Hybrid Variable Neighborhood Search Research Articles

Modelling a bi-objective airport gate scheduling with controllable processing time using hybrid NSGA-II and VNS algorithm

In this research, we address a bi-objective model in a more realistic situation such that airport gate processing time is controllable. It is assumed that the possible compression/expansion processing time of a flight can be continuously controlled. The aim is simultaneously: 1) minimise the total cost of tardiness, earliness, delay and compression as well as expansion costs of job processing time; 2) minimise the passengers overcrowding on gate. In this study, a mixed-integer programming model is proposed. For solving the problem, two multi-objective meta-heuristic algorithms, namely non-dominated sorting genetic algorithm II (NSGA-II) and hybrid NSGA-II and variable neighbourhood search (VNS) are applied. VNS is used for preventing the solution from trapping in the local optimum, instead of mutation operator in NSGA-II. The algorithms are tested with the real life data from Mehrabad International Airport. Computational experiments reveal that hybrid NSGA-II and VNS generate better Pareto-optimal solution as compared to NSGA-II.

Hybrid Genetic Algorithm for Optimization of Food Composition on Hypertensive Patient

The healthy food with attention of salt degree is one of the efforts for healthy living of hypertensive patient. The effort is important for reducing the probability of hypertension change to be dangerous disease. In this study, the food composition is build with attention nutrition amount, salt degree, and minimum cost. The proposed method is hybrid method of Genetic Algorithm (GA) and Variable Neighborhood Search (VNS). The three scenarios of hybrid GA-VNS types had been developed in this study. Although hybrid GA and VNS take more time than pure GA or pure VNS but the proposed method give better quality of solution. VNS successfully help GA avoids premature convergence and improves better solution. The shortcomings on GA in local exploitation and premature convergence is solved by VNS, whereas the shortcoming on VNS that less capability in global exploration can be solved by use GA that has advantage in global exploration.

Mathematical modelling and heuristic approaches to the location-routing problem of a cost-effective integrated solid waste management

Integrated solid waste management (ISWM) comprises activities and processes to collect, transport, treat, recycle and dispose municipal solid wastes. This paper addresses the ISWM location-routing problem in which different types of municipal solid wastes are factored concurrently into an integrated system with all interrelated facilities. To support a cost-effective ISWM system, the number of locations of the system’s components (i.e. transfer stations; recycling, treatment and disposal centres) and truck routing within the system’s components need to be optimized. A mixed-integer linear programming (MILP) model is presented to minimise the total cost of the ISWM system including transportation costs and facility establishment costs. To tackle the non-deterministic polynomial-time hardness of the problem, a stepwise heuristic method is proposed within the frames of two meta-heuristic approaches: (i) variable neighbourhood search (VNS) and (ii) a hybrid VNS and simulated annealing algorithm (VNS + SA). A real-life case study from an existing ISWM system in Tehran, Iran is utilized to apply the proposed model and algorithms. Then the presented MILP model is implemented in CPLEX environment to evaluate the effectiveness of the proposed algorithms for multiple test problems in different scales. The results show that, while both proposed algorithms can effectively solve the problem within practical computing time, the proposed hybrid method efficiently has produced near-optimal solutions with gaps of < 4%, compared to the exact results. In comparison with the current cost of the existing ISWM system in the study area, the presented MILP model and proposed heuristic methods effectively reduce the total costs by 20–22%.

Scheduling step-deteriorating jobs on bounded parallel-batching machines to maximise the total net revenue

This paper addresses a parallel-batching scheduling problem considering processing cost and revenue, with the objective of maximising the total net revenue. Specifically, the actual processing time of a job is assumed to be a step function of its starting time and the common due date. This problem involves assigning jobs to different machines, batching jobs, and sequencing batches on each machine. Some key structural properties are proposed for the scheduling problem, based on which an optimal scheduling scheme is developed for any given machine. Then, an effective hybrid VNS–IRG algorithm which combines Variable Neighborhood Search (VNS) and Iterated Reference Greedy algorithm (IRG) is proposed to solve this problem. Finally, the effectiveness and stability of the proposed VNS–IRG are demonstrated and compared with VNS, IRG, and Particle Swarm Optimization through computational experiments.

A hybrid VNS algorithm for solving the multi-level capacitated minimum spanning tree problem

This work addresses the multi-level capacitated minimum spanning tree (MLCMST) problem. It consists of finding a minimal cost spanning tree such that the flow to be transferred from a central node (root) to the other nodes is bounded by the edge capacities. In this paper, a hybrid algorithm, combining the Variable Neighborhood Search (VNS) metaheuristic and one mathematical programming formulation of the literature, is used for solving it. The formulation is used to give an initial solution to VNS. Five neighborhoods are used for exploring the solution space. Results show that the VNS is able to improve the initial solutions and to obtain small gap solutions for all instance sets.

A novel discrete PSO algorithm for solving job shop scheduling problem to minimize makespan

In this work, a discrete version of PSO algorithm is proposed to minimize the makespan of a job-shop. A novel schedule builder has been utilized to generate active schedules. The discrete PSO is tested using well known benchmark problems available in the literature. The solution produced by the proposed algorithms is compared with best known solution published in the literature and also compared with hybrid particle swarm algorithm and variable neighborhood search PSO algorithm. The solution construction methodology adopted in this study is found to be effective in producing good quality solutions for the various benchmark job-shop scheduling problems.

Variable neighborhood search incorporating a new bounding procedure for joint replenishment and delivery problem

In recent years, joint replenishment and delivery problem (JRD) has been examined extensively in the context of replenishment and inventory control. However, as an extension of joint replenishment problem, the JRD is more complex and difficult to optimize with an exact algorithm. In this study, lower and upper bounds of JRD are obtained approximately but quickly using a novel bounding procedure. Then, a variable neighborhood search (VNS) with the bounding method is developed to solve the JRD. Computational examples show that the bounding procedure can effectively and efficiently determine satisfactory bounds, which are helpful for the proposed VNS. Results of randomly generated examples further indicate that the hybrid VNS performs better than the best known heuristic and metaheuristic for JRD in terms of accuracy.

A hybrid variable neighborhood search algorithm for the hot rolling batch scheduling problem in compact strip production

Abstract This paper deals with a hot rolling batch scheduling (HRBS) problem arising from the compact strip production (CSP) process, which is one of the most popular production systems in the modern iron-steel industry to produce sheet strips. The HRBS problem aims to determine a sequence of the sheet strips in a predetermined number of rolling turns with the objective of minimizing average thickness change. In this paper, a mathematical model based on a comprehensive investigation is first given. Then a constructive heuristic based on the problem-specific characteristics is presented to generate initial feasible solutions. The heuristic can guarantee a minimum number of rolling turns to accommodate all the ordered sheet strips, but generally performs poorly in the objective of average thickness change. To improve the objective, a hybrid variable neighborhood search algorithm (HVNS) is proposed. In the HVNS, a thickness value permutation is used to encode the solution and four neighborhood structures are well designed. The fruit fly optimization algorithm, is integrated to improve search efficiency. Correspondingly, a neighborhood switching strategy is developed to improve local search ability. Moreover, a restart strategy based on the block swapping operator is used to help the algorithm escape from local optima. To investigate the effectiveness of the solution approach, two sets of instances are tested, including real-world instances and randomly generated instances. The performance of the proposed HVNS is evaluated by comparing with the other existing algorithms and the experimental results demonstrate that the proposed algorithm performs much better.

Electric Power Grids Distribution Generation System for Optimal Location and Sizing—A Case Study Investigation by Various Optimization Algorithms

In this paper, the approach focused on the variables involved in assessing the quality of a distributed generation system are reviewed in detail, for its investigation and research contribution. The aim to minimize the electric power losses (unused power consumption) and optimize the voltage profile for the power system under investigation. To provide this assessment, several experiments have been made to the IEEE 34-bus test case and various actual test cases with the respect of multiple Distribution Generation DG units. The possibility and effectiveness of the proposed algorithm for optimal placement and sizing of DG in distribution systems have been verified. Finally, four algorithms were trailed: simulated annealing (SA), hybrid genetic algorithm (HGA), genetic algorithm (GA), and variable neighbourhood search. The HGA algorithm was found to produce the best solution at a cost of a longer processing time.

Serial-batching group scheduling with release times and the combined effects of deterioration and truncated job-dependent learning

This paper investigates a single machine serial-batching scheduling problem considering release times, setup time, and group scheduling, with the combined effects of deterioration and truncated job-dependent learning. The objective of the studied problem is to minimize the makespan. Firstly, we analyze the special case where all groups have the same arrival time, and propose the optimal structural properties on jobs sequencing, jobs batching, batches sequencing, and groups sequencing. Next, the corresponding batching rule and algorithm are developed. Based on these properties and the scheduling algorithm, we develop a hybrid VNS–ASHLO algorithm incorporating variable neighborhood search (VNS) and adaptive simplified human learning optimization (ASHLO) algorithms to solve the general case of the studied problem. Computational experiments on randomly generated instances are conducted to compare the proposed VNS–ASHLO with the algorithms of VNS, ASHLO, Simulated Annealing (SA), and Particle Swarm Optimization (PSO). The results based on instances of different scales show the effectiveness and efficiency of the proposed algorithm.

Single-machine and parallel-machine serial-batching scheduling problems with position-based learning effect and linear setup time

This paper introduces the serial batching scheduling problems with position-based learning effect, where the actual job processing time is a function of its position. Two scheduling problems respectively for single-machine and parallel-machine are studied, and in each problem the objectives of minimizing maximum earliness and total number of tardy jobs are both considered respectively. In the proposed scheduling models, all jobs are first partitioned into serial batches, and then all batches are processed on the serial-batching machine. We take some practical production features into consideration, i.e., setup time before processing each batch increases with the time, regarded as time-dependent setup time, and we formalize it as a linear function of its starting time. Under the single-machine scheduling setting, structural properties are derived for the problems with the objectives of minimizing maximum earliness and number of tardy jobs respectively, based on which optimization algorithms are developed to solve them. Under the parallel-machine scheduling setting, a hybrid VNS–GSA algorithm combining variable neighborhood search (VNS) and gravitational search algorithm (GSA) is proposed to solve the problems with these two objectives respectively, and the effectiveness and efficiency of the proposed VNS–GSA are demonstrated and compared with the algorithms of GSA, VNS, and simulated annealing (SA). This paper demonstrates that the consideration of different objectives leads to various optimal decisions on jobs assignment, jobs batching, and batches sequencing, which generates a new insight to investigate batching scheduling problems with learning effect under single-machine and parallel-machine settings.

Drawing graphs with mathematical programming and variable neighborhood search

In the Graph Drawing problem a set of symbols must be placed in a plane and their connections routed. To produce clear, easy to read diagrams, this problem is usually solved trying to minimize edges crossing and the area occupied, resulting in a NP-Hard problem. Our research focuses in drawing Entity Relationship (ER) diagrams, a challenging version of the problem where nodes have different sizes. Mathematical Programming models for the two solution phases, node placement and connection routing, are discussed and their exact resolution by an Integer Programming (IP) solver is evaluated. As the first phase proved to be specially hard to be solved exactly, a hybrid Variable Neighborhood Search (VNS) heuristic is proposed. Using IP techniques we obtained provably optimal (or close to optimal) solutions for the two different phases, at the expense of a large computational effort. We also show that our VNS based heuristic approach can produce close to optimal solutions in very short times for the hardest part of the solution process. Using either methods we have produced clearly better drawings than existing solutions.

A hybrid genetic algorithm and variable neighborhood search for multi-family capacitated lot-sizing problem

The paper presents a genetic algorithm (GA) hybridized with variable neighborhood search (VNS) to solve multi-item capacitated lot-sizing multi-family problem with setup times. The problem has a practical application in production planning e.g., in foundry industry, so test cases for computational experiments were based on the data from the real production process in a foundry. The VNS algorithm is used after a certain number of GA generations for all individuals in the population to improve solutions. The presented method applied for large instances of the problem outperforms both a dedicated genetic algorithm and a CLPEX Solver-based rolling horizon methods known from the literature.

A hybrid Integer Programming and Variable Neighbourhood Search algorithm to solve Nurse Rostering Problems

The Nurse Rostering Problem (NRP) is defined as assigning a number of nurses to different shifts during a specified planning period, considering some regulations and preferences. This is often very difficult to solve in practice particularly by applying a sole approach. In this paper, we propose a novel hybrid algorithm combining the strengths of Integer Programming (IP) and Variable Neighbourhood Search (VNS) algorithms to design a hybrid method for solving the NRP. After generating the initial solution using a greedy heuristic, the solution is further improved by employing a Variable Neighbourhood Descent algorithm. Then IP, deeply embedded in the VNS algorithm, is employed within a ruin-and-recreate framework to assist the search process. Finally, IP is called again to further refine the solution during the remaining time. We utilise the strength of IP not only to diversify the search process, but also to intensify the search efforts. To identify the quality of the current solution, we use a new generic scoring scheme to mark the low-penalty parts of the solution. Based on the computational tests with 24 instances recently introduced in the literature, we obtain better results with our proposed algorithm, where the hybrid algorithm outperforms two state-of-the-art algorithms and Gurobi in most of the instances. Furthermore, we introduce 11 randomly generated instances to further evaluate the efficiency of the hybrid algorithm, and we make these computationally challenging instances publicly available to other researchers for benchmarking purposes.

Robust total energy demand estimation with a hybrid Variable Neighborhood Search – Extreme Learning Machine algorithm

Energy demand prediction is an important problem whose solution is evaluated by policy makers in order to take key decisions affecting the economy of a country. A number of previous approaches to improve the quality of this estimation have been proposed in the last decade, the majority of them applying different machine learning techniques. In this paper, the performance of a robust hybrid approach, composed of a Variable Neighborhood Search algorithm and a new class of neural network called Extreme Learning Machine, is discussed. The Variable Neighborhood Search algorithm is focused on obtaining the most relevant features among the set of initial ones, by including an exponential prediction model. While previous approaches consider that the number of macroeconomic variables used for prediction is a parameter of the algorithm (i.e., it is fixed a priori), the proposed Variable Neighborhood Search method optimizes both: the number of variables and the best ones. After this first step of feature selection, an Extreme Learning Machine network is applied to obtain the final energy demand prediction. Experiments in a real case of energy demand estimation in Spain show the excellent performance of the proposed approach. In particular, the whole method obtains an estimation of the energy demand with an error lower than 2%, even when considering the crisis years, which are a real challenge.

Hybrid Variable Neighbourhood Search for Multi-Objective Bus Driver Rostering

Hybrid Variable Neighbourhood Search for Multi-Objective Bus Driver Rostering

A hybrid variable neighborhood search for the Orienteering Problem with mandatory visits and exclusionary constraints

This paper addresses a variant of the Orienteering Problem in which some constraints related to mandatory visits and incompatibilities among nodes are taken into account. A hybrid algorithm based on a reactive GRASP and a general VNS is proposed. Computational experiments over a large set of instances show the efficiency of the algorithm. Additionally, we also validate the performance of this algorithm on some instances taken from the literature of the traditional Orienteering Problem.

A fast variable neighborhood search for p-hub median problem using social network analysis concepts

This study will contribute to the uncapacitated single allocation p-hub median problem (USApHMP) which is known as an NP-hard problem in the literature. This problem is concerned with locating of hub facilities in a network and allocating of each non-hub node to just one hub in order to minimize total transportation costs in the network. A hybrid variable neighborhood search (VNS) algorithm is proposed considering three structures of local search which are used as a combination of nested VNS and sequential VNS in the algorithm. For reduction of the dimensions in the nested part, social network analysis centrality measures for the node are used to choose elite points instead of all existing points in the local search structures. The obtained results demonstrate that this will not only retain quality of the solutions, but also reduce run time of the algorithm significantly. Three standard data sets (AP, CAB, and URAND) were used for numerical analysis. Computational results show that quality of the obtained solutions is good and able to compete with other heuristics addressed in the literature. From the viewpoint of execution time, it considerably outperforms all other algorithms. The intelligent search embedded in this algorithm makes it robust and efficient on networks with up to 400 nodes.

A hybrid variable neighborhood search algorithm for targeted offers in direct marketing

This paper focuses on the targeted offers problem in direct marketing campaigns. The main objective is to maximize the feedback of customers purchases, offering products for the set of customers with the highest probability of positively accepting the offer and, at the same time, minimizing the operational costs of the campaign. Given the combinatorial nature of the problem and the large volume of data, involving instances with up to one million customers, approaches solely based on mathematical programming methods, said exact, appear limited and infeasible. In this paper, the use of a hybrid heuristic algorithm, based on the Greedy Randomized Adaptive Search Procedures and General Variable Neighborhood Search, is proposed. Computational experiments performed on a set of test problems from the literature show that the proposed algorithm was able to produce competitive solutions.

Hybrid Genetic Algorithm and Variable Neighborhood Search for Dynamic Facility Layout Problem

This paper presents a novel hybrid metaheuristic GA-VNS matching genetic algorithm (GA) and variable neighborhood search (VNS) to the dynamic facility layout problem (DFLP). The DFLP is a well-known NP hard problem which aims at assigning a set of facilities to a set of locations over a time planning horizon so that the total cost including material handling cost and re-arrangement cost is minimized. The proposed hybrid approach in this paper elegantly integrates the exploitation ability of VNS and exploration ability of GA. To examine the performance of the proposed hybrid approach, a set of instance problems have been used from the literature. As demonstrated in the results, the GA-VNS is mighty of attaining high quality solution. Compared with some state-of-the-art algorithms, our proposed hybrid approach is competitive.