Neighborhood Search Procedure Research Articles

Two-stage multi-objective optimization based on knowledge-driven approach: A case study on production and transportation integration

The multi-objective evolutionary algorithm (MOEA) has been widely applied to solve various optimization problems. Existing search models based on dominance and decomposition are extensively used in MOEAs to balance convergence and diversity during the search process. In this paper, we propose for the first time a two-stage MOEA based on a knowledge-driven approach (TMOK). The first stage aims to find a rough Pareto front through an improved nondominated sorting algorithm, whereas the second stage incorporates a dynamic learning mechanism into a decomposition-based search model to reasonably allocate computational resources. To further speed up the convergence of TMOK, we present a Markov chain-based TMOK (MTMOK), which can potentially capture variable dependencies. In particular, MTMOK employs a marginal probability distribution of single variables and an N-state Markov chain of two adjacent variables to extract valuable knowledge about the problem solved. Moreover, a simple yet effective local search is embedded into MTMOK to improve solutions through variable neighborhood search procedures. To illustrate the potential of the proposed algorithms, we apply them to solve a distributed production and transportation-integrated problem encountered in many industries. Numerical results and comparisons on 54 test instances with different sizes verify the effectiveness of TMOK and MTMOK. We have made the 54 instances and the source code of our algorithms publicly available to support future research and real-life applications.

A variable neighborhood search approach for solving a real-world hierarchical multi-echelon vehicle routing problem involving HCT vehicles

This paper studies the Hierarchical Multi-Switch Multi-Echelon VRP (HMSME-VRP), a newly introduced VRP variant based on a real-world case involving High Capacity Vehicles (HCV). The problem originates from the policies of a distribution company in the Nordic countries where HCVs of up to 34.5 m and up to 76 tons are allowed. The HMSME-VRP offer a new way to model distribution problems to cover large geographical areas without substantial costs in infrastructure. Furthermore, it adds complexity to the standard VRP and, as such, remains NP-hard and difficult to solve to optimality. Indeed, it has been demonstrated that only very small instances can be solved to optimality by a commercial solver. Thus, in order to handle instances of real-world size, we propose two General Variable Neighborhood Search (GVNS) procedures, the second of which is adaptive, utilizing an intelligent reordering mechanism. In order to evaluate the proposed procedures, 48 benchmark instances of various sizes and characteristics are generated and made publicly available, comprising of clustered, random, and semi-clustered customers. The computational results show that both GVNS procedures outperform the exact solver. Additionally, the adaptive version outperforms the conventional version based on both average and best solutions. Furthermore, we present a statistical analysis to verify the superiority of the adaptive version.

Enhanced NSGA-II for multi-objective energy-saving flexible job shop scheduling

To achieve green targets, manufacturing enterprises need to propose an effective energy-saving strategy for production scheduling. In this paper, a multi-objective energy-saving flexible job shop-scheduling problem (MO_EFJSP) is formulated with three criteria of optimizing the makespan, the total delay time and the total power consumption. To efficiently solve the MO_EFJSP, an enhanced non-dominated sorting genetic algorithm II (ENSGA-II) is developed. The proposed ENSGA-II has two main innovative aspects: i) the diversity of children population in a local search is achieved by performing different neighborhood search procedures on the sparse solution space so that the accuracy of the current solution is improved; ii) the weighted method is applied to select the desirable compromised solution from the Pareto solution set. By conducting extensive computational experiments based on benchmark instances and real-world case studies, it is verified that the proposed ENSGA-II is applicable for saving power consumption in a flexible job shop system. Consequently, this study makes a significant contribution to the field of green (energy-saving or energy-efficient) production scheduling.

Solving the integrated planning and scheduling problem using variable neighborhood search based algorithms

In this paper, we address the Integrated Planning and Scheduling Problem (IPSP) on parallel and identical machines. Planning and scheduling are essential for the efficient management of supply chains. Although both pursue the same general objective, they are usually performed independently mostly because they relate to different timescales. As a consequence, the generated plans and schedules are typically sub-optimal from a global standpoint.The approaches followed in this paper explicitly consider the interdependence between the planning and scheduling activities by solving them simultaneously in an integrated way. We explore different heuristics based on variable neighborhood search procedures with new and specifically designed neighborhood structures relying on the properties of the IPSP. The quality of these approaches is evaluated through extensive computational experiments performed on a large set of benchmark instances. The results show that the proposed methods achieve high-quality solutions, with a substantially low computation time, outperforming other state-of-the-art results reported in the literature.

A Constructive Heuristics and an Iterated Neighborhood Search Procedure to Solve the Cost-Balanced Path Problem

This paper presents a new heuristic algorithm tailored to solve large instances of an NP-hard variant of the shortest path problem, denoted the cost-balanced path problem, recently proposed in the literature. The problem consists in finding the origin–destination path in a direct graph, having both negative and positive weights associated with the arcs, such that the total sum of the weights of the selected arcs is as close to zero as possible. At least to the authors’ knowledge, there are no solution algorithms for facing this problem. The proposed algorithm integrates a constructive procedure and an improvement procedure, and it is validated thanks to the implementation of an iterated neighborhood search procedure. The reported numerical experimentation shows that the proposed algorithm is computationally very efficient. In particular, the proposed algorithm is most suitable in the case of large instances where it is possible to prove the existence of a perfectly balanced path and thus the optimality of the solution by finding a good percentage of optimal solutions in negligible computational time.

Energy-efficient unrelated parallel machine scheduling with general position-based deterioration

ABSTRACT This paper investigates an energy-efficient scheduling problem on unrelated parallel machines considering general position-based deterioration which arises from the labour-intensive textile industry. The actual processing time of a job is not only associated with the job and the machine but also with its position in the processing sequence. The objective is to minimise the total energy consumption with a bounded makespan. To address this problem, we first establish a mixed-integer linear programming (MILP) model. Afterwards, the initial model is improved by deriving lower and upper bounds on the makespan, and an upper bound on the number of jobs processed on each machine. We also develop an iterative heuristic embedded with a variable neighbourhood search procedure (IHVNS). The algorithm obtains initial solutions iteratively by solving assignment problems and then repairs and improves them with the VNS procedure. Computational results demonstrate that the improved model is up to 230 times faster than the original one. Moreover, the proposed heuristic yields excellent solutions with average gaps of less than 0.73% for large-scale instances. Especially, the results reveal that the IHVNS algorithm is more suitable than MILP models for solving large-scale problems with tight makespan restrictions.

Discovering injury severity risk factors in automobile crashes: A hybrid explainable AI framework for decision support

Millions of car crashes occur annually in the US, leaving tens of thousands of deaths and many more severe injuries. Thus, understanding the most impactful contributors to severe injuries in automobile crashes and mitigating their effects are of great importance in traffic safety improvement. This paper develops a hybrid framework involving predictive analytics, explainable AI, and heuristic optimization techniques to investigate and explain the injury severity risk factors in automobile crashes. First, our framework examines various machine learning models to identify the one with the best prediction performance as the base model. Then, it utilizes two popular state-of-the-art explainable AI techniques from the literature (i.e., leave-one-covariate-out and TreeExplainer) and our proposed explanation method based on the variable neighborhood search procedure to construe the importance of the variables. Finally, by applying an information fusion technique, our approach identifies a unified ranking list of the most important variables contributing to severe car crash injuries. Transportation safety planners and policymakers can use our findings to reduce the severity of car accidents, improve traffic safety, and save many lives.

Solving the Cubic Cell Formation Problem Using Simulated Annealing

The Cubic Cell Formation Problem (CCFP) in cellular manufacturing systems consists in decomposing a production system into a set of manufacturing cells, and assigning workers to cells besides parts and machines. The major objective is to obtain manageable cells. Manageable cells mean cells with a minimum value of inter-cell moves of parts and workers and a minimum value of heterogeneity within cells. In this paper, a solution methodology based on a modified simulated annealing heuristic with a proposed neighbourhood search procedure is proposed. The methodology allows building multiple configurations by giving to the decision-maker the ability to control some parameters. Experimental results show that the proposed algorithm gives a promising performance for all problem instances found in the literature.

Intensification-driven local search for the traveling repairman problem with profits

The Traveling Repairman Problem with Profits is to select a subset of nodes (customers) in a weighted graph to maximize the collected time-dependent revenues. We introduce an intensification-driven local search algorithm for solving this challenging problem. The key feature of the algorithm is an intensification mechanism that intensively investigates bounded areas around each very-high-quality local optimum encountered. As for its underlying local optimization, the algorithm employs an extended variable neighborhood search procedure which adopts for the first time a K-exchange sampling based neighborhood and a concise perturbation procedure to obtain high-quality solutions. Experimental results on 140 benchmark instances show a high performance of the algorithm by reporting 36 improved best-known results (new lower bounds) and equal best-known results for 95 instances. Additional experiments are conducted to investigate the usefulness of the key components of the algorithm.

Multiple GEO satellites on-orbit repairing mission planning using large neighborhood search-adaptive genetic algorithm

This paper proposes a novel large neighborhood search-adaptive genetic algorithm (LNS-AGA) for many-to-many on-orbit repairing mission planning of geosynchronous orbit (GEO) satellites with mission deadline constraint. In the many-to-many on-orbit repairing scenario, several servicing spacecrafts and target satellites are located in GEO orbits which have different inclination, right ascension of ascending node (RAAN) and true anomaly. Each servicing spacecraft need to rendezvous with target satellites to perform repairing missions under limited fuel. The mission objective is to find the optimal servicing sequence and orbit rendezvous time of each servicing spacecraft to minimize total Δv cost of all servicing spacecrafts with all target satellites repaired. Firstly, a time-dependent orbital rendezvous strategy is proposed, which can handle the mission deadline constraint. Besides, it is also cost-effective compared with the existing strategy. Based on this strategy, the many-to-many on-orbit repairing mission planning model can be simplified to an integer programming problem, which is established based on the vehicle routing problem with time windows (VRPTW) model. In order to efficiently find a feasible optimal solution under complicated constraints, a hybrid adaptive genetic algorithm combining the large neighborhood search procedure is designed. The operations of “destroy” and “repair” are used on the elite individuals in each generation of the genetic algorithm to enhance local search capabilities. Finally, simulation results under several different scenarios show the effectiveness and superiority of the presented algorithm and orbital rendezvous strategy.

A pareto-based multi-objective network design approach for mitigating the risk of hazardous materials transportation

Hazardous materials (HazMat) transportation is one of the indispensable links in the chemical process industry and is closely related to safety, security, and environmental concerns. HazMat transportation routing is a major proactive risk management measure. Most related studies focus on diminishing the transportation risk for one single HazMat shipment. This work addresses a global perspective on the problem where the correlations of multiple simultaneous HazMat shipments are considered. A multi-objective transportation network design model is defined to optimize the objectives of the transportation risk and the transportation cost. A well-designed Pareto-based hybrid heuristic algorithm is proposed for model solving, which integrates a linear decomposition procedure for initial population construction, a Pareto-based scatter search procedure for population evolution, and a variable neighborhood search procedure for solution improvement. Computational results indicate that the proposed algorithm is competitive in solving large-scale instances since it is able to strike a great balance between effectiveness and efficiency. The detailed solution analysis shows that the proposed approach can effectively coordinate multiple simultaneous HazMat transportation processes. Moreover, we find that performing multiple short-distance shipments would significantly reduce the total transportation risk, but results in the higher transportation cost. This work can provide a set of Pareto optimal transportation networks for different industrial application scenarios to achieve the trade-off between economic and safety.

Vehicle routing problem with drones considering time windows

The cooperation of trucks and unmanned aerial vehicles (UAV) has become a new delivery method in the area of logistics and transportation. In this form of cooperation, the trucks are not only able to provide services to the customers, but also serve as a ‘launch pad’ for the drones, in which the drones can be launched to service a customer and then recovered at the rendezvous node. This study intends to explore this cooperation by developing a model for the vehicle routing problem with drones that considers the presence of customer time windows (VRPTWD). A mixed-integer programming (MIP) model is presented to minimize the total travelling costs. Then, a simple yet effective variable neighborhood search (VNS) procedure with a novel solution representation is proposed as a solver. The numerical results indicate the ability of the proposed VNS to solve the VRPTWD, as well as the improvement of delivery performance using drones.

A Hybrid Grasp-genetic Algorithm for Mixed-model Assembly Line Balancing Problem Type 2

In manufacturing systems, mixed model assembly lines are used to produce different products to deal with the problem of customers’ demands variety, and minimizing the cycle time in such assembly line is a critical problem. This paper addresses the mixed model assembly line balancing problem type 2 that consists in finding the optimal cycle time for a given number of workstations. A hybrid Greedy randomized adaptive search procedure-Genetic algorithm is proposed to find the optimal assignment of tasks among workstations that minimize the cycle. A Ranked Positional Weight heuristic is used in the construction phase of the proposed GRASP, and in the local search phase, a neighborhood search procedure is used to ameliorate the constructed solutions in the construction phase. The GRASP is executed many times in order to seed the initial population of the proposed genetic algorithm, and the results of the executions are compared with the final solutions obtained by the hybrid GRASP-GA. In order to test the proposed approaches, a numerical example is used.

A restart local search algorithm with Tabu method for the minimum weighted connected dominating set problem

The minimum weighted connected dominating set problem is a significant NP-hard problem with wide applications, and is an extension of the classical minimum dominating set problem. In order to solve this problem, we present a restart local search algorithm with tabu method (RLS Tabu). In our RLS Tabu algorithm, we firstly involve the random restart initialization method to jump out of the local optimum. Meanwhile, RLS Tabu algorithm also applies tabu method in neighborhood search procedure to mitigate the cycling problem. Secondly, we present two strategies in neighborhood search procedure for removing vertices properly, which one is greedy and random strategy, and another one is multiple deletion strategy. The two strategies are crucial to improve the solution quality. Thirdly, the solution connected vertex is important to guarantee the feasibility of solutions. Therefore, we maintain the solution connected vertex set during the neighborhood search, and select the vertex to be added from this set. Finally, in order to intensify the solution, RLS Tabu utilizes the pruning function to delete redundant vertices in the candidate solution. In experimental section, we will compare our algorithm with the other six algorithms on three types of benchmarks. Experimental results indicate that our algorithm significantly outperforms the comparative algorithms on most benchmark instances.

Optimisation and Static Equilibrium of Three-Dimensional LEGO Constructions

Combinatorial optimisation can be applied in a multitude of areas, and this article presents its application to the optimisation of LEGO constructions. Building LEGO constructions is an inherently combinatorial problem, with a large but finite number of possible brick combinations. The objective was to make an aesthetically pleasing construction which is cheap and is structurally stable. Through the application of an adaptive large neighbourhood search metaheuristic, in combination with a mixed integer programming model neighbourhood search procedure and a quadratic programming model ensuring static equilibrium, this article demonstrates how to optimise LEGO constructions with up to 77.000 brick positions.

GRASP with ALNS for solving the location routing problem of infectious waste collection in the Northeast of Thailand

This research proposes a heuristic to solve the problem of the location selection of incinerators and the vehicle routing of infectious waste collection for hospitals in the Northeast of Thailand. The developed heuristic is called the Greedy Randomized Adaptive Large Neighborhood Search Procedure (GRALNSP)and applies the principles of the Greedy Randomized Adaptive Search Procedure (GRASP) and Adaptive Large Neighborhood Search (ALNS) in the local search. The results from GRALNSP are compared with those from the exact method processed by the A Mathematical Programming Language (AMPL) program. For small-sized problems, experiments showed that both methods provided no different results with the global optimal solution, but GRALNSP required less computational time. When the problems were larger-scale and more complicated, AMPL could not find the optimal solution within the limited period of computational time while GRALNSP provided better results with much less computational time. In solving the case study with GRALNSP, the result shows that the suitable locations for opening infectious waste incinerators are the locations of Pathum Ratwongsa district, Amnat Charoen province and Nam Phong district, Khonkaen province. An incinerator with a burning capacity of 600 kilogram/hour is used at both locations. The monthly total distances for infectious waste collection are 24,055.24 and 38,401.88 kilometers, respectively, and the lowest total cost is 6,268,970.40 baht per month.

Picking-replenishment synchronization for robotic forward-reserve warehouses

Forward-reserve strategy is commonly applied when processing a large number of small orders. This paper considers robotic forward-reserve warehouses, where pick locations are brought to workers by mobile robots in the forward area. We treat the critical problem of unsatisfactory efficiency in the robotic forward area. A picking-replenishment synchronization mechanism (PRSM) is thereby proposed, which optimally attains a balance between replenishment efforts and picking efficiency. The resulting problem is formulated and solved by a tailored variable neighborhood search procedure integrated with a divide-and-conquer paradigm. Numerical results reveal remarkable benefits of PRSM over the conventional random schemes under different scenarios.

Dual Probability Learning Based Local Search for the Task Assignment Problem

The task assignment problem (TAP) is concerned with assigning a set of tasks to a set of agents subject to the limited processing and memory capacities of each agent. The objective to be minimized is the total assignment cost and total communication cost. TAP is a relevant model for many practical applications, yet solving the problem is computationally challenging. Most of the current metaheuristic algorithms for TAP adopt population-based search frameworks, whose search behaviors are usually difficult to analyze and understand due to their complex features. In this work, unlike previous population-based solution methods, we concentrate on a single trajectory stochastic local search model to solve TAP. Especially, we consider TAP from the perspective of a grouping problem and introduce the first probability learning-based local search algorithm for the problem. The proposed algorithm relies on a dual probability learning procedure to discover promising search regions and a gain-based neighborhood search procedure to intensively exploit a given search region. We perform extensive computational experiments on a set of 180 benchmark instances with the proposed algorithm and the general mixed integer programming solver CPLEX. We assess the composing ingredients of the proposed algorithm to shed light on their impacts on the performance of the algorithm. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by the problem of program modules designing and task allocation in parallel and distribution systems. It can also be applied to deal with job (task) grouping problems in practical industrial applications. This article presents a novel and effective learning-based local search algorithm to obtain high-quality solutions for the considered problem. The results of numerical experiments and comparisons show that our algorithm can achieve good search performances on problem instances of different scales and difficulties. Afterward, we use the proposed solution method to solve a real-life open-order slab assignment problem, which is derived from the production planning of silicon steel for an iron and steel company. The learning techniques of the proposed algorithm are of general interest and can be used in search algorithms for solving other real-life optimization problems with grouping features. For future research, we will design solution methods based on these learning techniques to address other practical optimization problems.

Hybrid Bees Approach based on Improved Search Sites Selection by Firefly Algorithm for Solving Complex Continuous Functions

The Bees Algorithm (BA) is a recent population-based optimization algorithm, which tries to imitate the natural behavior of honey bees in food foraging. This meta-heuristic is widely used in various engineering fields. However, it suffers from certain limitations. This paper focuses on improvements to the BA in order to improve its overall performance. The proposed enhancements were applied alone or in pair to develop enhanced versions of the BA. Three improved variants of BA were presented: BAMS-AN, HBAFA and HFBA. The new BAMS-AN includes memory scheme in order to avoid revisiting previously visited sites and an adaptive neighborhood search procedure to escape from local optima during the local search process. HBAFA introduces the Firefly Algorithm (FA) in local search of BA to update the positions of recruited bees, thus increasing exploitation in each selected site. The third improved BA, i.e. HFBA, employs FA to initialize the population of bees in the BA for a best exploration and to start the search from more promising regions of the search space. The proposed enhancements to the BA have been tested using several continuous benchmark functions and the results have been compared to those achieved by the standard BA and other optimization techniques. The experimental results indicate that the improved variants of BA outperform the standard BA and other algorithms on most of the benchmark functions. The enhanced BAMS-AN performs particularly better than others improved BAs in terms of solution quality and convergence speed.

A genetic algorithm with neighborhood search procedures for unrelated parallel machine scheduling problem with sequence-dependent setup times

PurposeThe purpose of this paper is to present a hybrid meta-heuristic based on genetic algorithms (GAs), simulated annealing, variable neighborhood descent and path relinking for solving the variant of the unrelated parallel machine scheduling problem considering sequence-dependent setup times.Design/methodology/approachThe authors carried out computational experiments on literature problem instances proposed by Vallada and Ruiz (2011) and Arnaout et al. (2010) to test the performance of the proposed meta-heuristic. The objective function adopted was makespan minimization, and the authors used relative deviation, average and population standard deviation as performance criteria.FindingsThe results indicate the competitivity of the proposed approach and its superiority in comparison with several other algorithms. In small instances proposed by Vallada and Ruiz (2011) and on small and large instances proposed by Arnaout et al. (2010), the proposed approach presented the best results in most tested problem instances.Practical implicationsIn small instances proposed by Vallada and Ruiz (2011) and on small and large instances proposed by Arnaout et al. (2010), the proposed approach presented the best results in most tested problem instances.Originality/valueThe proposed approach presented high-quality results, with an innovative hybridization of a GA and neighborhood search algorithms, tested in diverse instances of literature. Furthermore, the case study demonstrated that the proposed approach is recommended for solving real-world problems.