Path Relinking Procedure Research Articles

Solution strategies for integrated distribution, production, and relocation problems arising in modular manufacturing

Recently, there has been a paradigm shift by certain energy companies towards modular manufacturing, whereby transportable modular production units can be relocated between production facilities to meet the spatial and temporal changes in the availabilities, demands, and prices of the underlying commodities. We refer to the optimal distribution, production, and storage of commodities, including intermediary commodities, and the relocation and operation of the modular production units as the dynamic multiple commodity supply chain problem with modular production units. To this end, we present a “flow-based” and a “path-based” mixed-integer linear programming formulation to model the problem. In an effort to solve large-scale instances of the problem, we propose an iterative three-stage matheuristic for the “path-based” formulation. In the first stage of the matheuristic, a feasible solution to the problem is generated by an integrated column generation and Lagrangian relaxation based heuristic. In the second stage of the matheuristic, a path-relinking procedure is utilized as a local search heuristic to further improve the solution. And in the final stage of the matheuristic, the Lagrangian multipliers are updated via a subgradient method. The effectiveness of the matheuristic is illustrated through numerical experiments with a set of randomly generated test instances. For the large-scale test instances, the results show that the matheuristic produces quality solutions orders of magnitude faster than a “state-of-the-art” mixed-integer linear programming solver.

A hybrid algorithm with a new neighborhood structure for job shop scheduling problems

Job shop scheduling problems (JSP) arise from the scheduling of modern manufacturing enterprises. It is one of the most famous NP-complete problem. To evaluate the performance of algorithms, several famous benchmarks have been presented from 1990s. A few decades later, some instances had been found the optimal solutions, but more instances remain unresolved. Trying to update the new upper bounds, the paper presents a hybrid algorithm (HA) combining the genetic algorithm (GA) and the tabu search (TS) to solve JSP with the makespan criterion. GA has an excellent global search ability, and TS has a powerful local search ability. Our HA can combine their advantages and well balance the intensification and the diversification. In the GA part, the paper designs a crossover operator referring to a path relinking procedure and a mutation operator on a basis of critical paths. In the TS part, the paper adopts our previously proposed neighborhood structure, which can effectively expand the search space of neighborhood solutions. 135 famous benchmark instances are selected to evaluate the optimization effect of HA. Six state-of-the-art methods are selected to compare with HA. The results verify that the HA outperforms its compared algorithms in both computational efficiency and solution quality. Especially, the proposed HA has updated the upper bounds of two challenging instances, DMU56-4939 and DMU57-4647.

Optimal Open-Loop Control of Discrete Deterministic Systems by Application of the Perch School Metaheuristic Optimization Algorithm

A new hybrid metaheuristic method for optimizing the objective function on a parallelepiped set of admissible solutions is proposed. It mimics the behavior of a school of river perch when looking for food. The algorithm uses the ideas of several methods: a frog-leaping method, migration algorithms, a cuckoo algorithm and a path-relinking procedure. As an application, a wide class of problems of finding the optimal control of deterministic discrete dynamical systems with a nonseparable performance criterion is chosen. For this class of optimization problems, it is difficult to apply the discrete maximum principle and its generalizations as a necessary optimality condition and the Bellman equation as a sufficient optimality condition. The desire to extend the class of problems to be solved to control problems of trajectory bundles and stochastic problems leads to the need to use not only classical adaptive random search procedures, but also new approaches combining the ideas of migration algorithms and swarm intelligence methods. The efficiency of this method is demonstrated and an analysis is performed by solving several optimal deterministic discrete control problems: two nonseparable problems (Luus–Tassone and LiHaimes) and five classic linear systems control problems with known exact solutions.

A scatter search algorithm for time-dependent prize-collecting arc routing problems

Time-dependent prize-collecting arc routing problems (TD-PARPs) generalise the regular prize-collecting arc routing problems (PARPs). PARPs have arcs associated with collectable prizes along with travelling costs. TD-PARPs allow travel times to vary at the travelling horizon so that real-life uncertain factors such as traffic and weather conditions can be taken into account. A TD-PARP is to find a travelling route that maximises the profit i.e. total collected prizes minus total travelling costs. TD-PARPs have two facets: selecting a subset of arcs to be travelled and scheduling the selected arcs in the travelling route. TD-PARPs have not been studied much although they are more realistic and generic. In this paper, we first propose a set of deterministic heuristic search algorithms that range from a simple procedure producing quite good results in a fraction of a CPU second to a more extensive procedure producing high-quality results but at the expense of slightly extra CPU time. In this paper, we then propose a meta-heuristic based scatter search (SS) algorithm for TD-PARPs. For the improvement method in the SS algorithm, we propose a multi-operator algorithm that incorporates various neighbourhood operators to diversify the local exploration. For the combination method in the SS algorithm, we propose a 2-level path relinking procedure, which explores combinations of visited and unvisited arcs using two different operators. To control the diversity of the solutions in the SS algorithm, we propose a new effective distance measurement. The experimental results on standard benchmark problems indicate that the proposed SS algorithm significantly outperforms the state-of-the-art existing methods.

Using GRASP Approach and Path Relinking to Minimize Total Number of Tardy Jobs on a Single Batch Processing Machine

This paper considers the problem of scheduling a single batch processing machine such that the total number of tardy jobs is minimized. The machine can simultaneously process several jobs as a batch as long as the machine capacity is not violated. The batch processing time is equal to the largest processing time among those jobs in the batch. Two decisions are made to schedule jobs on the batch processing machine, namely grouping jobs to form batches and sequencing the batches on the machines. Both the decisions are interdependent as the composition of the batch affects the processing time of the batch. The problem under study is NP-hard. Consequently, solving a mathematical formulation to find an optimal solution is computationally intensive. A Greedy Randomized Adaptive Search Procedure (GRASP) is proposed to solve the problem under study with the assumption of arbitrary job sizes, arbitrary processing times and arbitrary due dates. A novel construction phase for the GRASP approach is proposed to improve the solution quality. In addition, a path relinking procedure is proposed for solving large-sized problems effectively. The performance of the proposed GRASP approach is evaluated by comparing its results to a commercial solver (which was used to solve the mathematical model) and a construction heuristic. Experimental studies suggest that the solution obtained from the GRASP approach is superior compared to the commercial solver and the construction heuristic.

Using GRASP approach and path relinking to minimise total number of tardy jobs on a single batch processing machine

This paper considers scheduling a single batch processing machine such that the total number of tardy jobs is minimised. The machine can simultaneously process several jobs as a batch as long as the machine capacity is not violated. The batch processing time is equal to the largest processing time among those jobs in the batch. As the problem under study is NP-hard solving a mathematical formulation optimality is computationally intensive. A greedy randomised adaptive search procedure (GRASP) is proposed with the assumption of arbitrary job sizes, arbitrary processing times and arbitrary due dates. A novel construction phase for the GRASP approach is proposed to improve the solution quality. In addition, a path relinking procedure is proposed for solving large-sized problems effectively. The performance of the proposed GRASP approach is evaluated by comparing its results to a commercial solver and a construction heuristic. Experimental studies suggest that GRASP is superior compared to the commercial solver and the construction heuristic.

A Hybrid GRASP Algorithm for an Integrated Production Planning and a Group Layout Design in a Dynamic Cellular Manufacturing System

Demand fluctuations influence the configuration of manufacturing workshops. Integration of optimal production planning via the replenishment organization, can significantly reduce the excessive++reconfigurations number in each period and, thereafter, the global managing costs. In this article, we discuss the joint machines Group layout design (GLD) and lot-sizing problem (LSP) in a dynamic cellular manufacturing system (DCMS). We propose a novel multi-period model to determine the best cell formation, necessary configurations over each period, and optimal production and inventory policy that minimizes intra and inter-cell material handling, holding costs, and multitasks machines relocation. We propose a novel mixed-integer programming (MIP) associated model which is then solved by using the commercial software Optimizer CPLEX. Additionally, we present a hybrid greedy randomized adaptive search procedure (GRASP) enhanced with a path relinking procedure (PR) to solve the problem. Computational results on several benchmarks and randomly generated instances show the effectiveness and the relevance of the proposed approach and highlight the integration value.

The Multi-Parent Biased Random-Key Genetic Algorithm with Implicit Path-Relinking and its real-world applications

In this paper, we present the Multi-Parent Biased Random-Key Genetic Algorithm with Implicit Path-Relinking (BRKGA-MP-IPR), a variant of the Biased Random-Key Genetic Algorithm that employs multiple (biased) parents to generate offspring instead of the usual two, and is hybridized with a novel, implicit path-relinking local search procedure. By operating over the standard unit hypercube, such path-relinking mechanism leverages the population representation of the BRKGA and thus provides complete independence between the local search procedure and the problem definition and implementation. This approach contrasts with traditional path-relinking procedures that are tied to the problem structure. Having both BRKGA and IPR operate over the same solution space not only makes the intensification/diversification paradigm more natural but also greatly simplifies the development effort from the perspective of the practitioner, as one only needs to develop a decoder to map unit random-key vectors to the solution space of the problem on hand. Apart from such key benefits, extensive computational experiments solving real-world problems, such as over-the-air software upgrade scheduling, network design problems, and combinatorial auctions, show that the BRKGA-MP-IPR offers performance benefits over the standard BRKGA as well as the BRKGA with multiple parents.

A Hybrid and Adaptive Metaheuristic for the Rebalancing Problem in Public Bicycle Systems

To meet the fluctuating demand for bicycles and for vacant lockers at each station, employees need to actively shift bicycles between stations by a fleet of vehicles. This is the rebalancing problem in public bicycle systems. In this paper, we propose a new objective function to the rebalancing problem, which meets the actual circs better. Then we explore a new method combines data mining process with GRASP-PR which incorporate GRASP and path-relinking procedure to experiment, not a single activation, but multiple and adaptive executions of the data mining process during the metaheuristic execution. And some improvements are made in some phases of the algorithm according to the feature of the bicycle rebalancing problem. Practice examples and comparison with the typical algorithm in the fields are made. The results show that the new proposals were able to find better results in less computational time for the rebalancing bicycle problem. The research result has been implemented in Hangzhou, China.

λ-GRASP with bi-directional path relinking for the bi-objective orienteering problem

This paper presents a new approach to solve the bi-objective orienteering problem (BOOP). The BOOP is a multi-objective extension of the well-known orienteering problem (OP). The multi-objective aspect stems from the personalised tourist routes planning problem, in which each point of interest in a city provides different profits associated with different categories. The aim of the BOOP is to find routes satisfying a given travel cost restriction, and visiting some points of interest that maximise the total collected of different profits. To generate a good approximation of Pareto-optimal solutions, we develop a new metaheuristic method based on hybridisation of λ-GRASP and a new variant of the path relinking procedure called bi-directional path relinking (BDPR). The latter is used as an intensification phase, with the goal to obtain new solutions that can eventually be part of the set of the Pareto-optimal solutions. The proposed approach is tested on benchmark instances taken from the literature. It is compared with the Pareto ant colony optimisation algorithm (P-ACO) and the variable neighbourhood search method (VNS). Computational results show that, compared to the P-ACO and the VNS procedures, the proposed method provide a good approximation of the Pareto front for the bi-objective orienteering problem.

λ-GRASP with bi-directional path relinking for the bi-objective orienteering problem

This paper presents a new approach to solve the bi-objective orienteering problem (BOOP). The BOOP is a multi-objective extension of the well-known orienteering problem (OP). The multi-objective aspect stems from the personalised tourist routes planning problem, in which each point of interest in a city provides different profits associated with different categories. The aim of the BOOP is to find routes satisfying a given travel cost restriction, and visiting some points of interest that maximise the total collected of different profits. To generate a good approximation of Pareto-optimal solutions, we develop a new metaheuristic method based on hybridisation of λ-GRASP and a new variant of the path relinking procedure called bi-directional path relinking (BDPR). The latter is used as an intensification phase, with the goal to obtain new solutions that can eventually be part of the set of the Pareto-optimal solutions. The proposed approach is tested on benchmark instances taken from the literature. It is compared with the Pareto ant colony optimisation algorithm (P-ACO) and the variable neighbourhood search method (VNS). Computational results show that, compared to the P-ACO and the VNS procedures, the proposed method provide a good approximation of the Pareto front for the bi-objective orienteering problem.

Design of public bicycle scheduling model based on data mining algorithm

Guangzhou Public Bicycle System has been the largest bike-sharing program in the world. The software of the system was developed by our research team. To meet the fluctuating demand for bicycles and for vacant lockers at each station, employees need to actively shift bicycles between stations by a fleet of vehicles. Hybrid GRA-SP metaheuristic which incorporate a path-relinking procedure have been successfully applied for different combinatorial problems. Data mining is a process that uses a variety of data analysis tools to discover patterns and relationships in data. In this paper, a new hybrid data mining metaheuristic combines GRA-SP which incorporate path-relinking procedure with data mining process is proposed and some improvement are made.

Application of a Memetic Algorithm for the Optimal Control of Bunches of Trajectories of Nonlinear Deterministic Systems with Incomplete Feedback

The application of a hybrid memetic constrained minimization algorithm that uses the ideas of evolutionary methods operating the concept of population and the algorithms of simulation and mutual learning of the population’s individuals for designing the optimal control of bunches of trajectories of nonlinear deterministic systems with incomplete feedback is proposed. Memetic algorithms use the concept of meme as a unit of information transmission between individuals of the population. In the proposed algorithm, the meme is a promising solution obtained in the course of executing a procedure to find an extremum. Since the proposed method uses a number of different heuristic procedures for solving the problem, in particular, the simulated annealing, ant colony optimization methods, and the path-relinking procedure for accelerating the search, the algorithm is a hybrid modified one. To demonstrate the efficiency of the proposed approach, the problem of stabilization and attitude control of a satellite is solved and the results are compared with those obtained using the local variation method.

The Vehicle Routing Problem with Release and Due Dates

A novel extension of the classical vehicle routing and scheduling problems is introduced that integrates aspects of machine scheduling into vehicle routing. Associated with each customer order is a release date that defines the earliest time that the order is available to leave the depot for delivery and a due date that indicates the time by which the order should ideally be delivered to the customer. The objective is to minimize a convex combination of the operational costs and customer service level, represented by the total distance traveled and the total weighted tardiness of delivery, respectively. A path-relinking algorithm (PRA) is proposed to address the problem, and a variety of benchmark instances are generated to evaluate its performance. The PRA exploits the efficiency and aggressive improvement of neighborhood search but relies on a new path-relinking procedure and advanced population management strategies to navigate the search space effectively. To provide a comparator algorithm to the PRA, we embed the neighborhood search into a standard iterated local search algorithm (ILS). Extensive computational experiments on the benchmark instances show that the newly defined features have a significant and varied impact on the problem, and the performance of the PRA dominates that of the ILS algorithm. The online supplement is available at https://doi.org/10.1287/ijoc.2017.0756 .

A multi-objective capacitated rural school bus routing problem with heterogeneous fleet and mixed loads

Four multi-objective meta-heuristic algorithms are presented to solve a multi-objective capacitated rural school bus routing problem with a heterogeneous fleet and mixed loads. Three objectives are considered: the total weighted traveling time of the students, the balance of routes among drivers, and the routing costs. The proposed methods were compared with one from the literature, and their performance assessed observing three multi-objective metrics: cardinality, coverage, and hyper-volume. All four devised methods outperformed the one from the literature. The algorithm with a path relinking procedure embedded during the crowding distance selection scheme had the best overall performance.

An Effective Hybrid Memetic Algorithm for the Minimum Weight Dominating Set Problem

The minimum weight-dominating set (MWDS) problem is NP-hard and has a lot of applications in the real world. Several metaheuristic methods have been developed for solving the problem effectively, but suffering from high CPU time on large-scale instances. In this paper, we design an effective hybrid memetic algorithm (HMA) for the MWDS problem. First, the MWDS problem is formulated as a constrained 0-1 programming problem and is converted to an equivalent unconstrained 0-1 problem using an adaptive penalty function. Then, we develop a memetic algorithm for the resulting problem, which contains a greedy randomized adaptive construction procedure, a tabu local search procedure, a crossover operator, a population-updating method, and a path-relinking procedure. These strategies make a good tradeoff between intensification and diversification. A number of experiments were carried out on three types of instances from the literature. Compared with existing algorithms, HMA is able to find high-quality solutions in much less CPU time. Specifically, HMA is at least six times faster than existing algorithms on the tested instances. With increasing instance size, the CPU time required by HMA increases much more slowly than required by existing algorithms.

A hybrid three-phase approach for the Max-Mean Dispersion Problem

This paper deals with the Max-Mean Dispersion Problem (Max-Mean DP) belonging to the general category of clustering problems which aim to find a subset of a set which maximizes a measure of dispersion/similarity between elements. A three-phase hybrid heuristic was developed, which combines a mixed integer non-linear solver, a local branching scheme and a path relinking procedure. Computational results performed on the literature instances show that the proposed procedure outperforms the state-of-the-art approaches.

An Integrated Method Based on PSO and EDA for the Max-Cut Problem.

The max-cut problem is NP-hard combinatorial optimization problem with many real world applications. In this paper, we propose an integrated method based on particle swarm optimization and estimation of distribution algorithm (PSO-EDA) for solving the max-cut problem. The integrated algorithm overcomes the shortcomings of particle swarm optimization and estimation of distribution algorithm. To enhance the performance of the PSO-EDA, a fast local search procedure is applied. In addition, a path relinking procedure is developed to intensify the search. To evaluate the performance of PSO-EDA, extensive experiments were carried out on two sets of benchmark instances with 800 to 20000 vertices from the literature. Computational results and comparisons show that PSO-EDA significantly outperforms the existing PSO-based and EDA-based algorithms for the max-cut problem. Compared with other best performing algorithms, PSO-EDA is able to find very competitive results in terms of solution quality.

Multi-neighborhood based path relinking for two-sided assembly line balancing problem

This paper presents a multi-neighborhood based path relinking algorithm (MN-PR) for solving the two-sided assembly line balancing problem. By incorporating an effective local search into a path relinking framework, the proposed MN-PR algorithm integrates a number of distinguishing features, such as a multi-neighborhood based local search procedure, a dedicated path relinking operator to generate new solutions and a strategy to fix an infeasible solution generated by the path relinking procedure to a feasible one. Our proposed MN-PR algorithm is tested on a set of totally 45 public instances widely used in the literature. Comparisons with other reference algorithms show the efficacy of the proposed algorithm in terms of the solution quality. Particularly, the proposed MN-PR algorithm is able to improve the best upper bounds for one instance with 65 tasks and 326 cycle time. This paper also presents an analysis to show the significance of the main components of the proposed algorithm.

Solving the Multi-Mode Resource Availability Cost Problem in Project Scheduling Based on Modified Particle Swarm Optimization

This paper proposes a model for multi-mode resource availability cost problem (MMRACP) in project scheduling which minimizes the resource availability cost required to finish all activities in a project at a given project deadline. Precedence relations exist among the activities of the project in the model. Furthermore, renewable and nonrenewable resources are both considered. MMRACP is a nondeterministic polynomial time hard (NP-hard) problem, as a result it is very difficult to use an exact method to solve it. For solving MMRACP, we developed a modified particle swarm optimization method combined with path relinking procedure and designed a heuristic algorithm to improve the fitness of the solution. At the end, a computational experiment including 180 instances was designed to test the performance of the modified particle swarm optimization. Comparative computational results show that the modified particle swarm optimization is very effective in solving MMRACP.