High Quality Initial Solutions Research Articles

Efficient Neural Collaborative Search for Pickup and Delivery Problems.

In this paper, we introduce Neural Collaborative Search (NCS), a novel learning-based framework for efficiently solving pickup and delivery problems (PDPs). NCS pioneers the collaboration between the latest prevalent neural construction and neural improvement models, establishing a collaborative framework where an improvement model iteratively refines solutions initiated by a construction model. Our NCS collaboratively trains the two models via reinforcement learning with an effective shared-critic mechanism. In addition, the construction model enhances the improvement model with high-quality initial solutions via curriculum learning, while the improvement model accelerates the convergence of the construction model through imitation learning. Besides the new framework design, we also propose the efficient Neural Neighborhood Search (N2S), an efficient improvement model employed within the NCS framework. N2S exploits a tailored Markov decision process formulation and two customized decoders for removing and then reinserting a pair of pickup-delivery nodes, thereby learning a ruin-repair search process for addressing the precedence constraints in PDPs efficiently. To balance the computation cost between encoders and decoders, N2S streamlines the existing encoder design through a light Synthesis Attention mechanism that allows the vanilla self-attention to synthesize various features regarding a route solution. Moreover, a diversity enhancement scheme is further leveraged to ameliorate the performance during the inference of N2S. Our NCS and N2S are both generic, and extensive experiments on two canonical PDP variants show that they can produce state-of-the-art results among existing neural methods. Remarkably, our NCS and N2S could surpass the well-known LKH3 solver especially on the more constrained PDP variant.

A multi-objective Immune Balancing Algorithm for Distributed Heterogeneous Batching-integrated Assembly Hybrid Flowshop Scheduling

Driven by economic globalization, global supply chain collaboration has gained significant importance, fostering the emergence of distributed manufacturing. This paper addresses the Distributed Heterogeneous Batching-integrated Assembly Hybrid Flowshop Scheduling (DHBIAHFS) problem within the pharmaceutical industry. Jobs are allocated to factories for processing, batched within defined lot sizes for transportation, and subsequently assembled into products to minimize the maximum completion time and tardy product count. Effective lot sizing during transport is emphasized between factories and assembly machines. Drawing inspiration from the biological immune system’s balancing mechanisms, we propose a Multi-objective Immune Balancing Algorithm (MOIBA) equipped with learning and repairing mechanisms. Each solution is structured with three nested sequences, and composite heuristic evaluations are employed to generate high-quality initial solutions. The performance of each solution is assessed based on both fitness and diversity metrics. Customized crossover and mutation operators are introduced with dynamically adjusted probabilities reflective of immune response dynamics. Quantitative analysis validates our mathematical model and the distinct components of MOIBA. We compare MOIBA’s efficiency against six other effective multi-objective strategies using three performance metrics. Stability and robustness assessments, conducted through variance examination and statistical testing, offer insights into MOIBA’s consistency and reliability across diverse problem instances.

An improved Coati Optimization Algorithm with multiple strategies for engineering design optimization problems

Aiming at the problems of insufficient ability of artificial COA in the late optimization search period, loss of population diversity, easy to fall into local extreme value, resulting in slow convergence and lack of exploration ability; In this paper, an improved COA algorithm based on chaotic sequence, nonlinear inertia weight, adaptive T-distribution variation strategy and alert updating strategy is proposed to enhance the performance of COA (shorted as TNTWCOA). The algorithm introduces chaotic sequence mechanism to initialize the position. The position distribution of the initial solution is more uniform, the high quality initial solution is generated, the population richness is increased, and the problem of poor quality and uneven initial solution of the Coati Optimization Algorithm is solved. In exploration phase, the nonlinear inertial weight factor is introduced to coordinate the local optimization ability and global search ability of the algorithm. In the exploitation phase, adaptive T-distribution variation is introduced to increase the diversity of individual population under low fitness value and improve the ability of the algorithm to jump out of the local optimal value. At the same time, the alert update mechanism is proposed to improve the alert ability of COA algorithm, so that it can search within the optional range. When Coati is aware of the danger, Coati on the edge of the population will quickly move to the safe area to obtain a better position, while Coati in the middle of the population will randomly move to get closer to other Coatis. IEEE CEC2017 with 29 classic test functions were used to evaluate the convergence speed, convergence accuracy and other indicators of TNTWCOA algorithm. Meanwhile, TNTWCOA was used to verify 4 engineering design optimization problems, such as pressure vessel optimization design and welding beam design. The results of IEEE CEC2017 and engineering design Optimization problems are compared with Improved Coati Optimization Algorithm (ICOA), Coati Optimization Algorithm (COA), Golden Jackal Optimization Algorithm (GJO), Osprey Optimization Algorithm (OOA), Sand Cat Swarm Optimization Algorithm (SCSO), Subtraction-Average-Based Optimizer (SABO). The experimental results show that the improved TNTWCOA algorithm significantly improves the convergence speed and optimization accuracy, and has good robustness. Three‑bar truss design problem, The Gear Train Design Problem, Speed reducer design problem shows a strong solution advantage. The superior optimization ability and engineering practicability of TNTWCOA algorithm are verified.

The constrained permutation flowshop problem: An effective two-stage iterated greedy algorithm to minimize weighted tardiness

In the domain of just-in-time permutation flowshop scheduling, most studies typically assume that all jobs either have their own soft due date or none of them do. However, in practice, scheduling a combination of hard and soft due date jobs, particularly with the context of emergency order insertion, remains a significant research topic. This paper addresses a constrained permutation flowshop scheduling problem with a mix of hard and soft due date jobs under total weighted tardiness criterion (CPFSP-TWT). We establish a mathematical model and propose an effective Two-Stage Iterated Greedy (ETSIG) algorithm tailored to the problem's characteristics, incorporating a two-stage constructive heuristic to generate a high-quality initial solution. We introduce problem-specific acceleration mechanisms based on position-bound considerations to enhance operational efficiency. We propose three knowledge-based repair strategies for handling infeasible solutions, along with a dynamic self-adjustment mechanism. Additionally, three efficient local search procedures integrate several specific perturbation operators to balance algorithmic exploitation and exploration abilities. Experimental evaluations affirm ETSIG's superiority over five state-of-the-art metaheuristics from closely related literature, establishing its efficacy in addressing CPFSP-TWT.

A multiobjective optimizer with a K-means cluster algorithm for a distributed flexible flowshop rescheduling problem

A distributed flexible flowshop problem (DFFSP) has been extensively studied over recent years. It is assumed that all jobs to be processed are exactly known in advance, and machines are able to work continuously. In practice, however, new jobs often arrive suddenly. Machines sometimes break down unexpectedly. These lower the performance of the scheduling generated, even make it infeasible. To address this problem, this paper considers a rescheduling DFFSP (DFFRP) with new job arrivals and machine breakdowns. The objective is to minimize makespan and the robustness metrics at the same time. Firstly, we propose a multi-objective mixed-integer linear programming model and a non-dominated sorting genetic algorithm-II based on K-means clustering algorithm (KNSGA-II). Secondly, the problem-specific knowledge is explored and a speed-up strategy is designed to save the algorithmic computation. Thirdly, an initialization strategy based on K-means clustering algorithm is developed to generate high-quality initial solutions. And a novel crossover and mutation operator is employed to accelerate the convergence of the algorithm. Finally, by comparing with a number of advanced multi-objective algorithms in the literature in comprehensive experiments, the proposed algorithm has been demonstrated to be much more effective for solving the DFFRP under consideration.

A Local Search Algorithm with Vertex Weighting Strategy and Two-Level Configuration Checking for the Minimum Connected Dominating Set Problem.

The minimum connected dominating set problem is a combinatorial optimization problem with a wide range of applications in many fields. We propose an efficient local search algorithm to solve this problem. In this work, first, we adopt a new initial solution construction method based on three simplification rules. This method can reduce the size of the original graph and thus obtain a high-quality initial solution. Second, we propose an approach based on a two-level configuration checking strategy and a tabu strategy to reduce the cycling problem. Third, we introduce a perturbation strategy and a vertex weighting strategy to help the algorithm be able to jump out of the local optimum effectively. Fourth, we combine the scoring functions Cscore and Mscore with the aforementioned strategies to propose effective methods for selecting vertices. These methods assist the algorithm in selecting vertices that are suitable for addition to or removal from the current candidate solution. Finally, we verify the performance advantages of the local search algorithm by comparing it with existing optimal heuristic algorithms on two sets of instances. The experimental results show that the algorithm exhibits better performance on two sets of classical instances.

Multi-objective optimization algorithm for multi-workflow computation offloading in resource-limited IIoT

Industrial internet of things (IIoT) connects traditional industrial devices with the network to provide intelligent services, which is regarded as the key technology for achieving Industry 4.0 and enabling the transformation of the manufacturing sector. Multi-access edge computing (MEC) has brought significant opportunities to expedite the development of IIoT. However, the unique task characteristics and dense deployment of IIoT devices, coupled with the resource starvation problem (RSP) arising from the limited resources of edge servers, pose challenges to the direct applicability of existing MEC algorithms in MEC-assisted IIoT scenarios. To this end, a multi-objective evolutionary algorithm is proposed to simultaneously optimize delay and energy consumption for multi-workflow execution in resource-limited IIoT. First, the initialization of execution location based on delay and the initialization of execution order satisfying the priority constraint can generate high-quality initial solutions. Then, the improved crossover and mutation operations guide the population evolution, which can span the large infeasible solution region. Finally, dynamic task scheduling (DTS) dynamically changes the execution location of tasks affected by RSP according to the execution efficiency, so as to avoid the tasks blindly waiting for server resources. The comprehensive simulation results demonstrate the effectiveness of the proposed method in achieving a balance between the execution delay and energy consumption of IIoT devices.

An improved ALNS for hybrid pickup and drones delivery system in disaster by penalizing deprivation time

Humanitarian logistics aims to reduce the time relief goods and services take to reach affected areas; deprivation time is one of the most significant factors in such conditions. Thus, utilizing a suitable transport fleet, including modern vehicles like drones, is essential. This paper introduces a new hybrid vehicle routing problem with pickup and delivery services, minimizing deprivation costs with multiple trucks and drones in a disaster. The model is presented as a mixed-integer linear programming problem focusing on minimizing deprivation cost in post-disaster situations through proper routing and inventory decisions made by heterogeneous vehicles. The deprivation time is divided into three main categories based on the arrival time of relief goods to affected areas and will be served by multiple relief goods. Due to the complexity of the problem, an improved adaptive large neighborhood search (ALNS) metaheuristic has been developed. This algorithm employs a heuristic algorithm to generate high-quality initial solutions and improve solutions with 17 destroy and repair operators. The algorithm was tested on a large-scale dataset based on real-world data from a crisis such as the Tehran earthquake, and the results demonstrate its superiority in providing better-quality solutions and lower solution time.

An iterated greedy algorithm with acceleration of job allocation probability for distributed heterogeneous permutation flowshop scheduling problem

Distributed manufacturing paradigm is becoming one of the dominant manufacturing models today. Heterogeneities between factories exist in fact due to the differences in process flexibility and machine performance. Most research focuses on identical distributed factories and overlooks the influence of heterogeneous factories on the subproblem of job allocation. This paper investigates a distributed heterogeneous permutation flowshop scheduling problem (DHPFSP) to minimize the makespan, and a mixed-integer linear programming (MILP) model is established. Building upon a special phenomenon of job assignment to a specific heterogeneous factory in DHPFSP, an iterated greedy algorithm with acceleration of job allocation probability (IGP) is proposed. To utilize this phenomenon, a job allocation probability matrix is introduced to describe the trend of job allocation, and a fast pass strategy with job allocation probability is suggested to speed up the algorithm search process. Furthermore, to generate a high-quality initial solution quickly for IGP, an NEH-based heuristic framework for distributed heterogeneous factory environment (NEHDHF) is proposed. In NEHDHF, several distinct initial job sequence generation strategies and a new first-f job allocation strategy are proposed for obtain a better initial solution. In computational experiments, there are 720 test instances designed and publicized. The IGP achieves 535 best solutions out of 720 instances. Statistically sound results demonstrate the effectiveness of the presented algorithms for the considered problem.

DDPG-Based Convex Programming Algorithm for the Midcourse Guidance Trajectory of Interceptor

To address the problem of low accuracy and efficiency in trajectory planning algorithms for interceptors facing multiple constraints during the midcourse guidance phase, an improved trajectory convex programming method based on the lateral distance domain is proposed. This algorithm can achieve fast trajectory planning, reduce the approximation error of the planned trajectory, and improve the accuracy of trajectory guidance. First, the concept of lateral distance domain is proposed, and the motion model of the midcourse guidance segment in the interceptor is converted from the time domain to the lateral distance domain. Second, the motion model and multiple constraints are convexly and discretely transformed, and the discrete trajectory convex model is established in the lateral distance domain. Third, the deep reinforcement learning algorithm is used to learn and train the initial solution of trajectory convex programming, and a high-quality initial solution trajectory is obtained. Finally, a dynamic adjustment method based on the distribution of approximate solution errors is designed to achieve efficient dynamic adjustment of grid points in iterative solving. The simulation experiments show that the improved trajectory convex programming algorithm proposed in this paper not only improves the accuracy and efficiency of the algorithm but also has good optimization performance.

Linearization Method for Large-Scale Hydro-Thermal Security-Constrained Unit Commitment

Security-constrained unit commitment (SCUC) is one of the most fundamental optimization problems in power systems. The objective of SCUC is to minimize the operating cost while respecting both system-wide and generator-specific constraints. It leads to a large-scale and mixed-integer programming (MIP) model with a large number of binary decision variables which is difficult to solve. This paper, based on the convex hull theory of single-unit, proposes a linearization method for the hydro-thermal SCUC problem with decoupled thermal units and variable-head hydro units. Then, the strategy of embedding two types of convex hulls in a multi-unit commitment and the heuristic method of constructing a feasible solution are designed, by which the multi-UC is approximated from large-scale mixed-integer programming to linear programming that can be solved in polynomial time. Finally, we theoretically prove that the optimal solution of the proposed LP model is always better than that of the Lagrangian Relaxation model. Numerical experiments on several large-scale test systems demonstrate the effectiveness and efficiency of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper proposes a linear programming model for the SCUC problem by lifting up to a higher-dimensional space. It realizes an important innovation in reducing the computational complexity of SCUC from the perspective of linearization. The proposed method can be well applied to large-scale long-term unit commitment problems. To better use this method, the following two properties should be highlighted: 1) the error of the proposed method is less than the Lagrangian relaxation method and decreases with the increasing system scales and 2) the computational efficiency of the proposed method is 10-100 times faster than that of the MIP model. We have tested many practical power systems and find that the error of the proposed LP model is usually very small compared with the precise MIP while the computational performance is significantly improved. In some practical cases, the decision makers usually do not want to find the precise optimal solution while only an approximation under a fast speed, because the boundary condition is imprecise. The proposed method is useful. Besides, for the cases that need the precise optimal solution, the proposed method can provide a high-quality initial solution for the MIP model to accelerate the convergence.

A knowledge-based iterated local search for the weighted total domination problem

For a simple undirected weighted graph G=(V,E,w,c), the weighted total domination problem is to find a total dominating set S with the minimum weight cost. A total dominating set S is a vertex subset satisfying that for each vertex in V there is at least one neighboring vertex in S. We propose a knowledge-based iterated local search algorithm for this problem that combines a reduction procedure to reduce the input graph, a learning-based initialization to generate high-quality initial solutions and a solution-based iterated local search to conduct intensive solution examination. Experiments on 342 benchmark instances show that the algorithm outperforms state-of-the-art algorithms. In particular, it reports 93 new upper bounds and 249 same results (including 165 known optimal results). The impact of each component of the algorithm is examined.

Autoencoder-Embedded Iterated Local Search for Energy-Minimized Task Schedules of Human–Cyber–Physical Systems

This work considers a task scheduling problem with deadline constraints in human-cyber-physical systems. To find its energy-efficient schedules in a short time, an autoencoder-embedded iterated local search algorithm is proposed to solve it. Iterated local search is selected as a main scheduler. In order to handle real-time requirements and high computational load involved in the problem solution, a Long Short-Term Memory-based AutoEncoder model (LSTM-AE) is constructed to capture the relevant and complementary features of the considered problem. The model is used to find low-order and high-fit sub-solutions via unsupervised end-to-end learning, and generates promising solutions in an informative low-dimensional solution space. To further reduce computational burden, a two-stage optimization framework is constructed, which includes an off-line training phase and an online optimization one. The former trains LSTM-AE by using expert knowledge and historical data. The latter designs optimal resource allocation strategies to build a high-quality initial solution. Then, LSTM-AE-assisted local search operators are proposed and used to reform the initial solution and generate better ones. Various numerical experiments are performed to compare the proposed method with several classic heuristics and some recently-developed methods. The results show its superiority over them. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In human-cyber-physical systems, a task scheduling problem is usually solved by using heuristics due to the limited computational resources. Nevertheless, fast dispatching rules tend to perform poorly. Meta-heuristics can find a relatively high-quality schedule but are time-consuming, especially for a population-based algorithm that requires to evaluate a fitness function for many candidate solutions at each iteration. To balance computational burden and solution quality, our idea is to combine machine-learning methods with meta-heuristics. Specially, we integrate a long short-term memory-based autoencoder model into iterated local search to improve the latter’s optimization ability. The combination of meta-heuristics and machine learning techniques makes it possible to obtain a high-quality schedule for the concerned problems in a short time. Theoretic analysis and experimental results show that the proposed method well outperforms its competitive peers.

An effective memetic algorithm for distributed flexible job shop scheduling problem considering integrated sequencing flexibility

Thus far, the available works on sequencing flexibility in shop floor scheduling only consider the sequencing flexibility with serial operation constraint. However, the sequencing flexibility with discrete and hybrid operation constraints are also widely existed in the actual production and have significant impact on production efficiency. Therefore, this work proposes a distributed flexible job shop scheduling problem considering integrated sequencing flexibility (DFJSPS), in which the serial, discrete and hybrid operation constraints are considered simultaneously. A mixed integer linear programming model is proposed to solve the DFJSPS by using the CPLEX solver. Then, an efficient memetic algorithm (EMA) is designed with the objectives of minimizing makespan and total energy consumption. In the EMA, a five-layer coding method and an efficient initialization method are presented to obtain high quality initial solutions; and an efficient local search operator is designed to help the algorithm to improve its convergence speed. Comprehensive experiments show that the EMA outperforms other three well-known algorithms in most of the instances, demonstrating the superior performance of EMA for solving DFJSPS in terms of both computational efficiency and solution quality. In summary, the research fills the research gap on integrated sequencing flexibility in the field of shop floor scheduling; on the other hand, it can help production managers to obtain the efficient scheduling schemas in the decision-making systems about various types of sequencing flexibility.

An effective population-based iterated greedy algorithm for solving the multi-AGV scheduling problem with unloading safety detection

With the increasing prevalence of automated guided vehicles (AGVs), the multi-AGV scheduling problem has become a hot research topic in recent years. However, little attention has been devoted to unloading safety detection for multi-AGV scheduling. This paper investigates a multi-AGV scheduling problem with unloading safety detection (MAGVSUSD) in a matrix manufacturing workshop. The aim is to minimize the total cost composed of travel cost, penalty cost and cost of AGV used. To address the MAGVSUSD, a mixed-integer linear programming model and a population-based iterated greedy (PIG) algorithm are proposed. In the PIG, a hyper-heuristic based on neighborhood operators and a population-based initialization method are proposed to obtain multiple high-quality initial solutions. The two-stage destruction strategy is designed to avoid falling into the local optimal solution and to enhance its ability to explore a larger solution space. The two-choice reconstruction strategy is developed to obtain better neighbor solutions by switching the search landscape. The local search based on the winning neighbor operators is proposed to dynamically adapt to each distribution situation in the workshop. A large number of experimental results demonstrate the proposed algorithm's superiority over existing algorithms in addressing the considered problem.

An improved solution methodology for the urban transit routing problem

An improved solution methodology is proposed in this paper for the urban transit routing problem (UTRP). This methodology includes a procedure for the generation of improved initial solutions as well as improved metaheuristic search approaches, involving the use of hyperheuristics to manage search operators in both trajectory-based and population-based metaheuristics. The UTRP variant considered in this paper is that of deciding upon efficient bus transit routes. The design criteria embedded in our UTRP model are the simultaneous minimisation of the expected average passenger travel time and minimisation of the system operator’s cost (measuring the latter as the sum total of all route lengths in the system). The model takes as input an origin–destination demand matrix for a pre-specified set of bus stops, along with an underlying road network structure, and returns as output a set of bus route trade-off solutions. The decision maker can then select one of these route sets subjectively, based on the desired degree of trade-off between the aforementioned transit system design criteria. This bi-objective minimisation problem is solved approximately in three distinct stages — a solution initialisation stage, an intermediate analysis stage, and an iterative metaheuristic search stage during which high-quality trade-off solutions are sought. A novel procedure is introduced for the solution initialisation stage, aimed at effectively generating high-quality initial feasible solutions. Two metaheuristics are implemented to solve instances of the problem, namely a dominance-based multi-objective simulated annealing algorithm and an improved non-dominated sorting genetic algorithm, each equipped with a hyperheuristic capable of managing the perturbation operators employed. Various novel operators are proposed for these metaheuristics, of which the most noteworthy take into account the demand of passengers.

Enhancing sparrow search algorithm with hybrid multi-strategy and its engineering applications

An enhancing sparrow optimization algorithm with hybrid multi-strategy (EGLTA-SSA) is proposed, to improve the defects of the sparrow search algorithm (SSA), which is easy to fall into local optimum. Firstly, the elite backward learning strategy is introduced to initialize the sparrow population, to generate high-quality initial solutions. Secondly, the leader position is updated by fusing multi-strategy mechanisms. On one hand, the high distributivity of arithmetic optimization algorithm operators are used to deflate the target position, and enhance the ability of SSA to jump out of the local optimum. On the other hand, the leader position is perturbed by adopting the golden levy flight method and the t-distribution perturbation strategy to improve the shortcoming of SSA in the late iteration when the population diversity decreases. Further, a probability factor is added for random selection to achieve more effective communication among leaders. Finally, to verify the effectiveness of EGLTA-SSA, CEC2005 and CEC2019 functions are tested and compared with state-of-the-art algorithms, and the experimental results show that EGLTA-SSA has a better performance in terms of convergence rate and stability. EGLTA-SSA is also successfully applied to three practical engineering problems, and the results demonstrate the superior performance of EGLTA-SSA in solving project optimization problems.

Multi-population cooperative multi-objective evolutionary algorithm for sequence-dependent group flow shop with consistent sublots

Inspired by the production model of pressure vessels for spacecraft, i.e., tanks and cylinders, this study addresses the sequence-dependent group flow shop scheduling problem with consistent sublots (SDGFSP_CS) to minimize makespan and total energy consumption. In the problem under consideration, there are several coupling sub-problems, namely, the group sequencing, job sequencing, lot assignment, and machine speed assignment. To solve these problems, a multi-population cooperative multi-objective evolutionary algorithm (MPCMOEA) is proposed. In the MPCMOEA, a hybrid initial method that combines two problem-specific heuristics is designed to generate high-quality initial solutions. Then, considering the problem features, a cooperative mechanism considering the co-evolution of multi-population and the archive set is designed to accelerate the optimization process. In the co-evolutionary stage, to deepen the exploitation ability of local search, an enhanced search with multiple problem-specific operators is implemented. Furthermore, a re-initialization method is developed to improve the global search abilities. Finally, 27 different scale instances are generated for a series of numerical experiments. For the hypervolume and inverse generational distance metrics, MPCMOEA gets 20/27 and 21/27 optimal values, respectively. It verifies that the MPCMOEA outperforms efficient algorithms in terms of the diversity and convergence performance.

Q-learning-based hyper-heuristic evolutionary algorithm for the distributed assembly blocking flowshop scheduling problem

Distributed shop scheduling problems (DSSPs) have attracted increasing interest in recent years due to the technical trends of smart manufacturing and Industry 4.0. The distributed assembly blocking flowshop scheduling problem (DABFSP) is a critical class of DSSPs with widespread applications in modern supply chains and manufacturing systems. In this paper, a Q-learning-based hyper-heuristic evolutionary algorithm (QLHHEA) is proposed to solve DABFSP with the objective of minimizing the makespan. Firstly, a mathematical model of DABFSP is formulated, and two insertion-based speedup strategies are devised to conserve the computational cost of evaluating solutions and to accelerate the search efficiency. Secondly, a problem-specific constructive heuristic is developed to produce high-quality initial solutions. Thirdly, twelve efficient heuristics are designed to construct low-level heuristics (LLHs). The Q-learning-based evolutionary algorithm is applied as a high-level strategy to manipulate the LLHs, which are then executed in order to search the solution space. Moreover, suitable solution encoding and decoding schemes are provided to produce feasible scheduling schedules. The design of experiments is implemented to investigate the impact of the parameters. Finally, a comprehensive comparison campaign is carried out based on a total of 1710 well-known instances to evaluate the efficacy of the proposed algorithm against several state-of-the-art algorithms. Experimental results and statistical analysis show that QLHHEA significantly outperforms the existing algorithms by a significant margin, demonstrating the effectiveness and efficiency of QLHHEA in solving DABFSP.

Effects of geographically stratified random sampling initial solutions on solving a continuous surface p-median location problem using the ALTERN heuristic

In the fields of location theory and spatial optimization, heuristic algorithms have been developed to overcome the NP-hard nature of solutions to their problems, which results in an exponential increase in computation time. These algorithms aim to generate good initial solutions, narrow the solution space, and guide the search process to optimality. Geographically stratified random sampling (GSRS) can be regarded as a method to generate such high-quality initial solutions. This study investigates the application of GSRS to solving the p-median location problem on a continuous surface solution space punctuated with weighted demand points, and its impact on the performance of the popular ALTERN heuristic algorithm. Results demonstrate the effectiveness of GSRS in finding optimal p-median solutions, but only for smaller p values: the ALTERN heuristic with initial solutions generated by local spatial means from GSRS for these smaller p always produces optimal final solutions. In contrast, implementing a random search by executing a large number of random initial solutions often produces non-optimal results. Findings reported in this paper also highlight that sample size and degree of positive spatial autocorrelation (PSA) in the geographic distribution of weights influence how close final solutions are to optimality for larger p. Increasing the sample size leads solutions to be concentrated near their optimal counterparts, as does increasing PSA levels.