an algorithm for a certain scenario. The results also show the practical ramifications of applying novel optimization techniques, especially in medium-scale instances..

An efficient hybrid adaptive large neighborhood search method for the capacitated team orienteering problem

This paper focuses on a NP-Hard vehicle routing problem with profits, and presents a hybrid heuristic solution approach for the Capacitated Team Orienteering Problem (CTOP), which is a variant of the well-known team orienteering problem. In the CTOP, given a set of homogeneous fleet and a set of clients to each is associated a deterministic profit and volume demand, one maximizes the collected profits for serving customers by operating a set of routes while respecting vehicles’ limited time and volume capacities. Our proposed method to solve the CTOP is a Hybrid Adaptive Large Neighborhood Search (HALNS) heuristic. Several removal and insertions operators with different node selection strategies and local search procedures are developed to generate solutions in the first step. In the second step, solutions’ routes are passed to a set packing problem which is solved using an exact branch-and-cut procedure in order to obtain the best solution. Compared to all the state-of-the-art methods, extensive computational experiments show that our method outperforms in terms of solution quality and/or computational times when tested on the small and large-scale benchmark CTOP instances respectively proposed by Archetti et al. (2009) and Tarantilis et al. (2023). Furthermore, our hybrid method improves 10 of the best known solutions for large-scale benchmark instances.

Pickup capacitated vehicle routing problem with three-dimensional loading constraints: Model and algorithms

This study addresses the pickup capacitated vehicle routing problem with three-dimensional loading constraints (3L-PCVRP), which combined the container loading problem (CLP) and the capacitated vehicle routing problem (CVRP). A mixed-integer linear programming model for 3L-PCVRP is designed with the objective of minimizing the total transportation cost. The basic constraints of CLP and CVRP as well as the practical constraints imposed by the pickup operations are incorporated in 3L-PCVRP. An improved branch-and-price-based (B&P) algorithm is proposed to solve 3L-PCVRP. The 3L-PCVRP model is decomposed into the restricted master problem (RMP) for selecting routes and the subproblem (SP) for generating routes that satisfy the loading and routing constraints. A label-correcting-based algorithm (LCA) is presented to solve the SP, which employs a two-stage method and two enhanced loading algorithms to ensure the loading feasibility of the routes. The two loading algorithms (tree search and greedy heuristic algorithms) are improved by a new evaluation function and an improved space-merging method. The two-stage method is designed to call the two loading algorithms at different frequencies to investigate the route feasibility accurately and efficiently. Numerical experiments are designed to test the performance of the proposed algorithms. The efficiency and effectiveness of the improved loading algorithms are demonstrated in hundreds randomly generated instances. For small-scale 3L-PCVRP instances, the B&P algorithm can generate solutions that are not worse than those of the solver within 0.14% of the solver’s running time. The efficiency and effectiveness of the improved B&P algorithm are also validated in large-scale benchmark instances.

Routing UAVs in landslides Monitoring: A neural network heuristic for team orienteering with mandatory visits

Unmanned aerial vehicles (UAVs) are widely used for surveillance in both civilian and military scenarios. The utilization of UAVs provides an opportunity for monitoring landslide-prone areas by automatically collecting geological information, thereby reducing the risks and the time required to be working in harsh environments. Due to the maximum travel time limit of UAVs and the geographical dispersion of landslide-prone areas, multiple UAVs are dispatched for surveillance tasks, and landslide-prone areas with high emergency priorities require mandatory visits. Here, we investigate a team orienteering problem with mandatory visits (TOPMV) for routing multi-UAVs to monitor scattered landslide-prone areas, with mandatory visits on those in poorly stable states. The proposed TOPMV aims to plan the optimal multi-UAV paths for maximizing the total amount of collected geological information. To solve the TOPMV with a realistic scale, we develop a large neighborhood search (LNS) algorithm embedding a neural network heuristic (NNH), in which the embedded NNH learns to perform adaptive destroy operators through a hierarchical recurrent graph convolutional network (HRGCN). We consider a real-world case study for monitoring of landslide-prone areas in three counties in southern Shaanxi Province, China. Finally, we test the proposed NNH on both small- and large-scale benchmark instances of the team orienteering problem. The experimental results demonstrate that our proposed NNH exhibits higher efficiency and provides better solution quality than state-of-the-art methods, especially in large-scale settings.

A Population-Based Iterated Greedy Algorithm for Distributed Assembly No-Wait Flow-Shop Scheduling Problem

This paper investigates a distributed assembly no-wait flow-shop scheduling problem (DANWFSP), which has important applications in manufacturing systems. The objective is to minimize the total flowtime. A mixed-integer linear programming model of DANWFSP with total flowtime criterion is proposed. A population-based iterated greedy algorithm (PBIGA) is presented to address the problem. A new constructive heuristic is presented to generate an initial population with high quality. For DANWFSP, an accelerated NR3 algorithm is proposed to assign jobs to the factories, which improves the efficiency of the algorithm and saves CPU time. To enhance the effectiveness of the PBIGA, the local search method and the destruction-construction mechanisms are designed for the product sequence and job sequence, respectively. A selection mechanism is presented to determine which individuals execute the local search method. An acceptance criterion is proposed to determine whether the offspring are adopted by the population. Last, the PBIGA and seven state-of-the-art algorithms are tested on 810 large-scale benchmark instances. The experimental results show that the presented PBIGA is an effective algorithm to address the problem and performs better than recently state-of-the-art algorithms compared in this paper.

A self-learning hyper-heuristic for the distributed assembly blocking flow shop scheduling problem with total flowtime criterion

The distributed assembly blocking flow shop scheduling problem, which is a significant scenario in modern supply chains and manufacturing systems, has attracted significant attention from researchers and practitioners. To formulate the problem, a mixed-integer linear programming model is introduced to optimize the total flowtime. A constructive heuristic (HHNRa) and a self-learning hyper-heuristic (SLHH) are proposed to address the scheduling problem. HHNRa is designed based on the problem-specific knowledge to obtain initial solutions with high quality. A self-learning high-level strategy based on the historical success rate of low-level heuristics is presented to manipulate the low-level heuristics to operate in the solution space. In addition, a restart scheme with three distinct constructive heuristics is utilized to maintain the diversity of the solution. Based on 900 small-scale benchmark instances and 810 large-scale benchmark instances, comprehensive numerical experiments are conducted to evaluate the performance of the proposed SLHH algorithm. The results of the statistical analysis indicate that the proposed self-learning hyper-heuristic is superior to the compared state-of-the-art algorithms for the problem under consideration. Consequently, the proposed constructive heuristic and the self-learning hyper-heuristic are effective methods for the distributed assembly blocking flow shop scheduling problem.

A modified Ant Colony System for the asset protection problem

• Time-efficient solutions of the Asset Protection Problem (APP). • The Modified Ant Colony System (MACS) is proposed. • Especially designed solution-improving heuristic techniques. • New best results in large-scale benchmark instances. • MACS outperforms previous APP solution approaches. During an escaped wildfire in a populated area’s vicinity, protective tasks should be carried out to secure crucial community assets, e.g., bridges, hospitals, power stations, and communication towers. In a real-life scenario, an important asset may require the combined effort of different fire suppression resources, which should be dispatched and scheduled to act synchronously in protecting the respective asset. The present research addresses the solution of a challenging routing problem in emergency response, the Asset Protection Problem (APP), which incorporates selective characteristics in routing a heterogeneous vehicle fleet with complex temporal and spatial constraints, i.e., time windows and synchronization requirements. Notably, the Modified Ant Colony System (MACS) algorithm is proposed to obtain effective APP solutions within a time suitable for operational purposes. Based on the conducted experiments, MACS outperforms the previously published solution approaches in the solution of large-scale APP benchmark instances. Notably, MACS obtained superior solutions in 159 out of 240 large-scale instances, while 87 of them represent new best results, considering the solutions achieved by the commercial solver CPLEX with a ten-hour time limit.

An effective water wave optimization algorithm with problem-specific knowledge for the distributed assembly blocking flow-shop scheduling problem

The distributed assembly blocking flow-shop scheduling problem (DABFSP), which is a promising area in modern supply chains and manufacturing systems, has attracted great attention from researchers and practitioners. However, minimizing the total tardiness in DABFSP has not captured much attention so far. For solving the DABFSP with the total tardiness criterion, a mixed integer linear programming method is utilized to model the problem, wherein the total tardiness during the production process and assembly process are optimized simultaneously. A constructive heuristic (KBNEH) and a water wave optimization algorithm with problem-specific knowledge (KWWO) are presented. KBNEH is designed by combining a new dispatching rule with an insertion-based improvement procedure to obtain solutions with high quality. In KWWO, effective technologies, such as the re-developed destruction–construction​ operator, four local search methods under the framework of the variable neighborhood search strategy (VNS), the path-relinking method are applied to improve the performance of the algorithm. Comprehensive numerical experiments based on 900 small-scale benchmark instances and 810 large-scale benchmark instances are conducted to evaluate the performance of the presented algorithm. The experimental results obtained by KWWO are 1 to 4 times better than those obtained by the other comparison algorithms, which demonstrate that the effectiveness of KWWO is superior to the compared state-of-the-art algorithms for the considered problem.

A Lagrangian heuristic for the multicommodity capacitated location problem with balancing requirements

We consider the multicommodity capacitated location problem with balancing requirements. This problem has applications in transportation and was introduced in the context of planning the movements of containers between ports and terminals, identified as depots in the problem formulation. We propose a Lagrangian relaxation based on a reformulation of the problem that allows the subproblem to be decomposed by depot, giving rise to a series of continuous knapsack subproblems. We optimize the Lagrangian dual by a bundle method and we develop a Lagrangian heuristic based on slope scaling. Numerical results are presented on a set of large-scale benchmark instances. We obtain good quality solutions within short computing times using the Lagrangian heuristic approach.

A hybrid adaptive large neighborhood search heuristic for the team orienteering problem

The Team Orienteering Problem (TOP) is a well-known NP-Hard vehicle routing problem in which one maximizes the collected profits for visiting some nodes. In this paper, we propose a Hybrid Adaptive Large Neighborhood Search (HALNS) to solve this problem. Our algorithm combines the exploration power of ALNS with local search procedures and an optimization stage using a Set Packing Problem to further improve the solutions. Extensive computational experiments demonstrate the high performance of our HALNS outperforming all the competing algorithms in the literature on a large set of benchmark instances in terms of solution quality and/or computational time. Our HALNS identifies all the 387 Best Known Solutions (BKS) from the literature on a first dataset including small-scale benchmark instances and all the 333 BKS for large-scale benchmark instances within very short computational times. Moreover, we improve one large-scale instance solution.

A comparison of separation routines for benders optimality cuts for two-level facility location problems

This paper studies two-level uncapacitated facility location problems, a class of discrete location problems that consider different hierarchies of facilities and their interactions. Benders reformulations for both single and multiple assignment variants and while several separation procedures for three classes of Benders cuts are presented: standard optimality cuts, lifted optimality cuts, and non-dominated optimality cuts. Extensive computational experiments are performed on difficult and large-scale benchmark instances to assess the performance of the considered separation routines.

Multi-objective teaching-learning-based meta-heuristic algorithms to solve multi-skilled project scheduling problem

In this paper, a novel multi-objective multi-skilled resource-constrained project scheduling problem based on learning effect is presented in which efficiency of the workforce is proportional with the time they spend to execute that skill. A mixed integer nonlinear programming formulation is presented to optimize conflicting objectives. Two hybrid multi-objective teaching–learning based optimization (TLBO) algorithms are developed with a new solution structure based on primary concepts of multi-objective particle swarm optimization and multi-objective invasive weeds optimization algorithms to find near optimal solutions of the model’s complicated instances in a reasonable computational time. The proposed algorithms encompass a novel solution structure that satisfies all the constraints and generates feasible solutions. The classical multi-objective teaching-learning based optimization algorithm and NSGA II are developed with the same chromosome structure to validate performance of the developed algorithms. In addition, all the algorithms are employed to solve small- and large-scale benchmark instances that are available on literature of project scheduling problems as well as 30 randomly generated test problems. Taguchi grey relational analysis is used to tune parameters of the algorithms and enhance their performance for generating more qualified solutions. In addition, statistical test is employed to compare performance of the proposed algorithms in terms of some multi-objective metrics. Finally, hybrid multi-attribute decision making approach is employed to prioritize algorithms and determine the algorithm with higher performance on solving small, medium and large scale instances.

A jigsaw puzzle inspired algorithm for solving large-scale no-wait flow shop scheduling problems

The no-wait flow shop scheduling problem (NWFSP), as a typical NP-hard problem, has important ramifications in the modern industry. In this paper, a jigsaw puzzle inspired heuristic (JPA) is proposed for solving NWFSP with the objective of minimizing makespan. The core idea behind JPA is to find the best match for each job until all the jobs are scheduled in the set of process. In JPA, a waiting time matrix is constructed to measure the gap between two jobs. Then, a matching matrix based on the waiting time matrix is obtained. Finally, the optimal scheduling sequence is built by using the matching matrix. Experimental results on large-scale benchmark instances show that JPA is superior to the state-of-the-art heuristics.

A hypergraph multi-exchange heuristic for the single-source capacitated facility location problem

In this paper, we introduce a large-scale neighborhood search procedure for solving the single-source capacitated facility location problem (SSCFLP). The neighborhood structures are induced by innovative split multi-customer multi-exchanges, where clusters of customers assigned to one facility can be moved simultaneously to multiple destination facilities and vice versa. To represent these exchanges, we use two types of improvement hypergraphs. The improvement hypergraphs are built dynamically and the moving customers associated with each hyperedge are selected by solving heuristically a suitably defined mixed-integer program. We develop a hypergraph search framework, including forward and backward procedures, to identify improving solutions efficiently. Our proposed algorithm can obtain improving moves more quickly and even find better solutions than a traditional multi-exchange heuristic (Ahuja, Orlin, Pallottino, & Scuttellà, 2004). In addition, when compared with the Kernel Search algorithm (Guastaroba & Speranza, 2014), which at present is the most effective for solving SSCFLP, our algorithm is not only competitive but can find better solutions or even the best known solution to some very large scale benchmark instances from the literature.

Finding a maximum k-club using the k-clique formulation and canonical hypercube cuts

Detecting low-diameter clusters is an important graph-based data mining technique used in social network analysis, bioinformatics and text-mining. Low pairwise distances within a cluster can facilitate fast communication or good reachability between vertices in the cluster. Formally, a subset of vertices that induce a subgraph of diameter at most k is called a k-club. For low values of the parameter k, this model offers a graph-theoretic relaxation of the clique model that formalizes the notion of a low-diameter cluster. Using a combination of graph decomposition and model decomposition techniques, we demonstrate how the fundamental optimization problem of finding a maximum size k-club can be solved optimally on large-scale benchmark instances that are available in the public domain. Our approach circumvents the use of complicated formulations of the maximum k-club problem in favor of a simple relaxation based on necessary conditions, combined with canonical hypercube cuts introduced by Balas and Jeroslow.

Branch-and-price algorithm for fuzzy integer programming problems with block angular structure

This paper deals with fuzzy integer linear programming problems with block angular structure in which the fuzzy constraints are simplified by using possibility and necessity relations. This main fuzzy problem is efficiently decomposed and is solved by a branch-and-price algorithm. In the nodes of the branch-and-price tree, the linear relaxation of the problem is solved by applying a column generation method. Also, the relationship between the optimal solutions of this problem under possibility and necessity relations is derived. To show the validation of the proposed algorithm, some results are proved. In addition, the application of this algorithm is illustrated on fuzzy multicommodity flow problem. For this case, a new branching scheme is proposed to preserve the network structure of the subproblems which are produced in the column generation method. Some examples are solved and their results are compared with the previous works. Also, the results of the proposed algorithm are reported on some large-scale benchmark instances.

Solving the Multiscenario Max-Min Knapsack Problem Exactly with Column Generation and Branch-and-Bound

Despite other variants of the standard knapsack problem, very few solution approaches have been devised for the multiscenario max-min knapsack problem. The problem consists in finding the subset of items whose total profit is maximized under the worst possible scenario. In this paper, we describe an exact solution method based on column generation and branch-and-bound for this problem. Our approach relies on a reformulation of the standard compact integer programming model based on the Dantzig-Wolfe decomposition principle. The resulting model is potentially stronger than the original one since the corresponding pricing subproblem does not have the integrality property. The details of the reformulation are presented and analysed together with those concerning the column generation and branch-and-bound procedures. To evaluate the performance of our algorithm, we conducted extensive computational experiments on large scale benchmark instances, and we compared our results with other state-of-the-art approaches under similar circumstances. We focused in particular on different relevant aspects that allow an objective evaluation of the efficacy of our approach. From different standpoints, the branch-and-price algorithm proved to outperform the other state-of-the-art methods described so far in the literature.

An Improved Decomposition-Based Memetic Algorithm for Multi-Objective Capacitated Arc Routing Problem

Capacitated Arc Routing Problem (CARP) has attracted the attention of many researchers during the last few years, because it has a wide application in the real world. Recently, a Decomposition-Based Memetic Algorithm for Multi-Objective CARP (D-MAENS) has been demonstrated to be a competitive approach. However, the replacement mechanism and the assignment mechanism of the offspring in D-MAENS remain to be improved. First, the replacement after all the offspring are generated decreases the convergence speed of D-MAENS. Second, the representatives of these sub-problems are reassigned at each generation by only considering one objective function. In response to these issues, this paper presents an improved D-MAENS for Multi-Objective CARP (ID-MAENS). The two improvements of the proposed algorithm are as follows: (1) the replacement of the solutions is immediately done once an offspring is generated, which references to the steady-state evolutionary algorithm. The new offspring will accelerate the convergence speed; (2) elitism is implemented by using an archive to maintain the current best solution in its decomposition direction during the search, and these elite solutions can provide helpful information for solving their neighbor sub-problems by cooperation. Compared with the Multi-Objective CARP algorithm, experimental results on large-scale benchmark instances egl show that the proposed algorithm has performed significantly better than D-MAENS on 23 out of the total 24 instances. Moreover, ID-MAENS find all the best nondominated solutions on 13 egl instances. In the last section of this paper, the ID-MAENS also proves to be competitive to some state-of-art single-objective CARP algorithms in terms of quality of solutions and computational efficiency.

Applying hybrid meta-heuristics for capacitated vehicle routing problem

The capacitated vehicle routing problem (CVRP) is one of the most important problems in the optimization of distribution networks. The objective of CVRP, known demands on the cost of originating and terminating at a delivery depot, is to determine the optimal set of routes for a set of vehicles to deliver customers. CVRP is known to be NP-hard problem, and then it is difficult to solve this problem directly when the problem size is large.In this paper, a hybrid algorithm of simulated annealing and tabu search is applied to solve CVRP. It takes the advantages of simulated annealing and tabu search for solving CVRP. Simulation results are reported on classical fourteen instances and twenty large-scale benchmark instances. From simulation results, the proposed algorithm finds eight best solutions of classical fourteen instances. Additionally, the solutions of the proposed algorithm have also admirable performance for twenty large-scale benchmark instances. It shows that the proposed algorithm is competitive with other existing algorithms for solving CVRP.