Greedy Randomized Adaptive Search Procedure Research Articles

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.

The greedy randomized adaptive search procedure method in formulating set covering model on cutting stock problem

This study aims to apply the Greedy Randomized Adaptive Search Procedure method in formulating the Set Covering model. Selected cutting patterns in the Cutting Stock Problem are generated by the Greedy Randomized Adaptive Search Procedure method and then formulating them to the Set Covering model. This study used a single stock with four types of items. The Greedy Randomized Adaptive Search Procedure method can show the maximum number of cutting patterns with minimum trim loss. Based on data analysis, it can be concluded that the Greedy Randomized Adaptive Search Procedure method will give different patterns depends on the number of the upper limits of demand. The Set Covering model, which was solved by LINGO 13.0, showed the optimal cutting patterns with minimum trim loss, but still has the lack of the product in one of the items.

EFFICIENT METAHEURISTIC ALGORITHMS FOR THE MULTI-STRIPE TRAVELLING SALESMAN PROBLEM

The Multi-stripe Travelling Salesman Problem (Ms-TSP) is an extension of the Travelling Salesman Problem (TSP). In the \textit{q}-stripe TSP with $q \geq 1$, the objective function sums the costs for travelling from one customer to each of the next \textit{q} customers along the tour. The resulting \textit{q}-stripe TSP generalizes the TSP and forms a special case of the Quadratic Assignment Problem. To solve medium and large size instances, a metaheuristic algorithm is proposed. The proposed algorithm has two main components, which are construction and improvement phases. The construction phase generates a solution using Greedy Randomized Adaptive Search Procedure (GRASP) while the optimization phase improves the solution with several variants of Variable Neighborhood Search, both coupled with a technique called Shaking Technique to escape from local optima. In addition, Adaptive Memory is integrated into our algorithms to balance between the diversification and intensification. To show the efficiency of our proposed metaheuristic algorithms, we extensively experiment on benchmark instances. The results indicate that the developed algorithms can produce efficient and effective solutions at a reasonable computation time.

Local search metaheuristic for solving hybrid flow shop problem in slabs and beams manufacturing

Solving optimization problems in the modern manufacturing industry is one of the most attractive areas of operational research. In this paper, we propose an industrial optimization case of slabs and beams production problem. The suggested approach consists in modeling the process as a hybrid flow shop with unrelated parallel machines under constraints of sequence dependent setup time. Jobs launched in production are of different characteristics and require a machine preparation time at each phase during their production cycle. The goal is to minimize the total tardiness of all jobs when they are completed on the last stage. The hybrid flow shop problem is considered as one of the NP-hard issues since it consists of at least two stages. To solve numerically this problem, we propose two methods, the iterative local search (ILS) and the iterated greedy (IG) metaheuristics. In addition, we suggest two new improvements, the first relates to the initial step while the second concerns the steps of the neighborhood exploration. In the initial phase, we consider an initial solution set generated from the priority rules whose scheduling is ensured by the Nawaz-Enscore-Ham (NEH) algorithm and the greedy randomized adaptive search procedure (GRASP). In the second phase, we suggest a new version of exploration of the neighborhood. In fact, from a single solution, we will generate a set of neighboring solutions and we will choose the best solution. In this new resolution approach, we develop a total of twelve algorithms based on neighborhood exploration. We note that the proposed algorithms are hybrid metaheuristics and are among the most powerful optimization algorithms in local search. A simulation study is conducted to verify the effectiveness of the suggested algorithms.This simulation is performed on a set of instances by varying the number of jobs, the number of machines per stage and the number of stages. We find that the IG algorithm based on NEH initialization heuristic gives good results in terms of quality and convergence time to the best solution.

Greedy randomized adaptive search for dynamic flexible job-shop scheduling

Dynamic flexible job shop scheduling problem is studied under the events such as new order arrivals, changes in due dates, machine breakdowns, order cancellations, and appearance of urgent orders. This paper presents a constructive algorithm which can solve FJSP and DFJSP with machine capacity constraints and sequence-dependent setup times, and employs greedy randomized adaptive search procedure (GRASP). Besides, Order Review Release (ORR) mechanism and order acceptance/rejection decisions are also incorporated into the proposed method in order to adjust capacity execution considering customer due date requirements. The lexicographic method is utilized to assess the objectives: schedule instability, makespan, mean tardiness and mean flow time. A group of experiments is also carried out in order to verify the suitability of the GRASP in solving the flexible job shop scheduling problem. Benchmark problems are formed for different problem scales with dynamic events. The event-driven rescheduling strategy is also compared with periodical rescheduling strategy. Results of the extensive computational experiment presents that proposed approach is very effective and can provide reasonable schedules under event-driven and periodic scheduling scenarios.

Metaheuristics applied for storage yards allocation in an Amazonian sustainable forest management area

In the sustainable management of Amazonian forests, it is essential to carry out the optimal planning of logging infrastructures to reduce costs and environmental impacts. However, there is a high degree of complexity due to the number of variables involved. Among these infrastructures, wood storage yards are of utmost importance as they directly influence the opening of forest roads and trails. The objective of this research was to evaluate the allocation of wood storage yards through exact solution and metaheuristics in a forest management area. The study area was a native forest under sustainable forest management regime located in the Brazilian Amazon. Three instances were formulated involving 5947 trees and 3172 wood storage yards facilities. We used a binary integer programming model solved by CPLEX and the metaheuristics Greedy Randomized Adaptive Search Procedure (GRASP), Tabu Search (TS), Variable Neighborhood Search (VNS) and Simulated Annealing (SA). GAP values increased as a function of instances. Although all metaheuristics obtained significant solutions with shorter processing times, only SA obtained feasible solutions in all executions for all three instances. In general, the metaheuristics were efficient in obtaining feasible solutions faster than CPLEX, which represents the feasibility of the planning of allocation storage large areas, and without significant losses of best-known solution. The SA presented the best performance in the three evaluated instances. Contribution of this study can be highlighted: evaluation of alternative computational methods for planning the allocation of wooden storage yards; evidence was obtained of effectiveness and efficiency of assessed metaheuristics and, the applicability of approximate methods in this problem was evaluated.

Matheuristics for Qualification Management Decisions in Wafer Fabs

In this paper, a qualification management problem arising in semiconductor wafer fabrication facilities (wafer fabs) is studied. The stepper machines, a common bottleneck in many wafer fabs, must be qualified to process lots of different families. A qualification time window is associated with each stepper and family. It can be reinitialized as needed and can be extended by on-time processing of lots from qualified families. Fast heuristic approaches, among them a Greedy Randomized Adaptive Search Procedure (GRASP), are proposed to solve large-sized problem instances using a small amount of computing time. The qualification decisions modeled by binary decision variables are made by heuristic procedures that exploit the problem structure while the real-valued quantities for each family and stepper are computed using linear programming. Computational experiments based on randomly generated problem instances are conducted. The results show that the proposed matheuristics are able to quickly provide high-quality solutions.

An effective real time GRASP-based metaheuristic: Application to order consolidation and dynamic selection of transshipment points for time-critical freight logistics

Time-critical freight logistics is an area within logistics research where the shipper’s orders need to be received relatively urgently using a third party logistics (3PL) that provides a quote (bid) to the shipper within a very short period. We solved this 3PL problem by developing an effective meta-heuristic based on the Greedy Randomized Adaptive Search Procedure (GRASP). This is achieved by introducing novel attributes in the construction of the restricted candidate list while incorporating flexible and intelligent rules, some of which are inspired by expert knowledge. The approach performs order consolidation, locates transshipment points and performs an optimal assignment of shipments to the selected consolidation points dynamically and in real time. This intelligent system embeds expert knowledge within the design of neighbourhood reduction schemes and data structures to speed up the search. This is achieved by recording computed data that does not need to be recomputed again while avoiding unnecessary computations of the non-promising alternatives.The performance of this real time optimisation and scheduling tool is tested with a European 3PL company over a 13 weeks period in late 2017 resulting in a significant cost saving and a considerable reduction in CO2 emissions. This powerful decision support system assists the 3PL company in gaining competitive leadership advantage through producing promising quotes that turn customer requests into real customer orders.

Minimum Initial Marking Estimation of Labeled Petri Nets Based on GRASP Inspired Method (GMIM)

This paper deals with the problem of estimating the Minimum Initial Marking (MIM) of Labeled Petri Nets (L-PN). By the observation of a sequence of labels, we determine the set of possible MIMs related to a given L-PN through an approach based on GRASP (Greedy Randomized Adaptive Search Procedure) inspired method – GMIM. The objective is to get the maximum of feasible MIMs by exploring the search space and giving best solutions for real time cyber systems in short time. We consider four basic assumptions during the reasoning: (i) the L-PN structure is known; (ii) for each transition of L-PN, a label is associated, (iii) the label sequence is known, and (iv) all transitions of L-PN are observable. We show the validity and efficiency of our approach by applying the proposed GMIM metaheuristic to two validation examples: Initialization of two parallel machines (example widely cited in literature) and resources allocation in a monitoring problem via mobile robot network.

Column generation-based stochastic school bell time and bus scheduling optimization

Given a trip plan (a sequence of bus stops), the integrated school bell time and bus scheduling problem simultaneously optimizes the school bell time and bus routes (the assignment of buses to serve trips at a specific time) while maintaining the minimum level-of-service requirements. The objective is to minimize the total number of buses and the total vehicle time. The previous efforts focused on the deterministic problem. However, uncertainty is unavoidable in a real-world problem. Thus, we consider this integrated problem with stochastic travel times. Two Mixed Integer Programming (MIP) models and a Column Generation-based algorithm are proposed. The algorithm incorporates the merits of the Column Generation, Simulated Annealing, Insertion Algorithm, and Greedy Randomized Adaptive Search Procedure and gains the computational power that the existing methods do not have. The experiments on a real-world problem show that, after the bell time optimization, up to 41% of current buses can be saved with even better service in terms of the higher punctuality and shorter student ride time.

Heuristics for the capacitated dispersion problem

AbstractIn this paper, we investigate the adaptation of the greedy randomized adaptive search procedure (GRASP) and variable neighborhood descent (VND) methodologies to the capacitated dispersion problem. Dispersion and diversity problems arise in the placement of undesirable facilities, workforce management, and social media, among others. Maximizing diversity deals with selecting a subset of elements from a given set in such a way that the distance among the selected elements is maximized. We target here a realistic variant with capacity constraints for which a heuristic with a performance guarantee was previously introduced. In particular, we propose a hybridization of GRASP and VND implementing within the strategic oscillation framework. To evaluate the performance of our heuristic, we perform extensive experimentation to first set key search parameters, and then compare the final method with the previous heuristic. Additionally, we propose a mathematical model to obtain optimal solutions for small‐sized instances, and compare our solutions with the well‐known LocalSolver software.

Heuristic/meta-heuristic methods for restricted bin packing problem

This paper addresses a special bin packing problem in which each item can only be assigned to a subset of the bins. We name this problem as the restricted bin packing problem (RBPP). This paper is designed to explore the relationships of RBPP with classic NP-complete problems, and to resolve the restrictions of assignment through heuristic and meta-heuristic algorithms. A new heuristic algorithm named ‘Max-fit Based on Zigzag Sorting with Retained Feasibility’ is proposed. In this heuristic algorithm, a feasibility retaining rule is constructed to assure the assignment of every item; a zigzag sorting method is designed to improve the performance of the algorithm. Our heuristic algorithm is able to generate better results in comparison with existing heuristics. Greedy Randomized Adaptive Search Procedure (GRASP) and Simulated Annealing (SA) are exploited to obtain better solutions for RBPP. A new construction method based on cliques and zigzag sorting are built for GRASP and SA. The proposed methods are shown to have higher efficiency than traditional ones through numeric examples.

Assessing road network vulnerability: A user equilibrium interdiction model

Road networks are vulnerable to natural and man-made disruptions. The loss of one or many critical links of the network often leads to increased traffic congestion. Therefore, quantitative models are necessary to identify these critical assets so that actions can be taken by decision makers to mitigate the impact of disruptions. This paper proposes an optimisation model to identify the set of arcs that, when lost, results in the worst congestion under user equilibrium traffic. The model is formulated as a bi-level non-linear problem. The challenging formulation is solved via a customised version of Greedy Randomised Adaptive Search Procedure (GRASP) meta-heuristic. Computational experiments are run on a dataset of artificial grids and managerial insights are provided based on popular Sioux and Berlin network case-studies.

Un modelo probabilístico de inventarios por demanda independiente mediante el uso de GRASP

El objetivo de este estudio es minimizar el gasto de pedido innecesario que realiza la pañalera “La mejor pañalera”, debido a la poca demanda que tienen ciertos productos. Esta problemática surge debido a que los dueños tienen una incorrecta percepción sobre la demanda de los productos, realizando pedidos de forma empírica provocando que exista excedentes de estos en el establecimiento y por consiguiente se producen perdidas monetarias. Para llevar a cabo el objetivo de este estudio, se implementará una metodología que implica la aplicación del algoritmo Greedy Randomized Adaptive Search Procedure (GRASP) y Simulación de Montecarlo, la cual permitirá estimar cómo se comportará la demanda de los productos en el año 2020 tomando los datos históricos del negocio del año 2017, 2018, 2019, generando el segundo semestre del año 2019 con la simulación de Montecarlo. Obteniendo como resultado que la simulación y los métodos metaheurísticos dan valores cercanos a la realidad, resultado se obtuvo un 19.33% de reducción en gastos para 1 producto.

A GRASP-Based Approach for Dynamic Cache Resources Placement in Future Networks

Dealing with the ever-increasing video traffic is certainly one of the major challenges facing Internet Service Providers (ISPs). In this context, the strategic placement of caches is seen as one of the most important remedies, especially with recent advances in the field of virtualization. Unlike the existing works, which only focus on the placement issue, we also consider the problem of determining the optimal amount of cache to place at each possible location. We formalize, in this paper, the problem of caches placement as a multi-objective optimization problem, in which we minimize both the average distance from which contents are retrieved and the peering links utilization. As the proposed problem is NP-hard, we propose to solve it using the Greedy Randomized Adaptive Search Procedure (GRASP) meta-heuristic. Simulations results reveal the quality of the obtained solutions compared to an exhaustive search method. At the same time, they reveal that the solution is not to put all resources at the edge or at the core, as some studies claim, but to partition them judiciously, which mainly depends on the objectives of the ISPs.

Improving a state‐of‐the‐art heuristic for the minimum latency problem with data mining

AbstractRecently, hybrid metaheuristics have become a trend in operations research. A successful example combines the Greedy Randomized Adaptive Search Procedures (GRASP) and data mining techniques, where frequent patterns found in high‐quality solutions can lead to an efficient exploration of the search space, along with a significant reduction of computational time. In this paper, a GRASP‐based state‐of‐the‐art heuristic for the minimum latency problem is improved by means of data mining techniques. Computational experiments showed that the hybrid heuristic with data mining was able to match or improve the solution quality for a large number of instances, together with a substantial reduction of running time. Besides, 32 new best‐known solutions are introduced to the literature. To support our results, statistical significance tests, analyses over the impact of mined patterns, comparisons based on running time as stopping criterion, and time‐to‐target plots are provided.

An Embedded GRASP-VNS based Two-Layer Framework for Tour Recommendation

The advance of tour recommendation allows people to get well-fit route plans, which contain a sequence of Points of Interest (POIs) based on tourists' constraints and preferences. Large-scale POIs, called Super-POIs in this paper, often contain multiple scenic spots and entrances. Tourists have to specify a suitable tour route inside Super-POI to obtain good tour experience. However, most of existing tour recommendation algorithms ignore the detailed information inside Super-POIs. By taking super-POIs into account, we propose Embedded Tour (eTOUR), a two-layer framework considering route design of POIs (Outer Model) and scenic routes inside the Super-POIs (Inner Model) respectively. To combine two models, an Embedded GRASP-VNS Algorithm is introduced based on an embedding strategy. For Outer Model, we apply Greedy Randomized Adaptive Search Procedure (GRASP) for route construction and Variable Neighborhood Search (VNS) for local improvement. Super-POI is treated as a meta node in outer route construction. For Inner Model, the optimal route inside Super-POI obtained by DFS-based Tree Search with Pruning is revised dynamically to adapt to the outer route. Furthermore, we discuss a special case in the Super-POI where a key graph is defined and treated as the must go route. We modify the solution of Chinese Postman Problem in this case to reduce the time complexity. Finally, experiments based on two real datasets demonstrate the effectiveness of our proposal.