Best-known Solutions Research Articles

An Efficient Optimization Model and Tabu Search–Based Global Optimization Approach for the Continuous p-Dispersion Problem

Continuous p-dispersion problems with and without boundary constraints are NP-hard optimization problems with numerous real-world applications, notably in facility location and circle packing, which are widely studied in mathematics and operations research. In this work, we concentrate on general cases with a nonconvex multiply connected region that are rarely studied in the literature due to their intractability and the absence of an efficient optimization model. Using the penalty function approach, we design a unified and almost everywhere differentiable optimization model for these complex problems and propose a tabu search–based global optimization (TSGO) algorithm for solving them. Computational results over a variety of benchmark instances show that the proposed model works very well, allowing popular local optimization methods (e.g., the quasi-Newton methods and the conjugate gradient methods) to reach high-precision solutions due to the differentiability of the model. These results further demonstrate that the proposed TSGO algorithm is very efficient and significantly outperforms several popular global optimization algorithms in the literature, improving the best-known solutions for several existing instances in a short computational time. Experimental analyses are conducted to show the influence of several key ingredients of the algorithm on computational performance. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72122006, 71821001, and 72471100] Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0089 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0089 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Knowledge-enhanced multidimensional estimation of distribution hyper-heuristic evolutionary algorithm for semiconductor final testing scheduling problem

The semiconductor final test scheduling problem (SFTSP), recognized as a crucial bottleneck in the semiconductor production process, holds immense significance for improving both quality control and scheduling efficiency within chip and integrated circuit enterprises. This article introduces the knowledge-enhanced multidimensional estimation of distribution hyper-heuristic evolutionary algorithm (KMEDHEA) for addressing the SFTSP with the aim of minimizing the makespan. First, a single-vector encoding scheme is used to represent feasible solutions, and a problem-specific constrained-separable left-shift decoding scheme is devised to transform these solutions into feasible scheduling schedules. Second, eight simple yet effective heuristics with problem-specific knowledge are developed that served as a suite of low-level heuristics (LLHs) for exploring the problem solution space. Third, the multidimensional estimation of distribution algorithm (MEDA) is employed as the high-level strategy to estimate the correlations and connections of the pre-designed LLHs, thereby guiding the search scope towards high-quality individuals. Finally, critical configurations of parameters are systematically analyzed by conducting a design-of-experiment (DOE) approach. Numerical experiments are conducted on well-known benchmark datasets, and the experimental results demonstrate the superiority of the KMEDHEA versus several state-of-the-art approaches. The best-known solutions are updated for nine out of ten benchmark instances, highlighting the effectiveness and efficiency of the proposed KMEDHEA in solving the SFTSP.

An Efficient Tour Construction Heuristic for Generating the Candidate Set of the Traveling Salesman Problem with Large Sizes

In this paper, we address the challenge of creating candidate sets for large-scale Traveling Salesman Problem (TSP) instances, where choosing a subset of edges is crucial for efficiency. Traditional methods for improving tours, such as local searches and heuristics, depend greatly on the quality of these candidate sets but often struggle in large-scale situations due to insufficient edge coverage or high time complexity. We present a new heuristic based on fuzzy clustering, designed to produce high-quality candidate sets with nearly linear time complexity. Thoroughly tested on benchmark instances, including VLSI and Euclidean types with up to 316,000 nodes, our method consistently outperforms traditional and current leading techniques for large TSPs. Our heuristic’s tours encompass nearly all edges of optimal or best-known solutions, and its candidate sets are significantly smaller than those produced with the POPMUSIC heuristic. This results in faster execution of subsequent improvement methods, such as Helsgaun’s Lin–Kernighan heuristic and evolutionary algorithms. This substantial enhancement in computation time and solution quality establishes our method as a promising approach for effectively solving large-scale TSP instances.

The set team orienteering problem

We introduce the Set Team Orienteering Problem (STOP), a generalised variant of the Set Orienteering Problem (SOP), in which customer locations are split into multiple clusters (or groups). Each cluster is associated with a profit that can be gained only if at least one customer from the cluster is visited. There is a fleet of homogeneous vehicles at a depot, and each vehicle has a limited travel time. The goal of the STOP is to find a set of feasible vehicle routes to collect the maximum profit. We first formulate the problem as a Mixed Integer Linear Programming (MILP) to mathematically describe it. A branch-and-price (B&P) algorithm is then developed to solve the problem to optimality. To deal with large instances, we propose a Large Neighbourhood Search (LNS), which relies on problem-tailored solution representation, removal, and insertion operators. Multiple experiments on newly generated instances confirm the performance of our approaches. Remarkably, when tested on the SOP using benchmarks available in the literature, our B&P method achieves optimality in 61.9% of these instances. This is the first time such a large number of SOP instances are solved to optimality. Our LNS outperforms existing algorithms proposed to solve the SOP in terms of solution quality. Out of 612 considered instances, it improves 40 best-known solutions.

Two-stage heuristic algorithm with pseudo node-based model for electric vehicle routing problem

Electric vehicle routing problem (EVRP) is a special vehicle routing problem, which owns several specific characteristics of EV technology including the limited charging stations and the limited cruising range of EVs. This paper proposes a two-stage heuristic algorithm for EVRP with a kind of pseudo node, termed EVRPPN-TSH, which not only contributes to the model innovation but also to the algorithm design. In model innovation, the pseudo node is introduced into the EVRP model, forming EVRPPN, to reduce the search space and time complexity for obtaining service orders of customers from O(n) to O(1). Moreover, different from other research works which only use total distance as the fitness function, an improved fitness function is proposed, which takes all the distance, the electricity and capacity constraints compliance into consideration. In algorithm design, we first adopt the two-stage idea, which divides EVRP into the capacitated vehicle routing problem (CVRP) and a fixed route vehicle charging problem (FRVCP). Then we design a two-stage heuristic algorithm, termed as TSH. Specifically, for CVRP, a route division heuristic algorithm and a depot move heuristic algorithm are designed to divide routes. Further, an adjustment strategy with three operators is designed for adjusting the customer order. For FRVCP, an existing heuristic algorithm is adopted and enhanced by a variable extent shaking algorithm to avoid local trapped. Experimental results show that EVRPPN-TSH generally outperforms other state-of-the-art algorithms. Moreover, EVRPPN-TSH can obtain the best-known solution in all the 7 test cases, and update the best-known solution in test case E101 from 834.84 to 834.22.

Balancing individual and collective strategies: A new approach in metaheuristic optimization

Metaheuristic approaches commonly disregard the individual strategies of each agent within a population, focusing primarily on the collective best solution discovered so far. While this methodology can yield promising results, it also has several significant drawbacks, such as premature convergence. This study introduces a new metaheuristic approach that emphasizes the balance between individual and social learning in agents. In this approach, each agent employs two strategies: an individual search technique performed by the agent and a social or collective strategy involving the best-known solution. The search strategy is considered a learning problem, and agents must adjust the use of both individual and social strategies accordingly. The equilibrium of this adjustment is determined by a counter randomly set for each agent, which determines the frequency of use invested in each strategy. This mechanism promotes diverse search patterns and fosters a dynamic and adaptive process, potentially improving problem-solving efficiency in intricate spaces. The proposed method was assessed by comparing it with several well-established metaheuristic algorithms using 21 test functions. The results demonstrate that the new method surpasses popular metaheuristic algorithms by offering superior solutions and attaining quicker convergence.

A fast local search algorithm for minimum sum coloring problem on massive graphs

The minimum sum coloring problem (MSCP) is an important extension of the graph coloring problem with wide real-world applications. Compared to the classic graph coloring problem, where lots of methods have been developed and even massive graphs with millions of vertices can be solved well, few works have been done for the MSCP, and no specialized MSCP algorithms are available for solving massive graphs. This paper explores how to solve MSCP on massive graphs, and then proposes a fast local search algorithm for the MSCP based on three main ideas including a coarse-grained reduction method, two kinds of scoring functions and selection rules as well as a novel local search framework. Experiments are conducted to compare our algorithm with several state-of-the-art algorithms on massive graphs. The proposed algorithm outperforms previous algorithms in almost all the massive graphs and also improves the best-known solutions for some conventional instances, which demonstrates the performance and robustness of the proposed algorithm.

A Swarm Intelligence Solution for the Multi-Vehicle Profitable Pickup and Delivery Problem

Delivery apps are experiencing significant growth, requiring efficient algorithms to coordinate transportation and generate profits. One problem that considers the goals of delivery apps is the multi-vehicle profitable pickup and delivery problem (MVPPDP). In this paper, we propose eight new metaheuristics to improve the initial solutions for the MVPPDP based on the well-known swarm intelligence algorithm, Artificial Bee Colony (ABC): K-means-GRASP-ABC(C)S1, K-means-GRASP-ABC(C)S2, Modified K-means-GRASP-ABC(C)S1, Modified K-means-GRASP-ABC(C)S2, ACO-GRASP-ABC(C)S1, ACO-GRASP-ABC(C)S2, ABC(S1), and ABC(S2). All methods achieved superior performance in most instances in terms of processing time. For example, for 250 customers, the average times of the algorithms was 75.9, 72.86, 79.17, 73.85, 76.60, 66.29, 177.07, and 196.09, which were faster than those of the state-of-the-art methods that took 300 s. Moreover, all proposed algorithms performed well on small-size instances in terms of profit by achieving thirteen new best solutions and five equal solutions to the best-known solutions. However, the algorithms slightly lag behind in medium- and large-sized instances due to the greedy randomised strategy and GRASP that have been used in the scout bee phase. Moreover, our algorithms prioritise minimal solutions and iterations for rapid processing time in daily m-commerce apps, while reducing iteration counts and population sizes reduces the likelihood of obtaining good solution quality.

An Adaptive Multi-Meme Memetic Algorithm for the prize-collecting generalized minimum spanning tree problem

In this paper, we address the prize-collecting generalized minimum spanning tree problem (PC-GMSTP) which aims to find a minimum spanning tree to connect a network of clusters using exactly one vertex per cluster, minimizing the total cost of connecting the clusters while considering both the costs of edges and the prizes offered by the vertices. An Adaptive Multi-meme Memetic Algorithm (AMMA) is proposed to tackle PC-GMSTP, which combines an adaptive reproduction procedure and a collaborated local search procedure. The adaptive reproduction procedure uses either crossover or mutation to produce offspring to maintain a good balance between exploration and exploitation of the search space, and the probability to use crossover or mutation is adaptively adjusted based on the diversity of population. The collaborated local search procedure, which includes two efficient local search operators, can effectively enhance the intensification ability of AMMA due to their complementary features. Extensive computational experiments on 126 challenging instances demonstrate the superiority of AMMA, outperforming 23 best-known solutions from existing literature while achieving similar solutions for the remaining 103 instances. Wilcoxon’s signed rank test confirms that the performance of AMMA is significantly better than the state-of-the-art algorithms.

Multi-depot vehicle routing problem with roaming delivery locations considering hard time windows: Solved by a hybrid ELS-LNS algorithm

This paper investigates the multi-depot vehicle routing problem with roaming delivery locations considering hard time windows. In the mentioned problem, each customer can determine several locations with a distinct hard time windows and the service provider can choose between the proposed locations to visit the customer. Also, several depots are considered for the vehicles. A mathematical model is presented for the problem. The objective function of the model is minimizing the total travel time. This objective function is important in problems that include hard time windows; because in addition to the route navigation time, it considers the waiting time of the vehicles, which is one of the integral cost factors in hard time window problems. Considering the proposed problem is NP-hard, we proposed two heuristic algorithms. Also, a hybrid algorithm based on ELS is designed to solve the problem on large scales. The results show the appropriate efficiency of the algorithm for solving small and large instances. Overall, based on the results, the proposed algorithm improved the best-known solution of two instances in the multi depot vehicle routing problem with time windows benchmark datasets.

AILS-II: An Adaptive Iterated Local Search Heuristic for the Large-Scale Capacitated Vehicle Routing Problem

A recent study on the classical capacitated vehicle routing problem (CVRP) introduced an adaptive version of the widely used iterated local search paradigm, hybridized with a path-relinking (PR) strategy. The solution method, called adaptive iterated local search (AILS)-PR, outperformed existing meta-heuristics for the CVRP on benchmark instances. However, tests on large-scale instances suggest that PR is too slow, making AILS-PR less advantageous in this case. To overcome this challenge, this paper presents an AILS combined with mechanisms to handle large CVRP instances, called AILS-II. The computational cost of this implementation is reduced, whereas the algorithm also searches the solution space more efficiently. AILS-II is very competitive on smaller instances, outperforming the other methods from the literature with respect to the average gap to the best-known solutions. Moreover, AILS-II consistently outperforms the state of the art on larger instances with up to 30,000 vertices. History: Accepted by Ted Ralphs, Area Editor for Software Tools. This paper has been accepted for the INFORMS Journal on Computing Special Issue on Software Tools for Vehicle Routing. Funding: This work was supported by the Fundação de Amparo à Pesquisa do Estado de São Paulo [Grants 2013/07375-0, 2019/22067-6, and 2022/05803-3] and the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 309385/2021-0 and 403735/2021-1]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0106 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0106 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

An ALNS metaheuristic for the family multiple traveling salesman problem

This paper presents a novel variant of the Family Traveling Salesman Problem (FTSP), a well-known NP-hard problem introduced by Morán-Mirabal et al. (2014). In the FTSP, the set of nodes is partitioned into several subsets called families, and the aim is to determine the minimum-cost cycle that begins and ends at the depot and visits a predefined number of nodes in each family. We extend the FTSP by requiring that m tours be generated, each having a number of nodes between a minimum and a maximum quantity, thus yielding the family multiple traveling salesman problem (FmTSP). We present a two-index MIP formulation and develop an ALNS metaheuristic as a solution method for large-sized instances. Our proposed ALNS was initially employed to solve the FTSP benchmark instances and allowed us to improve some of the best-known solutions. The results for new derived instances requiring multiple tours show that our ALNS also achieves optimality for all instances with proven-optimal solutions.

An effective multi-level memetic search with neighborhood reduction for the clustered team orienteering problem

The Clustered Team Orienteering Problem (CluTOP) extends the classic Clustered Orienteering Problem by considering the use of multiple vehicles. The problem is known to be NP-hard and can be used to formulate many real-life applications. This work presents a highly effective multi-level memetic search for CluTOP that combines a backbone-based edge assembly crossover to generate promising offspring solutions with an effective bilevel synergistic local search procedure at both cluster and customer levels to improve offspring solutions. Other novel features of the proposed approach include a joint use of three specific hash functions to identify the tabu status of candidate solutions at the cluster level, a multi-neighborhood search with inter-route and intra-route optimization at the customer level, a pre-processing neighborhood reduction strategy to avoid examining non-promising candidate solutions, and a strategy for controlled exploration of infeasible solutions. Extensive experimental results on 1848 benchmark instances convincingly demonstrate high competitiveness of the approach in terms of both solution quality and computational time, compared to the state-of-the-art heuristics from the literature. In particular, the proposed algorithm improves upon the existing best-known solutions for 294 instances, while matching the previous best-known results for all but 3 of the remaining instances. To gain further insights into the algorithm’s performance, additional experiments are conducted to analyze its main components.

A flexible variable neighbourhood search algorithm for different variants of the Electric Vehicle Routing Problem

This manuscript presents a flexible variable neighbourhood search (VNS)-based (Flexi-VNS) algorithm to tackle both the classical Electrical Vehicle Routing Problem (EVRP) and the Battery Swap Station Location-routing Problem with Capacitated Electric Vehicles (BSS-EV-LRP). The latter has been addressed in just a few studies. It incorporates into the EVRP the battery swapping stations (BSS) location requirement to be jointly taken with decisions on the routing of electric vehicles. The Flexi-VNS algorithm includes a Randomised Variable Neighbourhood Descent (RVND) method as the local search procedure, which incorporates a new intra-RVND procedure called every time a solution is modified and applied only to those routes that have been modified. We assess the performance of Flexi-VNS on EVRP and BSS-EV-LRP benchmark instances and compare it with some algorithms in the literature. The statistical test did not guarantee the existence of a statistical difference between the proposed algorithm and the best algorithm from the literature for each problem, considering a 95% confidence level. However, despite this, computational results showed the Flexi-VNS efficiency. It improved several of the best-known solutions and reduced the number of constructed battery swap stations. More specifically, Flexi-VNS was able to equal or improve the BKS values of 15 out of a total of 20 instances with available results in the literature for BSS-EV-LRP and 47 out of 52 instances available for the EVRP, totalling 75% of the BSS-EV-LRP instances and 90.38% of the EVRP instances. Furthermore, compared to the exact algorithms, the optimal solutions were found using only a fraction of the computational times reported. Additionally, Flexi-VNS was the first to provide solutions for some BSS-EV-LRP instances.

A new Hyper-heuristic based on Adaptive Simulated Annealing and Reinforcement Learning for the Capacitated Electric Vehicle Routing Problem

Electric vehicles (EVs) have been adopted in urban areas to reduce environmental pollution and global warming due to the increasing number of freight vehicles. However, there are still deficiencies in routing the trajectories of last-mile logistics that continue to impact social and economic sustainability. For that reason, in this paper, a hyper-heuristic (HH) approach called Hyper-heuristic Adaptive Simulated Annealing with Reinforcement Learning (HHASARL) is proposed. It is composed of a multi-armed bandit method and the self-adaptive Simulated Annealing (SA) metaheuristic algorithm for solving the problem called Capacitated Electric Vehicle Routing Problem (CEVRP). Due to the limited number of charging stations and the travel range of EVs, the EVs must require battery recharging moments in advance and reduce travel times and costs. The implementation of the HH improves multiple minimum best-known solutions and obtains the best mean values for some high-dimensional instances for the proposed benchmark for the IEEE WCCI2020 competition.

A competitive heuristic algorithm for vehicle routing problems with drones

We propose a heuristic algorithm capable of handling multiple variants of the vehicle routing problem with drones (VRPD). Assuming that the drone may be launched from a node and recovered at another, these variants are characterized by three axes, (1) minimizing the transportation cost or minimizing the makespan, (2) the drone is either allowed or not allowed to land while awaiting recovery, and (3) single or multiple trucks each equipped with a drone. In our algorithm, we represent a VRPD solution as a set of customer sequences and evaluate it via local search procedures solving for each sequence a problem that we refer to as the fixed route drone dispatch problem (FRDDP). Given a sequence of customers to be served by a single truck and its drone, the FRDDP selects a subset of customers to be served by the drone and determines drone launch and recovery nodes, while ensuring that each such customer is positioned between two nodes in the initial sequence. We introduce a heuristic dynamic program (HDP) to solve the FRDDP with reduced computational complexity compared to an exact solution algorithm for the problem. We reinforce our algorithm by developing filtering strategies based on the HDP. We benchmark the performance of our algorithm on nine benchmark sets pertaining to four VRPD variants resulting in 932 instances. Our algorithm computes 651 of 680 optimal solutions and identifies 189 new best-known solutions.

Fixed set search matheuristic applied to the knapsack problem with forfeits

This paper focuses on solving the knapsack problem with forfeits (KPF). This variation of the knapsack problem includes soft conflicts or forfeits, where forfeit pairs consist of two items and an associated penalty, which must be subtracted from the total profit if both items in the pair are chosen to be jointly in the knapsack. The proposed method combines the fixed set search (FSS) metaheuristic’s learning mechanism with integer programming to solve subproblems. A new ground set of elements for the KPF is introduced to augment the information provided by the fixed set, and the method for creating fixed sets is adjusted to increase the diversity of solutions. The conducted computational experiments show that the proposed method significantly outperforms current state-of-the-art methods and finds a large number of best-known solutions for the standard test instances. Moreover, the method performs well across a wide range of parameter values. The proposed approach does not significantly exploit any specific properties of the KPF and could potentially be applied to other 0–1 problems, such as the minimum vertex cover problem or the facility location problem, without significant modifications. Additionally, the method’s simplicity makes it suitable for hybridization with other metaheuristic approaches or the incorporation of specific KPF properties to improve its performance.

Particle Swarm Optimization for Wireless Sensor Network Lifespan Maximization

Despite the deployment of wireless sensor networks in diverse fields (health, environment, military applications, etc.) for tracking or monitoring, several challenges, such as extending the lifetime of the network under energy constraints, still need to be resolved. Lifetime is the operational time of the network during which it can perform dedicated tasks and satisfy the application requirements. The energy constraints dictate that the energy consumption of sensors should be minimized since in most cases the sensors are battery-powered. Various methods have been proposed to work around this problem using scheduling approaches. In this paper, particle swarm optimization-based scheduling was designed and implemented to maximize the lifetime of wireless sensor networks formulated as a Non-Disjoint Sets Cover (NDSC) problem. The experimental findings show that the proposed approach is extremely competitive to the state-of-the-art algorithms, as it is able to find the optimal and best-known solutions in the instances investigated.

Predicting hypertension control using machine learning.

Hypertension is a widely prevalent disease and uncontrolled hypertension predisposes affected individuals to severe adverse effects. Though the importance of controlling hypertension is clear, the multitude of therapeutic regimens and patient factors that affect the success of blood pressure control makes it difficult to predict the likelihood to predict whether a patient's blood pressure will be controlled. This project endeavors to investigate whether machine learning can accurately predict the control of a patient's hypertension within 12 months of a clinical encounter. To build the machine learning model, a retrospective review of the electronic medical records of 350,008 patients 18 years of age and older between January 1, 2015 and June 1, 2022 was performed to form model training and testing cohorts. The data included in the model included medication combinations, patient laboratory values, vital sign measurements, comorbidities, healthcare encounters, and demographic information. The mean age of the patient population was 65.6 years with 161,283 (46.1%) men and 275,001 (78.6%) white. A sliding time window of data was used to both prohibit data leakage from training sets to test sets and to maximize model performance. This sliding window resulted in using the study data to create 287 predictive models each using 2 years of training data and one week of testing data for a total study duration of five and a half years. Model performance was combined across all models. The primary outcome, prediction of blood pressure control within 12 months demonstrated an area under the curve of 0.76 (95% confidence interval; 0.75-0.76), sensitivity of 61.52% (61.0-62.03%), specificity of 75.69% (75.25-76.13%), positive predictive value of 67.75% (67.51-67.99%), and negative predictive value of 70.49% (70.32-70.66%). An AUC of 0.756 is considered to be moderately good for machine learning models. While the accuracy of this model is promising, it is impossible to state with certainty the clinical relevancy of any clinical support ML model without deploying it in a clinical setting and studying its impact on health outcomes. By also incorporating uncertainty analysis for every prediction, the authors believe that this approach offers the best-known solution to predicting hypertension control and that machine learning may be able to improve the accuracy of hypertension control predictions using patient information already available in the electronic health record. This method can serve as a foundation with further research to strengthen the model accuracy and to help determine clinical relevance.

Parallel self-avoiding walks for a low-autocorrelation binary sequences problem

A low-autocorrelation binary sequences problem with a high figure of merit factor represents a formidable computational challenge. An efficient parallel computing algorithm is required to reach the new best-known solutions for this problem. Therefore, we developed the sokolskew solver for the skew-symmetric search space. The developed solver takes the advantage of parallel computing on graphics processing units. The solver organized the search process as a sequence of parallel and contiguous self-avoiding walks and achieved a speedup factor of 387 compared with lssOrel, its predecessor. The sokolskew solver belongs to stochastic solvers and cannot guarantee the optimality of solutions. To mitigate this problem, we established the predictive model of stopping conditions according to the small instances for which the optimal skew-symmetric solutions are known. With its help and 99% probability, the sokolskew solver found all the known and seven new best-known skew-symmetric sequences for odd instances from L=121 to L=223. For larger instances, the solver cannot reach 99% probability within our limitations, but it still found several new best-known binary sequences. We also analyzed the trend of the best merit factor values, and it shows that as sequence size increases, the value of the merit factor also increases, and this trend is flatter for larger instances.