Greedy Randomized Adaptive Search Procedure Research Articles

An improved GRASP method for the multiple row equal facility layout problem

As it is well documented in the literature, an effective facility layout design of a company significantly increases throughput, overall productivity, and efficiency. Symmetrically, a poor facility layout results in increased work-in process and manufacturing lead time. In this paper we focus on the Multiple Row Equal Facility Layout Problem (MREFLP) which consists in locating a given set of facilities in a layout where a maximum number of rows is fixed. We propose a Greedy Randomized Adaptive Search Procedure (GRASP), with an improved local search that relies on an efficient calculation of the objective function, and a probabilistic strategy to select those solutions that will be improved. We conduct a through preliminary experimentation to investigate the influence of the proposed strategies and to tune the corresponding search parameters. Finally, we compare our best variant with current state-of-the-art algorithms over a set of 552 diverse instances. Experimental results show that the proposed GRASP finds better results spending much less execution time.

A modified artificial bee colony algorithm for the dynamic ride-hailing sharing problem

Ride-hailing sharing involves grouping ride-hailing customers with similar trips and time schedules to share the same ride-hailing vehicle to reduce their total travel cost. With the current information and communication technology, ride-hailing customers and drivers can be matched in real-time via a ride-hailing platform. This paper formulates a dynamic ride-hailing sharing problem that simultaneously maximizes the number of served customers, minimizes the travel cost and travel time ratios, and considers the capacity, time window, and travel cost constraints. The travel cost ratio is the ratio of actual passengers’ fare to the passengers’ fare without ride-hailing sharing, whereas the travel time ratio is defined as the actual travel time (including waiting time) over the maximum allowable travel time. To solve the dynamic problem, it is divided into many small and continuous static subproblems with an equal time interval. Each subproblem is solved by a modified artificial bee colony (MABC) algorithm with path relinking, while the contraction hierarchies and vantage point tree are used to determine the shortest path and accelerate the algorithm, respectively. Problem properties and the performance of the proposed solution method are demonstrated using large-scale real-time data from Didi that is the largest ride-hailing company in China. The proposed method is shown to outperform the benchmark, i.e., greedy randomized adaptive search procedure (GRASP) with path relinking. The proposed method also performs better when the length of each time interval is longer, and the tolerance for the incremental travel time caused by detours is higher. We also demonstrate that (a) considering both travel cost and travel time ratios in the objective can achieve a better sharing percentage, and balance the increase in the travel time ratio and the decrease in the travel cost ratio compared with the objective that misses either travel time or the travel cost ratio; and (b) the passengers can gain a large out-of-pocket cost saving in the case of ride-hailing sharing while enduring a relatively small increase in travel time compared with the case without ride-hailing sharing.

Reactive GRASP for the Prize-collecting Covering Tour Problem

This paper presents a Greedy Randomized Adaptive Search Procedure (GRASP) for the Prize-Collecting Covering Tour Problem (PCCTP), which is the problem of finding a route for traveling teams that provide services to communities geographically distant from large urban locations. We devised a novel hybrid heuristic by combining a reactive extension of the GRASP with Random Variable Neighborhood Search (VND) meta-heuristic for the purpose of solving the PCCTP. Computational experiments were conducted on a PCCTP benchmark from the literature, and the results demonstrate our approach provides a significant improvement in solving PCCTP and comparable with the state-of-the-art, mainly regarding the computational processing time.

Multiobjective optimization for complex flexible job-shop scheduling problems

In this paper, we are concerned with the resolution of a multiobjective complex job-shop scheduling problem stemming from semiconductor manufacturing. To produce feasible and industrially meaningful schedules, this paper extends the recently proposed batch-oblivious approach by considering unavailability periods and minimum time lags and by simultaneously optimizing multiple criteria that are relevant in the industrial context. A novel criterion on the satisfaction of production targets decided at a higher level is also proposed. Because the solution approach must be embedded in a real-time application, decision makers must express their preferences before the optimization phase. In addition, a preference model is introduced where trade-off is only allowed between some criteria. Two a priori multiobjective extensions of Simulated Annealing are proposed, which differ in how the simultaneous use of a lexicographic order and weights is handled when evaluating the fitness. A known a posteriori approach of the literature is used as a benchmark. All the metaheuristics are embedded in a Greedy Randomized Adaptive Search Procedure. The different versions of the archived GRASP approach are compared using large industrial instances. The numerical results show that the proposed approach provides good solutions regarding the preferences. Finally, the comparison of the optimized schedules with the actual factory schedules shows the significant improvements that our approach can bring.

Heuristics Applied to Minimization of the Maximum-Diameter Clustering Problem

This paper introduces two heuristic algorithms for the Maximum-Diameter Clustering Problem (MDCP), based on the Biased Random-Key Genetic Algorithm (BRKGA) and the Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristics. This problem consists of finding k clusters that minimize the largest within-cluster distance (diameter) among all clusters. The MDCP is classified as NP-hard and presents increased difficulty when attempting to determine the optimal solution for any instance. The results obtained in the experiments using 50 well-known instances indicate a good performance of proposed heuristics, that outperformed both three algorithms and an integer programming model from the literature.

The Concept of a Novel Path Planning Strategy for Wire + Arc Additive Manufacturing of Bulky Parts: Pixel

An innovative trajectory strategy was proposed and accessed for wire arc additive manufacturing (WAAM), applicable to different and more complex geometries, rather than being a single solution. This strategy, named Pixel, can be defined as a complex multitask procedure to carry out optimized path planning, whose operation is made through computational algorithms (heuristics), with accessible computational resources and tolerable computational time. The model layers are fractioned in squared grids, and a set of dots is systematically generated and distributed inside the sliced outlines, resembling pixels on a screen, over which the trajectory is planned. The Pixel strategy was based on creating trajectories from the technique travelling salesman problem (TSP). Unlike existing algorithms, the Pixel strategy uses an adapted greedy randomized adaptive search procedure (GRASP) metaheuristic, aided by four concurrent trajectory planning heuristics, developed by the authors. Interactions provide successive trajectories from randomized initial solutions (global search) and subsequent iterative improvements (local search). After all recurrent loops, a trajectory is defined and written in machine code. Computational evaluation was implemented to demonstrate the effect of each of the heuristics on the final trajectory. An experimental evaluation was eventually carried out using two different not easily printable shapes to demonstrate the practical feasibility of the proposed strategy.

A Metaheuristic for the Bounded Single-Depot Multiple Traveling Repairmen Problem

Multiple Traveling Repairmen Problem (mTRP) is a class of NP-hard combinatorial optimization problems which has many practical applications. In this paper, a general variant of mTRP, also known as Bounded Single-Depot Multiple Traveling Repairmen Problem (Bounded-mTRP) is introduced. In Bounded-mTRP problem, fleet of identical vehicles is dispatched to serve a set of customers. Each vehicle that starts from the depot is only allowed to visit the number of customers within a predetermined interval and each customer must be visited exactly once. Such restrictions appear in real-life applications where the purpose is to have a good balance of workloads for the repairmen. The goal is to find the order of customer visits that minimizes the sum of waiting times. In our work, we propose a metaheuristic algorithm which is mainly based on the principles of Greedy Randomized Adaptive Search Procedure (GRASP) and Variable Neighborhood Search (VNS) to solve the problem. GRASP is used to build an initial solution in a construction phase. In a cooperative way, VNS is employed to generate various neighborhoods in an improvement phase, therefore, it can prevent the search to escape from local optimal. In addition, we also introduce a new novel neighborhoods' structure in VNS for the problem. Extensive numerical experiments on benchmark instances show that our algorithm can reach the optimal solutions for the problems with 50 vertices in a reasonable amount of time. Moreover, the new best known solutions can be found in comparison with the state-of-the-art metaheuristic algorithms.

The secure time-dependent vehicle routing problem with uncertain demands

This paper addresses the transportation of valuable goods in which security carriers are interested to optimize the operating costs and the vehicle routes’ security. In real operations, route planning and scheduling are normally performed manually based on individual experience. Hereupon, an optimizing approach should be developed to target the robbery risk reduction and the distribution network’ operational costs. Facing the dangerous nature of operations, some considerations play an important role, including demand fluctuations and traffic congestion of the urban environment. To handle these issues, we respectively benefit from the robust optimization theory and considering time-dependent travel speeds with satisfying the “first-in-first-out” property. This paper proposes a rich vehicle routing problem denoted by the secure time-dependent vehicle routing problem with time windows including pickup and delivery with uncertain demands (S-TD-VRPTWPD-UD). A mathematical formulation and an efficient solution approach combining the greedy randomized adaptive search procedure (GRASP) and the iterated local search (ILS) are developed to minimize the predictability of route plans using an integrated risk index, besides the travel costs. Extensive computational experiments on this problem are performed to analyze the impact of the demand uncertainty and the speed time-dependency and to show the efficiency of the GRASP×ILS implementation. The results show the significant improvements due to the time-dependency as well as the extra cost of protecting the model against the worst-case scenario of demand requests by deriving the robust counterpart of the S-TD-VRPTWPD-UD.

Household Energy Management

Ensuring flexibility and security in power systems requires the use of appropriate management measures on the demand side. The article presents the results of work related to energy management in households in which renewable energy sources (RES) can be installed. The main part of the article is about the developed elastic energy management algorithm (EEM), consisting of two algorithms, EEM1 and EEM2. The EEM1 algorithm is activated in time periods with a higher energy price. Its purpose is to reduce the power consumed by the appliances to the level defined by the consumer. In contrast, the EEM2 algorithm is run by the Distribution System Operator (DSO) when peak demand occurs. Its purpose is to reduce the power of appliances in a specified time period to the level defined by the DSO. The optimization tasks in both algorithms are based on the Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic algorithm. The EEM1 and EEM2 algorithms also provide energy consumer comfort. For this purpose, both algorithms take into account the smart appliance parameters proposed in the article: sections of the working devices, power reduction levels, priorities and enablingof time shifting devices. The EEM algorithm in its operation also takes into account the information about the production of power, e.g., generated by the photovoltaic systems. On this basis, it makes decisions on the control of smart appliances. The EEM algorithm also enables inverter control to limit the power transferred from the photovoltaic system to the energy system. Such action is taken on the basis of the DSO request containing the information on the power limits. Such a structure of EEM enables the balancing of energy demand and supply. The possibility of peak demand phenomenon will be reduced. The simulation and experiment results presented in the paper confirmed the rationality and effectiveness of the EEM algorithm.

A GRASP-based algorithm for solving the emergency room physician scheduling problem

This paper addresses a physician scheduling problem in an Emergency Room (ER) requiring a long-term work calendar to allocate work days and types of shift among all the doctors. The mathematical model is created without simplifications, using the real calendar, including holidays. This precludes the possibility of cyclic-type solutions, and involves numerous and varied constraints (demand, workload, ergonomics, fairness, etc.). An effective solution to this very difficult practical problem cannot be obtained, for large instances, with exact solution methods. We formulate a mathematical representation of a real-world ER physician scheduling problem featuring a hybrid algorithm combining continuous linear programming with a greedy randomized adaptive search procedure (GRASP). Linear programming is used to model a general physician-demand covering problem, where the solution is used to guide the construction phase of the GRASP, to obtain initial full schedules for subsequent improvement by iterative application of Variable Neighborhood Descent Search (VNDS) and Network Flow Optimization (NFO). A computational study shows the superiority of our approach over the Integer Linear Programming method in a set of instances of varying size and difficulty inspired by a real setting. The methodology is embedded in a software tool for generating one-year-ahead physician schedules for a local ER. These solutions, which are now in use, outperform the manually-created schedules used previously.

Metaheuristics for the distance constrained generalized covering traveling salesman problem

In this work, we present an extension of the generalized covering salesman problem as distance constrained generalized m-covering salesman problem. Given a set of vertices including a depot, facilities, customer locations and demand associated with each customer location, the objective is to determine an optimal tour of each salesman such that the total covered demand is maximized and the tour length is minimized. A bi-objective mixed-integer programming model is formulated for the problem. The proposed model is solved using GUROBI 8.0 solver’s in-built hierarchical optimization approach. However, the computational complexity of the problem demands a specialized solution approach. To solve the problem efficiently, we propose two metaheuristics ant colony optimization (ACO) algorithm and greedy randomized adaptive search procedure (GRASP). Extensive computational experiments were performed using the benchmark instances from the literature. The results of computational experiments show the efficiency and effectiveness of the proposed metaheuristics algorithms. Although, the GRASP metaheuristics outperform the ACO algorithm in case of medium and large size instances.

QoS based deliver model of the packages transportation by the passenger train and solution algorithm

In recent years, statistics show that the percentage of household consumption in GDP is getting higher and higher. One of the subsequent influences is that the transport demand for packages has increased sharply. Hence it is very necessary to propose diverse transport organization modes in accordance with the different situation in different countries. A kind of new transportation mode, multi-package multi-train pickup and delivery problem with time window (MPMT-PDPTW) is proposed in this paper. It aims to achieve express package transportation with minimum cost and maximize utilization of luggage car of a passenger train at the same time. Considering the multiple constraints, such as limited carrying capacity, fixed departing and accepting time, we define the quality of service (QoS) as the evaluation criteria for package express transportation by the passenger train. A kind of meta-heuristic algorithm, greedy randomized adaptive search procedure (GRASP), is designed to make full use of the redundant capacity of railway luggage car. An example is designed according to the railway passenger train timetable released by China Railway Corporation (CRC), the assignment schemes of packages at different railway stations reveal that the new transportation mode proposed in this paper is feasible and practical in package express transportation, and also has advantages in speed comparing with the highway and in transport cost over the airline.

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.

An Optimization Framework for Solving Integrated Planning and Scheduling Problems for Dense Energy Carriers

Abstract Due to rapid population growth, the global demand of energy and water resources are accelerating. Simultaneously, there is a global trend to transition to renewable energy systems. Recently, researchers have begun to investigate how green dense energy carriers (DECs) can be apart of this transition. In this work, we present an optimization framework for solving large-scale supply chain problems and we apply it to explore the economic and environmental impacts of DECs. Specifically, we look at utilizing DECs to transport renewable energy produced in areas with high solar and wind potentials to regions with low renewable potential. To reduce the computational burden of the large-scale optimization problem, we have developed a greedy randomized adaptive search procedure (GRASP). The GRASP leverages the linear programming (LP) relaxation of the problem to generate feasible solutions. We have found that the GRASP is able to reduce the computational time by approximately two orders of magnitude as compared to a commercial grade mixed-integer linear programming (MILP) solver ran out-of-the-box on large-scale instances.

A metaheuristic to support the distribution of COVID-19 vaccines

Paper aims The aim is to develop a vaccine distribution routing model (VDRM) in order to support governments to mitigate the pandemic caused by COVID-19. Originality As far as we know, no metaheuristics has been developed for vaccine distribution, and specifically, to support the Brazilian government. Research method A metaheuristic is developed based on the combination and adaptation of GRASP (Greedy Randomized Adaptive Search Procedure) with VND (Variable Neighborhood Descent), considering different refinement operators. Finally, as a way of validating the model, a numerical application in the state of Pernambuco (Brazil) was performed. Main findings Metaheuristic proved to be effective for developing adequate planning for the allocation of ampoules with vaccines to combat COVID-19. Effective analysis was obtained in the evaluation of the proposed algorithm, both in terms of computational effort and the quality of the final solution. An efficiency of approximately 75% was obtained in relation to the current distribution procedure adopted by the state of Pernambuco. Implications for theory and practice To mitigate disease, adequate logistics for transporting and distributing vaccines is essential, especially in emergency situations to face pandemic crises. Thus, the developed metaheuristic can support governments and companies in any situation demanded, making the decision of how the distribution of the ampoules will be more agile.

Joint optimization of container slot planning and truck scheduling for tandem quay cranes

This paper examines the loading operations of a new type of quay crane, the tandem quay crane (TQC), which has been designed to increase the terminal productivity by lifting more containers simultaneously. Due to the special characteristics of the TQC, more than one truck is required to serve a tandem-lift of it, and the containers handled in a tandem-lift must be loaded into two neighboring rows in the same tier of the containership. Of particular importance in schedules at the terminal is to coordinate the truck scheduling and container stowage slot plan with the TQCs, which is a key challenge in practice. This paper is an attempt to tackle this issue by developing a mixed integer linear programming (MILP) model with an objective of minimizing the completion time of the loading operation under the full utilization of the TQC. Due to the complexity of the MILP model, we then propose a model to derive lower bounds of the problem, and a greedy randomized adaptive search procedure (GRASP) to solve the problem. Computational experiments are conducted with a variety of instances. The results derived by GRASP for solving small size problems are within 0.04% of the optimal results obtained by the Gurobi. For large scale instances, GRASP outperforms the Gurobi in terms of the solution quality and computation time. Additionally, on average results derived by GRASP are within 8.2% of the lower bound. Further experiments demonstrate the advantage of the integrated optimization of container slot planning and truck scheduling for TQCs.

The constrained forward shortest path tour problem: Mathematical modeling and GRASP approximate solutions

AbstractThis paper deals with the Constrained Forward Shortest Path Tour Problem, an NP‐complete variant of the Forward Shortest Path Tour Problem. Given a directed weighted graph G = (V, A), where the set of nodes V is partitioned into clusters T1, …, TN, the aim is determining a shortest path between two given nodes, s and d, with the properties that clusters must be visited according to a given order, and each arc can be crossed at most once. We introduce a mathematical formulation of the problem, and a reduction procedure to reduce the number of variables involved in the model. Furthermore, we propose a Greedy Randomized Adaptive Search Procedure (GRASP) algorithm to solve large instances of the problem. Computational tests show that the reduction procedure is very effective and its application significantly speeds up the resolution of the model. Moreover, the computational results certify the effectiveness of GRASP that often finds the optimal solution and, in general, provides quickly high‐quality sub‐optimal solutions.

An integrated method for berth allocation and quay crane assignment to allow for reassignment of vessels to other terminals

With globalization increasing countries’ trade volumes, resource management at container terminals has become more complex. To realistically address this problem, this paper proposes a methodology to solve the berth allocation and quay crane assignment problem (BACAP) while allowing the reassignment of vessels to other terminals in a multiuser container terminal. A filtered beam search (FBS)-based heuristic, a greedy randomized adaptive search procedure (GRASP)-based heuristic, and an iterative approach are integrated to provide a solution within a reasonable time frame. Numerical experiments are conducted with realistic instances from a container terminal located in Busan, Republic of Korea. The results show that the proposed approach yields a near-optimal solution with a significantly shorter computational time, compared with a commercial solver.

A heuristic for the convex recoloring problem in graphs

AbstractWe consider a coloring as a function that assigns a color to a vertex, regardless of the color of its neighbors. In this sense, a coloring is said to be convex if every set of all same colored vertices induces a connected subgraph. The Convex Recoloring Problem finds the minimum number of recolored vertices needed to turn a coloring convex. This problem is most commonly studied considering trees due to its origins in Computational Biology, but in this paper, we focus on general graphs. We propose a heuristic based on the Greedy Randomized Adaptive Search Procedure to solve the problem. We present computational experiments for our heuristic and compare it to an Integer Linear Programming (ILP) model from the literature. In these experiments, our heuristic recolored at most one vertex more than the ILP model, and it was also able to give better solutions when the ILP model was unable to find the optimal solution within the time limit. We also introduce a set of benchmark instances for the problem.

GRASP and Iterated Local Search-Based Cellular Processing algorithm for Precedence-Constraint Task List Scheduling on Heterogeneous Systems

High-Performance Computing systems rely on the software’s capability to be highly parallelized in individual computing tasks. However, even with a high parallelization level, poor scheduling can lead to long runtimes; this scheduling is in itself an NP-hard problem. Therefore, it is our interest to use a heuristic approach, particularly Cellular Processing Algorithms (CPA), which is a novel metaheuristic framework for optimization. This framework has its foundation in exploring the search space by multiple Processing Cells that communicate to exploit the search and in the individual stagnation detection mechanism in the Processing Cells. In this paper, we proposed using a Greedy Randomized Adaptive Search Procedure (GRASP) to look for promising task execution orders; later, a CPA formed with Iterated Local Search (ILS) Processing Cells is used for the optimization. We assess our approach with a high-performance ILS state-of-the-art approach. Experimental results show that the CPA outperforms the previous ILS in real applications and synthetic instances.