Multi-objective Variable Neighborhood Search Research Articles

GNN Representation Learning and Multi-Objective Variable Neighborhood Search Algorithm for Wind Farm Layout Optimization

GNN Representation Learning and Multi-Objective Variable Neighborhood Search Algorithm for Wind Farm Layout Optimization

Two-echelon multi-depot multi-period location-routing problem with pickup and delivery

Efficient logistics network designs can contribute to operational cost savings and efficiency improvements. In this study, a two-echelon multi-depot multi-period location-routing problem with pickup and delivery (2E-MDMPLRPPD) is proposed, seeking to construct a logistics network with high efficiency by optimizing periodic location decisions and routing schemes. On the basis of the changing time windows of customers and facilities, the proposed 2E-MDMPLRPPD explores their potential periodicity and divides the whole planning horizon into multiple periods for conducting location decisions and arranging customer services. Vehicle-sharing strategies, which encourage vehicles to be shared by facilities across multiple periods, have also been integrated into the 2E-MDMPLRPPD optimization to improve resource utilization and sustainability. The 2E-MDMPLRPPD is formulated as a bi-objective mathematical model, with the minimization of the total operational cost and number of vehicles as the two objective functions. To solve the optimization model, this study develops a hybrid multi-objective particle swarm optimization (HMOPSO) algorithm and introduces a three-dimensional (3D) k-means clustering to assist the proposed hybrid algorithm. The 3D k-means is the key to providing initial feasible candidate location strategies and simplifying the logistics network, reducing the complexity and difficulty for the following further optimization by HMOPSO. The proposed HMOPSO, integrating the Clarke–Wright saving algorithm and variable neighborhood search (VNS) into the standard MOPSO, shows good performance in solving the proposed 2E-MDMPLRPPD optimization, which is demonstrated through an algorithm comparison with MOPSO, multi-objective VNS and non-dominated sorting genetic algorithm-II. Finally, the proposed model and algorithm are applied to a real-world case study of 2E-MDMPLRPPD in Chengdu, China. A two-period location-routing strategy can achieve the best optimization results, and based on the period division and periodic location strategy, the operating cost and required vehicles can save $15,394 and 25, respectively. A series of comparative analyses in different period divisions and location selection scenarios are implemented, and the practical significance in cost-saving and efficiency improvements is verified. Thus, this study can provide insights for logistics enterprises and facilitate sustainable and efficient urban logistics operations.

Multi-objective home health care routing: a variable neighborhood search method.

Health and convenience are two indispensable indicators of the society promotion. Nowadays, to improve community health levels, the comfort of patients and those in need of health services has received much attention. Providing Home Health Care (HHC) services is one of the critical issues of health care to improve the patient convenience. However, manual nurse planning which is still performed in many HHC institutes results in a waste of time, cost, and ultimately lower efficiency. In this research, a multi-objective mixed-integer model is presented for home health care planning so that in addition to focusing on the financial goals of the institution, other objectives that can help increase productivity and quality of services are highlighted. Therefore, four different objectives of the total cost, environmental emission, workload balance, and service quality are addressed. Taking into account medical staff with different service levels, and the preferences of patients in selecting a service level, as well as different vehicle types, are other aspects discussed in this model. The epsilon-constraint method is implemented in CPLEX to solve small-size instances. Moreover, a Multi-Objective Variable Neighborhood Search (MOVNS) composed of nine local neighborhood moves is developed to solve the practical-size instances. The results of the MOVNS are compared with the epsilon-constraint method, and the strengths and weaknesses of the proposed algorithm are demonstrated by a comprehensive sensitivity analysis. To show the applicability of the algorithm, a real example is designed based on a case study, and the results of the algorithm over real data are evaluated.

A Multiobjective Variable Neighborhood Search with Learning and Swarm for Permutation Flowshop Scheduling with Sequence-Dependent Setup Times

In recent years, the permutation flowshop scheduling problem (PFSP) with sequence-dependent setup times has been widely investigated in the literature, most focusing on the single-objective optimization problem. However, in a practical production environment, schedulers usually need to handle several conflicting objectives simultaneously, which makes the multiobjective PFSP with sequence-dependent setup times (MOPFSP-SDST) more difficult and time consuming to be solved. Therefore, this paper proposes a learning and swarm based multiobjective variable neighborhood search (LS-MOVNS) for this problem to minimize makespan and total flowtime. The main characteristic of the proposed LS-MOVNS is that it can achieve the balance between exploration and exploitation by integrating swarm-based search with VNS in the multiobjective environment through machine learning technique. For example, the learning-based selection of solutions for multiobjective local search and the adaptive determination of neighborhood sequence to perform the local search are presented based on clustering and statistics to improve the search efficiency. Experimental results on benchmark problems illustrate that the proposed LS-MOVNS algorithm is very effective and competitive to solve MOPFSP-SDST.

Multi-Objective Model and Variable Neighborhood Search Algorithms for the Joint Maintenance Scheduling and Workforce Routing Problem

This paper addresses a problem faced by maintenance service providers: performing maintenance activities at the right time on geographically distributed machines subjected to random failures. This problem requires determining for each technician the sequence of maintenance operations to perform to minimize the total expected costs while ensuring a high level of machine availability. To date, research in this area has dealt with routing and maintenance schedules separately. This study aims to determine the optimal maintenance and routing plan simultaneously. A new bi-objective mathematical model that integrates both routing and maintenance considerations is proposed for time-based preventive maintenance. The first objective is to minimize the travel cost related to technicians’ routing. The second objective can either minimize the total preventive and corrective maintenance cost or the failure cost. New general variable neighborhood search (GVNS) and variable neighborhood descent (VND) algorithms based on the Pareto dominance concept are proposed and performed over newly generated instances. The efficiency of our approach is demonstrated through several experiments. Compared to the commercial solver and existing multi-objective VND and GVNS, these new algorithms obtain highly competitive results on both mono-objective and bi-objective variants.

A Multi-objective variable neighborhood search for the maximal covering location problem with customer preferences

A Multi-objective variable neighborhood search for the maximal covering location problem with customer preferences

A two-phase approach for solving the multi-skill resource-constrained multi-project scheduling problem: a case study in construction industry

PurposeThe purpose of this research is to study the Multi-Skill Resource-Constrained Multi-Project Scheduling Problem (MSRCMPSP), where (1) durations of activities depend on the familiarity levels of assigned workers, (2) more efficient workers demand higher per-day salaries, (3) projects have different due dates and (4) the budget of each period varies over time. The proposed model is bi-objective, and its objectives are minimization of completion times and costs of all projects, simultaneously.Design/methodology/approachThis paper proposes a two-phase approach based on the Statistical Process Control (SPC) to solve this problem. This approach aims to develop a control chart so as to monitor the performance of an optimizer during the optimization process. In the first phase, a multi-objective statistical model has been used to obtain control limits of this chart. To solve this model, a Multi-Objective Greedy Randomized Adaptive Search Procedure (MOGRASP) has been hired. In the second phase, the MSRCMPSP is solved via a New Version of the Multi-Objective Variable Neighborhood Search Algorithm (NV-MOVNS). In each iteration, the developed control chart monitors the performance of the NV-MOVNS to obtain proper solutions. When the control chart warns about an out-of control state, a new procedure based on the Conway’s Game of Life, which is a cellular automaton, is used to bring the algorithm back to the in-control state.FindingsThe proposed two-phase approach has been used in solving several standard test problems available in the literature. The results are compared with the outputs of some other methods to assess the efficiency of this approach. Comparisons imply the high efficiency of the proposed approach in solving test problems with different sizes.Practical implicationsThe proposed model and approach have been used to schedule multiple projects of a construction company in Iran. The outputs show that both the model and the NV-MOVNS can be used in real-world multi-project scheduling problems.Originality/valueDue to the numerous numbers of studies reviewed in this research, the authors discovered that there are few researches on the multi-skill resource-constrained multi-project scheduling problem (MSRCMPSP) with the aforementioned characteristics. Moreover, none of the previous researches proposed an SPC-based solution approach for meta-heuristics in order to solve the MSRCMPSP.

Matheuristics for Multi-UAV Routing and Recharge Station Location for Complete Area Coverage.

This paper presents matheuristics for routing a heterogeneous group of capacitated unmanned air vehicles (UAVs) for complete coverage of ground areas, considering simultaneous minimization of the coverage time and locating the minimal number of refueling stations. Whereas coverage path planning (CPP) is widely studied in the literature, previous works did not combine heterogeneous vehicle performance and complete area coverage constraints to optimize UAV tours by considering both objectives. As this problem cannot be easily solved, we designed high-level path planning that combines the multiobjective variable neighborhood search (MOVNS) metaheuristic and the exact mathematical formulation to explore the set of nondominated solutions. Since the exact method can interact in different ways with MOVNS, we evaluated four different strategies using four metrics: execution time, coverage, cardinality, and hypervolume. The experimental results show that applying the exact method as an intraroute operator into the variable neighborhood descent (VND) can return solutions as good as those obtained by the closest to optimal strategy but with higher efficiency.

A bi-objective two-echelon pollution routing problem with simultaneous pickup and delivery under multiple time windows constraint

Pollution emitted by a vehicle can be checked by reducing the distance traveled and through operational adjustments. Optimized route and simultaneous pickup and delivery in a vehicle routing problem (VRP) can achieve the same. This paper investigates a two-echelon pollution routing problem with simultaneous pickup and delivery by considering multiple time windows (2E-PRPSPD-MTW) for customers’ visit. The first echelon consists of depots and intermediate depots (called satellites), whereas the second echelon consists of the satellites and customers. Two fleets (one for each echelon) of heterogeneous vehicles accomplish pickup and delivery operations. The 2E-PRPSPD-MTW is developed in a bi-objective framework, focusing on minimization of both travel time and fuel consumption. The proposed bi-objective 2E-PRPSPD-MTW is an NP-hard problem. So, in order to optimize it, multi-objective variable neighborhood search (MOVNS) is modified and used. In this process, six operators are proposed in order to improve the neighborhood structure. The suggested operators explore the entire solution space to find the near optimal solution. With the aim of providing much richer insights, the efficacy of the proposed method and mathematical formulation is demonstrated through numerical experiment for a number of instances varying from small to large scale.

A multi-objective parallel variable neighborhood search for the bi-objective obnoxious p-median problem

Researchers and practitioners have addressed many variants of facility locations problems. Each location problem can be substantially different from each other depending on the objectives and/or constraints considered. In this paper, the bi-objective obnoxious p-median problem (Bi-OpM) is addressed given the huge interest to locate facilities such as waste or hazardous disposal facilities, nuclear power or chemical plants and noisy or polluting services, among others. The Bi-OpM aims to locate p facilities maximizing two different objectives: the distance between each customer and their nearest facility center and the dispersion among facilities. To address the Bi-OpM problem a Multi-objective Parallel Variable Neighborhood Search approach (Mo-PVNS) is implemented. Computational results indicate the superiority of the Mo-PVNS compared to the state-of-art algorithms.

A Multi-Objective Variable Neighborhood Search Algorithm for Precast Production Scheduling

In real life, precast production schedulers face the challenges of creating a reasonable schedule to satisfy multiple conflicting objectives. Practical constraints and objectives encountered in the precast production scheduling problem (PPSP) were addressed, with the goal to minimize makespan and total earliness and tardiness penalties. A multi-objective variable neighborhood search (MOVNS) algorithm was proposed and the performance was tested on 11 problem instances. Ten of these were generated using precast concrete production information taken from the literature. One real industrial problem from a precast concrete company was considered as a case study. Extensive experiments were conducted, and the spread and distance metrics were used to evaluate the quality of the non-dominated solutions set. Statistical analysis demonstrated that the result was statistically convincing. Computational results showed that the proposed MOVNS algorithm was significantly better when compared to the other nine algorithms. Therefore, the proposed MOVNS algorithm was a very competitive method for the considered PPSP.

Multi-objective matheuristic for minimization of total tardiness and energy costs in a steel industry heat treatment line

This research focuses on solving a scheduling problem in a heat treatment line of a multinational steel company. A bi-objective model is proposed to minimize the line total energy costs and total tardiness. The solution is carried out through a matheuristic technique that combines metaheuristics and mathematical programming. A Mixed Integer Linear Programming (MILP) model is designed to generate initial solutions to a Multi-objective Variable Neighborhood Search (MOVNS) algorithm. One benefit of this approach is the ability to handle large-scale problems, common in real production scheduling cases, with reasonable computational time and alternative quality planning. The suggested matheuristic is proven to be statistically superior to an only metaheuristic approach, taking as performance metric the final approximated Pareto solutions’ hypervolume. Tests performed with data from the industry showed improvements in the scheduling of the heat treatment line with reductions of energy costs and tardiness up to 13% and 90%, respectively. The methodology can also be extended to other similar scheduling processes.

Energy-efficient no-wait permutation flow shop scheduling by adaptive multi-objective variable neighborhood search

This paper considers an energy-efficient no-wait permutation flow shop scheduling problem to minimize makespan and total energy consumption, simultaneously. The processing speeds of machines can be dynamically adjusted for different jobs. In general, lower processing speeds require less energy consumption but result in longer processing times, while higher speeds take the opposite effect. To reach the Pareto front of the problem, we propose an adaptive multi-objective variable neighborhood search (AM-VNS) algorithm. Specifically, we first design two basic speed adjusting heuristics which can reduce the energy consumption of a given solution without worsening its makespan. Two widely used neighborhood-generating operations, i.e., insertion and swap, are adapted and integrated into the variable neighborhood descent phase. With respect to their executing order, two variable neighborhood descent structures can be designed. We adopt an adaptive mechanism to dynamically determine which structure will be selected to handle the current solution. To further improve the performance of the algorithm, we develop a novel problem-specific shake procedure. We also introduce accelerating techniques to speed up the algorithm. Computational results show that the AM-VNS algorithm outperforms multi-objective evolutionary algorithms NSGA-II and SPEA-II.

Multi-Objective Sustainable Truck Scheduling in a Rail–Road Physical Internet Cross-Docking Hub Considering Energy Consumption

In the context of supply chain sustainability, Physical Internet (PI or π ) was presented as an innovative concept to create a global sustainable logistics system. One of the main components of the Physical Internet paradigm consists in encapsulating products in modular and standardized PI-containers able to move via PI-nodes (such as PI-hubs) using collaborative routing protocols. This study focuses on optimizing operations occurring in a Rail–Road PI-Hub cross-docking terminal. The problem consists of scheduling outbound trucks at the docks and the routing of PI-containers in the PI-sorter zone of the Rail–Road PI-Hub cross-docking terminal. The first objective is to minimize the energy consumption of the PI-conveyors used to transfer PI-containers from the train to the outbound trucks. The second objective is to minimize the cost of using outbound trucks for different destinations. The problem is formulated as a Multi-Objective Mixed-Integer Programming model (MO-MIP) and solved with CPLEX solver using Lexicographic Goal Programming. Then, two multi-objective hybrid meta-heuristics are proposed to enhance the computational time as CPLEX was time consuming, especially for large size instances: Multi-Objective Variable Neighborhood Search hybridized with Simulated Annealing (MO-VNSSA) and with a Tabu Search (MO-VNSTS). The two meta-heuristics are tested on 32 instances (27 small instances and 5 large instances). CPLEX found the optimal solutions for only 23 instances. Results show that the proposed MO-VNSSA and MO-VNSTS are able to find optimal and near optimal solutions within a reasonable computational time. The two meta-heuristics found optimal solutions for the first objective in all the instances. For the second objective, MO-VNSSA and MO-VNSTS found optimal solutions for 7 instances. In order to evaluate the results for the second objective, a one way analysis of variance ANOVA was performed.

Multi-objective protein encoding: Redefinition of the problem, new problem-aware operators, and approach based on Variable Neighborhood Search

Synthetic biology is currently involved in improving the expression levels of proteins. A preeminent strategy herein is to encode multiple copies of the same amino acid sequence (protein) and integrate these copies into the genome of an organism. However, this is a challenging task. First, the different protein-coding sequences (CDSs) should be as different as possible to avoid homologous recombination. The second challenge lies in the fact that some synonymous codons are better adapted than others. Therefore, the best adapted synonymous codons should be employed if possible. These two challenges are conflicting and multi-objective optimization has to be consequently used. For this purpose, we design and implement a Multi-Objective Variable Neighborhood Search (MOVNS) algorithm with new problem-aware mutation operators. Following the related work, we initially define the multi-objective problem based on three optimization objectives. However, after the first experiments, we realize that one of the objectives can be discarded, simplifying the problem without degrading the solutions’ quality. The obtained results confirm the attainment of statistically significant improvements in comparison to related works.

An intelligent simulation platform for train traffic control under disturbance

ABSTRACTRailway disturbance management is inherently a multi-objective optimization problem that concerns both the operators’ cost and passenger’s service level. This study proposes a multi-objective simulation-based optimization framework to effectively manage the train conflicts after the occurrences of a disturbance caused by a temporary line blockage. The simulation model enhanced with a dynamic priority dispatching rule in order to speed up the optimization procedure. A multi-objective variable neighborhood search meta-heuristic is proposed to solve the train rescheduling model. The obtained Pareto optimal solutions for disturbance management model support the decision maker to find a trade-off between both user and operator viewpoints. The proposed approach has been validated on a set of disruption scenarios covering a large part of the Iranian rail network. The computational results prove that the proposed model can generate good-quality timetables with the minimum passenger delay and deviation from the initial timetable. The outcomes indicate that the developed simulation-based optimization approach has substantial advantages in producing practical solution quickly when compared to currently accepted solutions.Abbreviation: MOVNS: multi-objective variable neighbourhood search; DES: discrete-event simulation; SO: simulation-optimization; AG: Alternative Graph; FCFS: First Come First Served; MIP: mixed integer programming; MILP: mixed-integer linear programming; B&B: branch and bound algorithm; VND: Variable Neighborhood Descent; NSGA-II: Non-dominated Sorting Genetic Algorithm–II; CD: crowding distance; DP: dynamic priority; EDD: earliest due date first; SRTT: shortest remaining traveling time; LST: least slack time first

A Multi-objective Variable Neighborhood Search algorithm for solving the Hybrid Flow Shop Problem

This paper addresses the Hybrid Flow Shop Problem (HFSP) through the Multi-objective Variable Neighborhood Search metaheuristic (MOVNS). In this problem, we have a set of jobs that must be performed on a set of stages. At each stage, we have a set of unrelated parallel machines. Some jobs may skip stages. In this paper we considere two evaluation criteria under simultaneous analysis: the minimization of the makespan and the minimization of the weighted sum of tardiness. Instances of the HFSP from literature are solved by four versions of the MOVNS algorithm. The results are evaluated using the Hypervolume, Epsilon, Spacing and Sphere counting metrics.

Calibration of a type 2 controller applied to a buck converter: a multi-objective analysis

Control lops are nowadays everywhere, from tiny devices to robust industrial applications. However, even when only few parameters are being dealt, manually fine-tuning has been shown to be a meticulous task for achieving designers' desired performance. Fine-tuning a controller parameters is an arduous job that requests expertise of the domain. On the other hand, metaheuristics have been barely applied for accomplishing this task. In particular, due to different behaviors that a control loop can have, a multi-objective analysis shows up as essential. In this work, we apply a Multi-Objective Variable Neighborhood Search based algorithm for assisting the design of a Buck Converter, integrating the optimization process with an evaluation mechanism integrated with a circuit simulation software. The obtained Pareto Front presented various response behaviors, optimizing different desired characteristics. We suggest that the proposed framework is a promising tool for assisting decision makers to design more efficient and dynamic systems.

Exact and approximate approaches for the Pareto front generation of the single path multicommodity flow problem

A major problem in communication networks is how to efficiently define the routing paths and to allocate bandwidths in order to satisfy a given collection of transmission requests. In this paper, we study this routing problem by modeling it as a bi-objective single path multicommodity flow problem (SMCFP). Two conflicting objective functions are simultaneously optimized: the delay and reliability of the generated paths. To tackle the complexity of this problem (NP-hard), most of the existing studies proposed approximate methods and metaheuristics as solution approaches. In this paper, we propose to adapt the augmented $$\epsilon $$ -constraint method in order to solve small sized instances of the bi-SMCFP. For large scale problems, we develop three metaheuristics: a multiobjective multi-operator genetic algorithm, an adaptive multiobjective variable neighborhood search and new hybrid method combining the $$\epsilon $$ -constraint with the evolutionary metaheuristic. The idea of the hybridization schema is to first use the metaheuristic to generate a good approximation of the Pareto front, then to enhance the quality of the solutions using the $$\epsilon $$ -constraint method to push them toward the exact Pareto front. An intelligent decomposition scheme is used to reduce the size of the search space before applying the exact method. Computational results demonstrate the efficiency of the proposed hybrid algorithm using instances derived from real network topology and other randomly generated instances.

Metaheuristics for solving the biobjective single‐path multicommodity communication flow problem

AbstractSingle‐path multicommodity flow problem (SMCFP) is a well‐known combinatorial optimization problem, in which the flow of each commodity can be transmitted using only one path linking its destination to an appropriate origin within the addressed network. In this paper, we study the SMCFP in a multiobjective context by considering the simultaneous optimization of paths' delay and average reliability. The network is modeled as a finite set of nodes that can communicate using preestablished connections where each connection is characterized by a capacity, a lead time, and a reliability. A node can be an information producer or/and information consumer. The contention problem is solved by assigning a path and a dedicated bandwidth to each flow. The problem is formulated as a biobjective nonlinear optimization problem. This biobjective problem has not been considered in the literature. We design three alternative procedures for approximating the Pareto front. We proposed an MGA based on NSGA‐II, a multiobjective variable neighborhood search and a new distance‐based hybrid metaheuristic. The hybridization integrates a local search into the framework of genetic algorithm to effectively drive the search toward a better approximating of the Pareto front. The propounded algorithms' efficiencies are experimentally investigated on a test bed of instances applied to a planar and a grid network. A comparative study is conducted based on different multiobjective performance indicators.