Greedy Randomized Adaptive Search Procedure Research Articles

Greedy randomized adaptive search procedure for supply chain network resilience optimization considering risk diffusion

Supply disruption risks occurring at individual nodes in a supply chain network can propagate to other nodes through the links in the network affecting the overall performance of the supply chain. In this context, mitigation strategies are commonly implemented to respond to these disruptions and improve the resilience of the supply chain. This study proposes a mathematical model to optimize the resilience of the supply chain network by selecting critical nodes and identifying the appropriate type of mitigation strategies to be implemented under a limited budget. The resilience of the supply chain network is evaluated by the degree of propagation of risks from individual nodes to the entire supply chain network, using a risk diffusion model where a disruption risk decreases exponentially as it progresses downstream in the supply chain. A greedy randomized adaptive search procedure (GRASP)-based solution approach was developed to solve the proposed formulation and its performance was compared to other solution procedures for different scenarios showing it to be the most effective and robust. A summary of the insights developed from the solutions obtained for the different scenarios is presented along with directions for future research.

Strategic placement of volunteer responder system defibrillators.

Volunteer responder systems (VRS) alert and guide nearby lay rescuers towards the location of an emergency. An application of such a system is to out-of-hospital cardiac arrests, where early cardiopulmonary resuscitation (CPR) and defibrillation with an automated external defibrillator (AED) are crucial for improving survival rates. However, many AEDs remain underutilized due to poor location choices, while other areas lack adequate AED coverage. In this paper, we present a comprehensive data-driven algorithmic approach to optimize deployment of (additional) public-access AEDs to be used in a VRS. Alongside a binary integer programming (BIP) formulation, we consider two heuristic methods, namely Greedy and Greedy Randomized Adaptive Search Procedure (GRASP), to solve the gradual Maximal Covering Location (MCLP) problem with partial coverage for AED deployment. We develop realistic gradually decreasing coverage functions for volunteers going on foot, by bike, or by car. A spatial probability distribution of cardiac arrest is estimated using kernel density estimation to be used as input for the models and to evaluate the solutions. We apply our approach to 29 real-world instances (municipalities) in the Netherlands. We show that GRASP can obtain near-optimal solutions for large problem instances in significantly less time than the exact method. The results indicate that relocating existing AEDs improves the weighted average coverage from 36% to 49% across all municipalities, with relative improvements ranging from 1% to 175%. For most municipalities, strategically placing 5 to 10 additional AEDs can already provide substantial improvements.

Modeling and geometrization in PGNAA

Prompt Gamma Neutron Analysis Activation is a widely used technique for analyzing materials. This technique defines graphs (reference spectrum collection, or libraries) of spectral intensity as a function of energy (channels) for the elements inserted in a sample. The Monte Carlo Library Least Squares (MCLLS) is the dominant approach in the PGNAA technique. The main difficulties faced in the MCLLS domain are (1) numerical instabilities in the least-squares stage (Library Least Squares (LLS)); (2) overdetermination of the system of equations; (3) linear dependence in the libraries; (4) gamma radiation scattering; (5) high computational costs. The present work proposes optimizing the LLS module to face the abovementioned problems using the Greedy Randomized Adaptive Search Procedure (GRASP) and Continuous Greedy Randomized Adaptive Search Procedure (CGRASP) algorithms. The search for the spectral count peaks of the libraries leads to a partitioning of the data before applying the GRASP and CGRASP algorithms. The methodological procedures also address estimating the spectral counts of an unknown library possibly integrates the sample. The results show (1) efficient partitioning of the input data (2) evidence of suitable precision of the weight fractions of the libraries that make up the sample (average precision of the order of 3.16% against 8.8% of other methods); (3) success in the approximation and estimation of the unknown library (average precision of 4.25%) present in the sample. Our method proved to be promising in improving the determination of percentage count fractions by the least-squares module and showing the advantages of data partitioning.

Reactive tabu search and mixed-integer linear programming for multi-day assignment, scheduling, and routing problems of specialised education and home-care services

In this paper, we address the Multi-Day Assignment, Scheduling, and Routing Problem for Specialized Education and Home Care Services (SEHCS-MASRP), which involves heterogeneous employees and missions, posing a complex optimisation challenge. To tackle this, we propose a novel Mixed-Integer Linear Programming (MILP) model that considers employee qualifications, service requirements, scheduling constraints, routing decisions, and multiple objectives across the planning horizon. Additionally, we develop two metaheuristic approaches: a Reactive Tabu Search (RTS) algorithm incorporating either a Probabilistic Greedy Heuristic (PGH) or a Greedy Randomized Adaptive Search Procedure (GRASP) for initial solutions and a tailored genetic algorithm (GA). The three approaches aim to minimise wasted and overtime hours, total travel distances, and the number of assignments with an unsatisfied specialty while balancing wasted hours, overtime hours, and travel distances among the employees. Gurobi uses the proposed MILP model to find the optimal solutions, which are then compared with RTS and GA results across various instance sizes based on real-life SEHCS scenarios. Experimental results demonstrate the efficiency of MILP, RTS, and GA. MILP achieves proven optimal solutions for smaller to large instances. For huge instances, RTS generates high-quality solutions within reasonable computing times, outperforming GA performance. Notably, RTS consistently finds solutions within 5% of optimality for most instances.

A GRASP algorithm for the concrete delivery problem

This paper addresses a novel variant of the Concrete Delivery Problem (CDP), which involves the efficient scheduling of ready-mixed concrete deliveries to construction sites while balancing the conflicting goals of minimizing transportation costs and maximizing customer satisfaction. In this study, we propose an exact formulation and a heuristic approach based on the Greedy Randomized Adaptive Search Procedure (GRASP) to tackle this challenging CDP variant. This variant introduces realistic side constraints, including driver working shifts, a minimum driver working time, and overtime penalties. Additionally, it considers the case where customers may request multiple types of concrete delivered within the same time window. We assess the performance of our heuristic using new instances generated for this problem and provide a comparative analysis with another CDP variant from the literature to demonstrate its effectiveness.

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.

Strategic flood impact mitigation in developing countries’ urban road networks: Application to Hanoi

Due to climate change, the frequency and scale of flood events worldwide are increasing dramatically. Flood impacts are especially acute in developing countries, where they often revert years of progress in sustainable development and poverty reduction. This paper introduces an optimization-based decision support tool for selecting cost-efficient flood mitigation investments in developing countries’ urban areas. The core of the tool is a scenario-based, multi-period, bi-objective Mixed Integer Linear Programming model which minimizes infrastructure damage and traffic congestion in urban road networks. The tool was developed in collaboration with Vietnamese stakeholders (e.g., local communities and government authorities), and integrates data and inputs from other disciplines, including social science, transport economics, climatology and hydrology. A metaheuristic, combining a Greedy Randomized Adaptive Search Procedure with a Variable Neighborhood Descent algorithm, is developed to solve large scale problem instances. An extensive computational campaign on randomly generated instances demonstrates the efficiency of the metaheuristic in solving realistic problems with hundreds of interdependent flood mitigation interventions. Finally, the applicability of the interdisciplinary approach is demonstrated on a real case study to generate a 20-year plan of mitigation investments for the urban area of Hanoi. Policy implications and impacts of the study are also discussed.

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.