Greedy Randomized Adaptive Search Procedure Research Articles

Utilizing Heuristics and Metaheuristics for Solving the Set Covering Problem

A basic combinatorial optimization problem, the Set Covering Problem (SCP) finds extensive use in computer science, operations research, and logistics, among other domains. The SCP’s goal is to determine the smallest number of subsets, or sets, needed to cover every element precisely once given a finite set of items and a collection of subsets of these elements. Numerous practical uses for the SCP exist, such as crew scheduling, truck routing, and facility locating. This paper focuses on obtaining feasible solutions, applying to the obtained solutions constructive heuristics (CH), followed by a redundancy elimination procedure to remove unnecessary sets. To further optimize the quality of the solution, a local search method is also implemented based on the First and Best improvement algorithms. Additionally, the Greedy Randomized Adaptive Search Procedure (GRASP) and Variable Neighborhood Search (VNS) metaheuristics are designed and implemented. Each implemented heuristic underwent testing across 42 instances, with the average deviation from the optimal solution calculated for each instance. The GRASP heuristic demonstrated the most favorable performance, achieving a maximum deviation of 2.26% from the optimal solution, while the VNS approach yielded a maximum deviation of 11.46% from the optimal solution at its best.

Utilizing Heuristics and Metaheuristics for Solving the Set Covering Problem

A basic combinatorial optimization problem, the Set Covering Problem (SCP) finds extensive use in computer science, operations research, and logistics, among other domains. The SCP’s goal is to determine the smallest number of subsets, or sets, needed to cover every element precisely once given a finite set of items and a collection of subsets of these elements. Numerous practical uses for the SCP exist, such as crew scheduling, truck routing, and facility locating. This paper focuses on obtaining feasible solutions, applying to the obtained solutions constructive heuristics (CH), followed by a redundancy elimination procedure to remove unnecessary sets. To further optimize the quality of the solution, a local search method is also implemented based on the First and Best improvement algorithms. Additionally, the Greedy Randomized Adaptive Search Procedure (GRASP) and Variable Neighborhood Search (VNS) metaheuristics are designed and implemented. Each implemented heuristic underwent testing across 42 instances, with the average deviation from the optimal solution calculated for each instance. The GRASP heuristic demonstrated the most favorable performance, achieving a maximum deviation of 2.26% from the optimal solution, while the VNS approach yielded a maximum deviation of 11.46% from the optimal solution at its best.

The home health care routing with heterogeneous electric vehicles and synchronization

AbstractThis paper studies the problem of heterogeneous electric vehicles, fast chargers, and synchronized jobs that have time windows in home healthcare routing and scheduling. We consider a problem that aims to establish daily routes and schedules for healthcare nurses to provide a variety of services to patients located in a scattered area. Each nurse should be assigned to an electric vehicle (EV) from a heterogeneous fleet of EVs to perform the assigned jobs within working hours. We consider three different types of EVs in terms of battery capacity and energy consumption. We aim to minimize the total cost of energy consumption, fixed nurse cost, and costs arising from the patients that cannot be served within the working day. We model the problem as a mixed integer programming formulation. We develop a hybrid metaheuristic based on a greedy random adaptive search procedure heuristic, to generate good quality initial solutions quickly, and an adaptive variable neighborhood search algorithm to generate high quality solutions in reasonable time. The hybrid metaheuristic employs a set of new advanced efficient procedures designed to handle the complex structure of the problem. Through extensive computational experiments, the performance of the mathematical model and the hybrid metaheuristic are evaluated. We conduct analyses on the robustness of the metaheuristic and the performance contribution of employing adaptive probabilities. We analyze the impact of problem parameters such as competency requirements, job duration, and synchronized jobs.

A greedy randomized adaptive search procedure for scheduling IoT tasks in virtualized fog–cloud computing

AbstractVirtualized fog–cloud computing (VFCC) has emerged as an optimal platform for processing the increasing number of emerging Internet of Things (IoT) applications. VFCC resources are provisioned to IoT applications in the form of virtual machines (VMs). Effectively utilizing VMs for diverse IoT tasks with varying requirements poses a significant challenge due to their heterogeneity in processing power, communication delay, and energy consumption. In addressing this challenge, in this article, we propose a system model for scheduling IoT tasks in VFCCs, considering not only individual task deadlines but also the system's overall energy consumption. Subsequently, we employ a greedy randomized adaptive search procedure (GRASP) to determine the optimal assignment of IoT tasks among VMs. GRASP, a metaheuristic‐based technique, offers appealing characteristics, including simplicity, ease of implementation, a limited number of tuning parameters, and the potential for parallel implementation. Our comprehensive experiments evaluate the effectiveness of the proposed method, comparing its performance with the most advanced algorithms. The results demonstrate that the proposed approach outperforms the existing methods in terms of deadline satisfaction ratio, average response time, energy consumption, and makespan.

General VNS for asymmetric vehicle routing problem with time and capacity constraints

We consider a real-life transportation problem from a hypermarket company in Serbia that consists of delivering online ordered and possibly perishable goods from a single depot to multiple customers. It can be modeled as an asymmetric vehicle routing problem that requires visiting and serving all customers using a limited number of homogeneous vehicles and taking into account time and capacity constraints. The objective function to be minimized is the total distance traveled. We provide a mixed-integer programming (MIP) formulation of the problem and develop several Local Search based metaheuristic methods exploring combinatorial formulation of the considered problem: Multistart Local Search (MLS), Greedy Randomized Adaptive Search Procedure (GRASP), and several variants of General Variable Neighborhood Search (GVNS) methods. All methods are compared on real-life instances provided by the hypermarket company and benchmark instances from the relevant literature. The obtained results show the superiority of GVNS-based methods with respect to both solution quality and running time, confirming that systematic search procedures have more success when dealing with hard optimization problems.

Solving the Set Covering Problem with Conflicts on Sets: A new parallel GRASP

In this paper, we analyze a new variant of the well-known NP-hard Set Covering Problem, characterized by pairwise conflicts among subsets of items. Two subsets in conflict can belong to a solution provided that a positive penalty is paid. The problem looks for the optimal collection of subsets representing a cover and minimizing the sum of covering and penalty costs. We introduce two integer linear programming formulations and a quadratic one for the problem and provide a parallel GRASP (Greedy Randomized Adaptive Search Procedure) that, during parallel executions of the same basic procedure, shares information among threads. We tailor such a parallel processing to address the specific problem in an innovative way that allows us to prevent redundant computations in different threads, ultimately saving time. To evaluate the performance of our algorithm, we conduct extensive experiments on a large set of new instances obtained by adapting existing instances for the Set Covering Problem. Computational results show that the proposed approach is extremely effective and efficient providing better results than Gurobi (tackling three alternative mathematical formulations of the problem) in less than 1/6 of the computational time.

The integrated planning of outgoing coil selection for retrieval, multi-crane scheduling, and location assignment to the incoming and blocking coils in steel coil warehouses

In this paper, the problem of scheduling crane-operated warehouses in a triangle stacking style is investigated. In a steel supply chain, warehouses play a significant role in establishing a connection between the producer and the customers. Therefore, improving their performance results in a competitive advantage in the supply chain. One of the challenges of steel coil warehouses is the selection of outgoing coils out of the candidate coils for retrieval. Despite its importance, this problem has not been investigated in the studies relevant to steel coil warehouses. In this study, in addition to the selection of outgoing coils, sequencing of the operations on the incoming, outgoing, and blocking coils, location assignment to the incoming and blocking coils, and crane scheduling are considered in an integrated manner. First, a mixed integer linear programming model is proposed. Further, a Greedy heuristic algorithm and two metaheuristics are developed to solve large-sized instances of the problem. Metaheuristics include a Greedy Randomized Adaptive Search Procedure (GRASP) and a hybrid algorithm that combines Ant Colony System with the GRASP (ACS-GRASP). Finally, performances of the proposed algorithms are compared over randomly generated instances as well as instances which are generated based on the real data obtained from Isfahan’s Mobarakeh Steel Company. To conduct this analysis, various performance evaluation metrics are applied. Computational results indicate that ACS-GRASP converges slower than GRASP, but is more reliable and efficient. On the other hand, in large-sized instances, the Greedy algorithm runs extremely fast and can find solutions which are comparable to the metaheuristic solutions.

A Hybrid Clustered Ant Colony Optimization Approach for the Hierarchical Multi-Switch Multi-Echelon Vehicle Routing Problem with Service Times

In this paper, the Hierarchical Multi Switch Multi Echelon Vehicle Routing Problem with Service Times (HMSME-VRP-ST) is presented. This novel problem considers distribution applications in which goods are delivered either directly from a central depot or through intermediate facilities called switch points. Commodities are loaded into interchangeable containers called swap bodies at the central depot, and can be transferred from one vehicle to another at the switch points. The goal is to minimize fixed and variable costs of the vehicle fleet and swap-bodies while serving a predetermined set of customers. The routes are constrained by time and swap bodies by loading capacity. A mathematical model of the HMSME-VRP-ST is presented, and a Hybrid Clustered Ant Colony Optimization (HCACO) algorithm is proposed to address the complexity of the problem. The approach utilizes the ant-based clustering algorithm, combining the density and connectivity properties of clustering for creating promising neighborhoods with the solution construction methodology and pheromone-based memory of the Ant Colony Optimization framework. Additionally, two local search schemes based on Variable Neighborhood Descent are incorporated to further improve the generated solutions. The behavior of each HCACO variant is analyzed, and their results are compared to a Greedy Randomized Adaptive Search Procedure metaheuristic in 36 newly generated benchmarks comprising of clustered, uniformly random, and mixed clustered-random instances.

Customized GRASP for rehabilitation therapy scheduling with appointment priorities and accounting for therapist satisfaction

Physical therapy in acute care hospitals plays an important role in the rehabilitation of patients. Nevertheless, the profession must deal with staff shortages caused by a lack of potential employees and absenteeism which are results of high physical and mental workloads. The therapist shortage negatively affects the total number of daily appointments the department can fulfill. For appointments that can be successfully scheduled, continuity of care with the same therapist cannot be guaranteed for individual patients. Lack of continuity of care negatively influences the therapist's satisfaction. Therapist preferences for individual appointments in general cannot always be guaranteed when designing schedules, which also hurts satisfaction. This paper develops a multi-criteria model for the daily therapy appointment-scheduling problem. The primary objective is to minimize the total sum of priority violations for unscheduled appointments. To improve therapist satisfaction, we consider therapist preferences including continuity of care as a secondary objective. Here, our integer programming formulation aims to minimize the total sum of preference violations for scheduled appointments. We are dealing with an operational planning problem with a daily planning horizon. The operational objective is to achieve therapist schedules in at most two hours. The therapists’ schedules together need to include several hundred appointments for a planning day. Due to intractability, the developed integer program cannot provide schedules for such problem sizes. Therefore, we develop a customized Greedy Randomized Adaptive Search Procedure (GRASP) with six innovative local search operations to improve an initially constructed solution. We test the heuristic algorithm on realistic data instances. The metaheuristic provides high-quality schedules for various problem sizes in short runtimes, i.e., within minutes. Comparisons with the optimal solutions for small problem instances show very good results of the GRASP with a similar number of scheduled appointments and good adherence to continuity of care and therapist preference requirements.

Green Algorithms for Energy-efficient Distributed Flow-Shop Manufacturing Problem

Minimizing energy consumption is one of the most interesting issues in recent industrial production. Energy-efficient scheduling is a promising approach to reducing energy consumption in manufacturing systems. However, energy-efficient scheduling is a problem of great interest, especially for the Distributed permutation Flow-Shop Manufacturing Problem (DPFSMP). This paper addresses the critical challenge of energy efficiency in the industry of DPFSMP optimization, where task processing times depend closely on their position in the production line. The objective is to minimize the total energy consumption (TEC) for all machines in distributed workshops. To solve this problem, we propose two efficient constructive algorithms for energy-efficient scheduling of this type of problem with speed-dependent tasks: the Nawaz Enscore and Ham (NEH) based algorithm and the Greedy Random Adaptive Search Procedure (GRASP) based algorithm. We evaluate the performance of the two proposed algorithms on a set of benchmark problems to identify the one with the best performance. The results show that the (NEH) algorithm outperforms the GRASP algorithm in terms of energy efficiency and solution quality. In fact, the proposed algorithms can be used by manufacturers to reduce energy consumption in their production systems. This can help manufacturers save money, reduce environmental impact and improve overall sustainability.

A GRASP Approach for the Energy-Minimizing Electric Vehicle Routing Problem with Drones

This study addresses the Electric Vehicle Routing Problem with Drones (EVRPD) by implementing and comparing two variants of the Greedy Randomized Adaptive Search Procedure (GRASP). The primary objective of the EVRPD is to optimize the routing of a combined fleet of ground and aerial vehicles, with the aim of improving delivery efficiency and minimizing energy consumption, which is directly influenced by the weight of the packages. The study assumes a standardized packing system consisting of three weight classes, where deliveries are exclusively performed by drones, while ground vehicles function as mobile depots. The two employed GRASP variants vary in their methods of generating the Restricted Candidate List (RCL), with one utilizing a cardinality-based RCL and the other adopting a value-based RCL. To evaluate their performance, benchmark instances from the existing EVRPD literature are utilized, extensive computational experiments are conducted, and the obtained computational results are compared and discussed. The findings of the research highlight the considerable impact of RCL generation strategies on solution quality. Lastly, the study reports four new best-known values.

The cumulative vehicle routing problem with arc time windows

In this paper, we introduce a new variant of the cumulative Vehicle Routing Problem (cum-VRP), where certain arcs of the undirected complete graph can only be utilized within specified time constraints. The problem is referred to as the Cumulative Vehicle Routing Problem with Arc Time Windows (Cum-VRPATW) and emerges in routing situations with flow disruptions across road segments, which generally emerges from military and civilian transportation. We devise a mixed integer programming (MIP) formulation to model the problem and solve it using CPLEX. To effectively address this problem, an effective algorithm is designed. It is a hybrid algorithm that combines principles of the Greedy Randomized Adaptive Search Procedure (GRASP) and decomposition strategies reducing computational complexity. Also, we propose two indexes, the RatioIn and the RatioTWL index that can identify difficult problems. Furthermore, we compare the CPLEX results vis-a-vis the new hybrid heuristic we have developed. Computational tests on converted Solomon (1987) data sets show that the new hybrid heuristic provides extremely good performance results for the cum-VRPATW large size test problems, justifying its effectiveness and robustness.

A hybrid metaheuristic with learning for a real supply chain scheduling problem

In recent decades, research on supply chain management (SCM) has enabled companies to improve their environmental, social, and economic performance.This paper presents an industrial application of logistics that can be classified as an inventory-route problem. The problem consists of assigning orders to the available warehouses. The orders are composed of items that must be loaded within a week. The warehouses provide an inventory of the number of items available for each day of the week, so the objective is to minimize the total transportation costs and the costs of producing extra stock to satisfy the weekly demand. To solve this problem a formal mathematical model is proposed. Then a hybrid approach that involves two metaheuristics: a greedy randomized adaptive search procedure (GRASP) and a genetic algorithm (GA) is proposed. Additionally, a meta-learning tuning method is incorporated into our hybridized approach, which yields better results but with a longer computation time. Thus, the trade-off of using it is analyzed.An extensive evaluation was carried out over realistic instances provided by an industrial partner. The proposed technique was evaluated and compared with several complete and incomplete solvers from the state of the art (CP Optimizer, Yuck, OR-Tools, etc.). The results showed that our hybrid metaheuristic outperformed the behavior of these well-known solvers, mainly in large-scale instances (2000 orders per week). This hybrid algorithm provides the company with a powerful tool to solve its supply chain management problem, delivering significant economic benefits every week.

Heuristic approach for bandwidth consecutive multi-coloring problem

Bandwidth consecutive multicoloring problem is also known as a b-coloring problem. Let G = (V, E) be a graph where V is the set of vertices and E is the set of edges. Let each vertex v of V has a positive integer weight b (v) and each edge (v, w) of E has a non-negative integer weight b (v, w). A bandwidth consecutive multicoloring of a graph is a problem of assigning b (v) consecutive positive integers to each vertex v of V in such a manner that the difference between all the integers of vertex v and all the integers of vertex w is greater than b (v, w). The maximum integer assigned in this coloring is called the span of the coloring. The b-coloring is the problem of minimizing this span. No metaheuristic is proposed for general graphs so far for this problem till date as it is strongly NP-hard. In this paper, we proposed three heuristics for the problem including a greedy randomized adaptive search procedure (GRASP). The efficiency of these algorithms is tested on benchmark graphs and their performance is compared among themselves. Experimental results showed that among all three proposed heuristics, GRASP performed well for the given problem.

A two-stage data-driven metaheuristic to predict last-mile delivery route sequences

On delivery operations, vehicle routing problems regularly focus on optimizing route-solution quality. However, the real-life execution of routes often differs from the computed routing plan. Therefore, the routing algorithms should use information from historic routes and drivers’ decisions to make the planned route as similar as possible to the actual executed route. We study the problem of predicting route sequences that drivers follow in last-mile parcel delivery in the context of the 2021 Amazon Last-Mile Routing Research Challenge. We propose extracting information from historic routes using a probability estimation method that learns transition probabilities between clusters or zones, coupled with a simple yet effective two-stage Greedy Randomized Adaptive Search Procedure (GRASP) to incorporate the information from historical route data into route planning. Our GRASP includes components in the objective function that consider decisions observed on the historical route sequences supplied by Amazon. We evaluate the predicted route sequences using the score similarity metric provided in the Amazon challenge. The results show that our method obtains a similarity score of 0.0328, which is comparable to the scores achieved by the three winning teams of the Amazon challenge. The proposed method successfully uses historical routes to predict route sequences on a last-mile delivery setting.

A GRASP/VND algorithm for the energy minimizing drone routing problem with pickups and deliveries

In recent years, the growth of online markets in social media and auction websites, has resulted in a significant increase in direct trading between people. Unlike traditional commerce, which relies on a multi-layered supply chain, person-to-person transactions depend on courier companies for delivering the items, thus, it can be considered a third-party logistics scheme. The utilization of unmanned aerial vehicles (UAVs), also known as drones, is ideal for this type of commerce, as most of the traded items are small-sized and light-weight. Logistic companies are already experimenting with using drones in their delivery operations, as their benefits are both financial and environmental. This paper, introduces the Energy Minimizing Drone Routing Problem with Pickups and Deliveries (EM-DRP-PD), to address scenarios of direct trading between individuals, where the logistics company provides the courier service using drones. The EM-DRP-PD focuses on minimizing the total energy consumption of operations and accounts for the range constraints imposed by the drones, which is influenced by the weight of the packages carried. The formulation of the EM-DRP-PD is presented. Three variants of a Greedy Randomized Adaptive Search Procedure metaheuristic algorithm are implemented for solving the EM-DRP-PD. The algorithms are compared based on generated EM-DRP-PD benchmark instances ranging from 50 to 200 customers. The study compares both, energy and distance, objective approaches and discusses the results.

Metaheuristic planner for cooperative multi-agent wall construction with UAVs

This paper introduces a wall construction planner for Unmanned Aerial Vehicles (UAVs), which uses a Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic to generate near-time-optimal building plans for even large walls within seconds. This approach addresses one of the most time-consuming and labor-intensive tasks, while also minimizing workers’ safety risks. To achieve this, the wall-building problem is modeled as a variant of the Team Orienteering Problem and is formulated as Mixed-Integer Linear Programming (MILP), with added precedence and concurrence constraints that ensure bricks are built in the correct order and without collision between cooperating agents. The GRASP planner is validated in a realistic simulation and demonstrated to find solutions with similar quality as the optimal MILP, but much faster. Moreover, it outperforms all other state-of-the-art planning approaches in the majority of test cases. This paper presents a significant advancement in the field of automated wall construction, demonstrating the potential of UAVs and optimization algorithms in improving the efficiency and safety of construction projects.

Minimizing Makespan in a Permutation Flow Shop Environment: Comparison of Scatter Search, Genetic Algorithm and Greedy Randomized Adaptive Search Procedures

Solving scheduling problems enables more efficient use of production capacity. It involves defining the sequence of operations, determining the capacity of resources, and balancing workloads. Different methods, especially metaheuristics, have been used to solve these problems. This study presents the application of Scatter Search (SS), Genetic Algorithm (GA), and Greedy Randomized Adaptive Search Procedures (GRASP) for minimizing makespan in a permutation flow shop environment. In this study, the performances of these methods are compared through various test problems in the literature and a real-life problem of a company operating in the automotive sector. Study comprises 48 jobs that must be planned within a day for eight consecutive operations. In cellular manufacturing, the sequence in which each job is processed in eight operations is the same. In solving permutation flow shop scheduling problems (PFSP), one of the NP-hard problems, meta-heuristic methods are widely applied due to their successful results. From this point of view, SS, GA, and GRASP are employed in this study, and their performances are compared.

Exact and metaheuristic approaches to solve the integrated production scheduling, berth allocation and storage yard allocation problem

This work studies an industrial complex specialized in producing and exporting fertilizers. The integration of the production scheduling, berth allocation, and storage yard allocation decisions is necessary to improve the overall performance of the complex as these problems are interrelated. Exact and metaheuristic approaches are proposed to solve the problem. First, a mixed-integer linear formulation along with a branch-and-cut procedure are proposed. The numerical experiments show that these exact methods solve small-sized instances optimally but fail to provide good quality solutions for industrial-sized instances. Therefore, a multi-start GRASP-ILS is proposed where initial solutions are constructed using a greedy randomized adaptive search procedure (GRASP) and improved using an iterated local search algorithm (ILS). The metaheuristic approach is based on a disjunctive graph representation and additional conditions to respect the storage yard constraints and other operational constraints. The results show that the multi-start GRASP-ILS can be effectively used to solve larger instances of the problem.

Fixed set search applied to the clique partitioning problem

The Clique Partitioning Problem (CPP) seeks to decompose a set of vertices into disjoint subsets (cliques) maximizing the sum of edge weights over all the cliques. The interest for the CPP comes from the fact that it represents well many practical problems from areas like data mining, engineering, bio-informatics, etc. To address this NP-hard combinatorial optimization problem, the novel fixed set search (FSS) metaheuristic is applied. This is performed, firstly, by developing a greedy randomized adaptive search procedure (GRASP) using a new type of neighborhood in the local search. The GRASP is further extended to the FSS by adding a learning mechanism. The FSS application to the CPP provides a new approach for generating fixed sets for problems with solution symmetries. This approach opens the application of the FSS to new families of combinatorial optimization problems. The conducted computational experiments show that the FSS significantly outperforms state-of-the-art metaheuristics for the CPP. The proposed approach obtains a large number of new best solutions for commonly used CPP test instances.