Applying GRASP to solve the multi-item three-echelon uncapacitated facility location problem

The constrained shortest path tour problem

A reactive GRASP and path relinking for a combined production–distribution problem

• Examines scheduling on m identical parallel machines with a common server. • Considers sequence-dependent setup times in parallel machine scheduling. • Introduces an arc-based MILP formulation for makespan minimization. • Presents a GRASP-enhanced Iterated Greedy algorithm with strong performance. • Reports 21 new best-known solutions across benchmark test instances. The identical parallel machine scheduling problem with a single server and sequence-dependent setup times is a challenging optimization problem with important applications in manufacturing and service industries. In such environments, several machines depend on a common server to perform setup operations before production can begin, which creates strong interdependencies and demands more effective scheduling strategies. This characteristic highlights the practical relevance of the problem. The interaction between machine availability and server operations often becomes a critical bottleneck. This study introduces two complementary approaches. The first is an exact method based on a novel arc-based mixed-integer linear programming (ABF) model, which extends the modeling capability of existing formulations by capturing server-related constraints more effectively. The second is an approximation method built on an Iterated Greedy (IG) algorithm. The IG procedure is improved by two evaluation mechanisms: one model-based evaluation derived from the proposed ABF model, and another employing a greedy randomized adaptive search procedure (GRASP)-based strategy that integrates greedy selection, randomization, and reconstruction to enhance solution quality. Computational experiments are conducted on existing benchmark instances. The results show that the proposed ABF model performs well on small and medium-sized instances compared to existing exact methods, while the IG variants, particularly the proposed GRASP-based version, deliver strong performance against state-of-the-art metaheuristics developed for this problem. In addition, 21 new best-known solutions are reported, further demonstrating the effectiveness of the proposed approaches.

This study investigates the capacitated planar multi-facility location-allocation problem by considering various capacity constraints. The problem is also known as the capacitated multi-source Weber problem, where the number of facilities to be located is specified and each of which has a capacity constraint. An efficient greedy randomised adaptive search procedure (GRASP) is proposed to deal with the problem. A scheme that applies the furthest distance rule (FDR) and self-adjusted threshold parameters to generate initial facility locations that are situated sparsely within GRASP framework is also presented. The construction of the restricted candidate list (RCL) within GRASP is also guided by applying a concept of restricted regions that prevents new facility locations to be sited too close to the previous selected facility locations. The performance of the proposed GRASP heuristics is tested using benchmark data sets from literature. The computational experiments show that the proposed methods provide encouraging solutions when compared to recently published papers. Some future research avenues on the subject are also briefly highlighted.

Disrupted flight schedules trouble passengers travelling, and increase operation cost in airline. Irregular flight recovery is an NP-hard problem. This article develops a new hybrid heuristic procedure based on Greedy Random Adaptive Search Procedure (GRASP), and Ant Colony Optimization (ACO) is presented to solve this problem. As compared with the original GRASP method, the proposed algorithm demonstrates quite high global optimization capability. Computational experiments on large-scale problems show that the proposed procedure is able to generate feasible revised flight schedules of a good quality in less than 5 seconds.

This paper presents route planning for a tourist as tourist trip design problem (TTDP) using discrete cuckoo search algorithm (DCS). The DCS algorithm is based on brood parasitic nature of cuckoo bird which is characterized by levy flight. The experiment of proposed DCS is conducted on orienteering problem (OP) benchmark instances and their performance compared with existence data of iterative local search (ILS) and greedy randomized adaptive search procedure (GRASP). Result showed that proposed DCS is required less computational time as compared to ILS and GRASP. It concluded that DCS is efficient method for exploring and exploiting search space in reasonable amount of time.

Scheduling in a production workshop consists of assigning a number of different tasks to the existing machines with respect to the constraints of the problem in order to optimise the objective function. In this paper, we focus on the NoWait Flow Shop Scheduling Problem (NWFSSP) with the makespan objective. We present a new hybrid algorithm NEWGRASP-DE that combines Greedy Randomised Adaptive Search Procedure (GRASP) with Differential Evolution Algorithm (DEA). Furthermore, we used an Iterative Local Search (ILS) as an improvement phase in the GRASP method. Our algorithm is tested on instances that have been proposed in the literature. We compared our results with those of different authors. The experimental results show the effectiveness of our algorithm.

In this paper we present a new population based metaheuristic called the fixed set search (FSS). The proposed approach represents a method of adding a learning mechanism to the greedy randomized adaptive search procedure (GRASP). The basic concept of FSS is to avoid focusing on specific high quality solutions but on parts or elements that such solutions have. This is done through fixing a set of elements that exist in such solutions and dedicating computational effort to finding near optimal solutions for the underlying subproblem. The simplicity of implementing the proposed method is illustrated on the traveling salesman problem. Our computational experiments show that the FSS manages to find significantly better solutions than the GRASP it is based on, the dynamic convexized method and the ant colony optimization combined with a local search.

This paper proposes an idea of using heuristic local search procedures specific for single-objective optimisation in multiobjectie evolutionary algorithms (MOEAs). In this paper, a multiobjective evolutionary algorithm based on decomposition (MOEA/D) hybridised with a multi-start single-objective metaheuristic called greedy randomised adaptive search procedure (GRASP). In our method a multiobjetive optimisation problem (MOP) is decomposed into a number of single-objecive subproblems and optimised in parallel by using neighbourhood information. The proposed GRASP alternates between subproblems to help them escape local Pareto optimal solutions. Experimental results have demonstrated that MOEA/D with GRASP outperforms the classical MOEA/D algorithm on the multiobjective 0–1 knapsack problem that is commonly used in the literature. It has also demonstrated that the use of greedy genetic crossover can significantly improve the algorithm performance.

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.

In real optimization problems it is generally desirable to optimize more than one performance criterion (or objective) at the same time. The goal of the multiobjective combinatorial optimization (MOCO) is to optimize simultaneously r > 1 objectives. As in the single-objective case, the use of heuristic/metaheuristic techniques seems to be the most promising approach to MOCO problems because of their efficiency, generality and relative simplicity of implementation. In this work, we develop algorithms based on Greedy Randomized Adaptive Search Procedure (GRASP) and Iterated Local Search (ILS) metaheuristics for the multiobjective knapsack problem. Computational experiments on benchmark instances show that the proposed algorithms are very robust and outperform other heuristics in terms of solution quality and running times.

This paper addresses the capacitated lot sizing problem (CLSP) with a single stage composed of multiple plants, items and periods with setup carry-over among the periods. The CLSP is well studied and many heuristics have been proposed to solve it. Nevertheless, few researches explored the multi-plant capacitated lot sizing problem (MPCLSP), which means that few solution methods were proposed to solve it. Furthermore, to our knowledge, no study of the MPCLSP with setup carry-over was found in the literature. This paper presents a mathematical model and a GRASP (Greedy Randomized Adaptive Search Procedure) with path relinking to the MPCLSP with setup carry-over. This solution method is an extension and adaptation of a previously adopted methodology without the setup carry-over. Computational tests showed that the improvement of the setup carry-over is significant in terms of the solution value with a low increase in computational time.

We consider the optimization problem related to the sugar beet transportation when supplying sugar mills in the sugar production. The sugar beet transportation comprises of loading the beet collected at storage piles and then delivering it to sugar mills. An essential prerequisite to guarantee a viability of the considered sugar mill, is to transport the required quantities of sugar beet while maximizing technological quality and minimizing transportation costs. Some growers may be privileged to conduct collection activities in days of a planning period when sugar beet is fresh and contains larger amount of sucrose, while others do not. This unfair collect scheduling plan should be avoided to provide equal treatment of growers. We propose an Integer Linear Programming (ILP) model with the aim of simultaneously maximizing the amount of collected sucrose during the planning period while minimizing the number of vehicles of a homogenous vehicle fleet, including constraints that provide equal opportunities for growers in sugar beet collection. The problem is denoted by the Sugar Beet Transportation Problem under Growers’ Equity Regulations (SBT-GER). By applying the weighted sum method, the two objective functions are combined to transform the bi-objective problem into a single-objective one. Equity regulations are expressed through the requirement that the minimum percentage of the quantity of sugar beet is guaranteed to be collected from each grower on the day of harvest. For real-sized instances, we propose two metaheuristic algorithms, based on Variable Neighborhood Search (VNS) and Greedy Randomized Adaptive Search Procedure (GRASP), respectively. The developed mathematical model and the proposed metaheuristic approaches are evaluated on a set of randomly generated test instances. The obtained results show that VNS outperforms exact solver and GRASP for the majority of examples.

A new MILP model and fast heuristics for the variable-sized bin packing problem with time windows

A two-stage flow-shop scheme for the multi-satellite observation and data-downlink scheduling problem considering weather uncertainties