Random-key Genetic Algorithm Research Articles

Decomposition methods for cost and tardiness reduction in aircraft manufacturing flow lines

A manufacturing system consisting of two subsystems is considered in low-volume manufacturing as found in the aerospace industry. The first subsystem consists of parallel mixed-model assembly lines whereas identical parallel stations form the second one. A finite buffer is between the subsystems. A combined objective function is used which accounts for total labor and inventory costs at the first subsystem and for the makespan and total weighted tardiness (TWT) at the second subsystem. The jobs have to be assigned to one of the parallel assembly lines. They then have to be sequenced at each single assembly line. Workers have to be assigned to each job and station. Assignment and sequencing decisions have to be made for the jobs at the second subsystem to calculate the makespan and the TWT value. A random-key genetic algorithm (RKGA) assigns jobs to the assembly lines and sequences them there. The RKGA is hybridized with heuristics and exact approaches to determine start and completion times of the jobs at the stations. A list scheduling approach makes the decisions associated with the second subsystem. Outsourcing is applied to deal with the finite buffer between the two subsystems. Results of computational experiments based on randomly generated problem instances demonstrate that the decomposition approaches perform well.

Hybrid algorithms for the earliness–tardiness single-machine multiple orders per job scheduling problem with a common due date

In this paper, we study an earliness–tardiness scheduling problem for a single machine that is motivated by process conditions found in semiconductor wafer fabrication facilities (wafer fabs). In modern 300-mm wafer fabs, front opening unified pods (FOUPs) transfer wafers. The number of FOUPs is limited to avoid a congestion of the Automated Material Handling System. Several orders can be grouped in one FOUP. A nonrestrictive common due date for all the orders is assumed. Only orders that belong to the same family can be processed together in a single FOUP at the same time. We present a Mixed Integer Linear Programming (MILP) formulation for this problem. Moreover, we show that this scheduling problem is NP-hard. We propose several simple heuristics based on dispatching rules and assignment strategies from bin packing. Moreover, genetic algorithms are designed that assign the orders to the set of early and tardy orders, respectively. In addition, a random key genetic algorithm (RKGA) is described that proposes order sequences. The different algorithms are hybridized with job formation and sequencing heuristics. A more specialized algorithm that is based on the generalized assignment problem is presented for the special case of a single order family. Results of computational experiments based on randomly generated problem instances are presented. They demonstrate that the genetic algorithms perform well with respect to solution quality and computing time under a broad range of experimental conditions.

A BRKGA-DE algorithm for parallel-batching scheduling with deterioration and learning effects on parallel machines under preventive maintenance consideration

This paper introduces a parallel-batching scheduling problem with deterioration and learning effects on parallel machines, where the actual processing time of a job is subject to the phenomena of deterioration and learning. All jobs are first divided into different parallel batches, and the processing time of the batches is equal to the largest processing time of their belonged jobs. Then, the generated batches are assigned to parallel machines to be processed. Motivated by the characteristics of machine maintenance activities in a semiconductor manufacturing process, we take the machine preventive maintenance into account, i.e., the machine should be maintained after a fixed number of batches have been completed. In order to solve the problem, we analyze several structural properties with respect to the batch formation and sequencing. Based on these properties, a hybrid BRKGA-DE algorithm combining biased random-key genetic algorithm (BRKGA) and Differential Evolution (DE) is proposed to solve the parallel-batching scheduling problem. A series of computational experiments is conducted to demonstrate the effectiveness and efficiency of the proposed algorithm.

Solving CCVRPTW using biased random key genetic algorithm (BRKGA) with multiple parent

This research addresses a Capacitated Vehicle Routing Problem with Time Windows (CCVRPTW) which is a Vehicle Routing Problem (VRP) with fleet capacity and delivery time constraints. In the research, a Biased Random Key Genetic Algorithm (BRKGA) is proposed to solve the problem. The standard BRKGA is improved by modifying the crossover process accommodating Multiple-Parent. The proposed BRKGA is coded using the Matlab programming language. A case of soft drink distribution is used to evaluate the performance of the algorithm. From the research, it can be concluded that (1) The proposed BRKGA is better than the heuristic method proposed by previous research for dealing with the same case; (2) the Multiple-Parent BRKGA can further improve the general BRKGA; (3) The Multiple-Parent BRKGA with third parent selected randomly from NON-ELITE group results in a better solution than that of selected randomly from the whole population.

A biased random-key genetic algorithm for the two-stage capacitated facility location problem

This paper presents a new metaheuristic approach for the two-stage capacitated facility location problem (TSCFLP), which the objective is to minimize the operation costs of the underlying two-stage transportation system, satisfying demand and capacity constraints. In this problem, a single product must be transported from a set of plants to meet customers demands passing out by intermediate depots. Since this problem is known to be NP-hard, approximated methods become an efficient alternative to solve real-industry problems. As far as we know, the TSCFLP is being solved in most cases by hybrid approaches supported by an exact method, and sometimes a commercial solver is used for this purpose. Bearing this in mind, a BRKGA metaheuristic and a new local search for TSCFLP are proposed. It is the first time that BRKGA had been applied to this problem and the computational results show the competitiveness of the approach developed in terms of quality of the solutions and required computational time when compared with those obtained by state-of-the-art heuristics. The approach proposed can be easily coupled in intelligent systems to help organizations enhance competitiveness by optimally placing facilities in order to minimize operational costs.

Adaptive biased random-key genetic algorithm with local search for the capacitated centered clustering problem

Abstract This paper proposes an adaptive Biased Random-key Genetic Algorithm (A-BRKGA), a new method with on-line parameter control for combinatorial optimization problems. A-BRKGA has only one problem-dependent component, the decoder and all other parts can be reused. To control diversification and intensification, a novel adaptive strategy for parameter tuning is introduced. This strategy is based on deterministic rules and self-adaptive schemes. For exploitation of specific regions of the solution space we propose a local search in promising communities. The proposed method is evaluated on the Capacitated Centered Clustering Problem (CCCP), which is an NP-hard problem where a set of n points, each having a given demand, is partitioned into m clusters each with a given capacity. The objective is to minimize the sum of the Euclidean distances between the points and their geometric cluster centroids. Computational results show that the A-BRKGA with local search is competitive with other methods of literature.

Bi-objective scheduling on a restricted batching machine

In this work, we consider a batching machine that can process several jobs at the same time. Batches have a restricted batch size, and the processing time of a batch is equal to the largest processing time among all jobs within the batch. We solve the bi-objective problem of minimizing the maximum lateness and number of batches. This function is relevant as we are interested in meeting due dates and minimizing the cost of handling each batch. Our aim is to find the Pareto-optimal solutions by using an epsilon-constraint method on a new mathematical model that is enhanced with a family of valid inequalities and constraints that avoid symmetric solutions. Additionally, we present a biased random-key genetic algorithm to approximate the optimal Pareto points of larger instances in reasonable time. Experimental results show the efficiency of our methodologies.

A biased random-key genetic algorithm for the maximum quasi-clique problem

Given a graph G=(V,E) and a threshold γ ∈ (0, 1], the maximum cardinality quasi-clique problem consists in finding a maximum cardinality subset C* of the vertices in V such that the density of the graph induced in G by C* is greater than or equal to the threshold γ. This problem is NP-hard, since it admits the maximum clique problem as a special case. It has a number of applications in data mining, e.g. in social networks or phone call graphs. In this work, we propose a biased random-key genetic algorithm for solving the maximum cardinality quasi-clique problem. Two alternative decoders are implemented for the biased random-key genetic algorithm and the corresponding algorithm variants are evaluated. Computational results show that the newly proposed approaches improve upon other existing heuristics for this problem in the literature. All input data for the test instances and all detailed numerical results are available from Mendeley.

A random-keys genetic algorithm for scheduling unrelated parallel batch processing machines with different capacities and arbitrary job sizes

A batch processing machine (BPM) can simultaneously process several jobs and has wide applications in various industrial environments. This paper studies the problem of minimizing makespan on unrelated parallel BPMs with non-identical job sizes and arbitrary release times. In the environment of unrelated machines, each machine has a processing speed for each job. The unrelated BPM problem is the most general case of parallel BPM problems and is closer to actual production conditions. The problem under study is NP-hard. We present two lower bounds for the problem. Then a genetic algorithm based on random-keys encoding is proposed to solve the problem. The performance of the proposed algorithm is compared with a commercial solver (ILOG CPLEX) and two meta-heuristics published in the literature: a recent iterated greedy algorithm and a particle swarm optimization algorithm. Computational experiments show that the proposed algorithm produces better solutions compared to the other methods. The quality of the proposed lower bounds is evaluated as well.

Solving Capacitated Closed Vehicle Routing Problem with Time Windows (CCVRPTW) using BRKGA with local search

The main issue in vehicle routing problem (VRP) is finding the shortest route of product distribution from the depot to outlets to minimize total cost of distribution. Capacitated Closed Vehicle Routing Problem with Time Windows (CCVRPTW) is one of the variants of VRP that accommodates vehicle capacity and distribution period. Since the main problem of CCVRPTW is considered a non-polynomial hard (NP-hard) problem, it requires an efficient and effective algorithm to solve the problem. This study was aimed to develop Biased Random Key Genetic Algorithm (BRKGA) that is combined with local search to solve the problem of CCVRPTW. The algorithm design was then coded by MATLAB. Using numerical test, optimum algorithm parameters were set and compared with the heuristic method and Standard BRKGA to solve a case study on soft drink distribution. Results showed that BRKGA combined with local search resulted in lower total distribution cost compared with the heuristic method. Moreover, the developed algorithm was found to be successful in increasing the performance of Standard BRKGA.

A biased random-key genetic algorithm for the project scheduling problem with flexible resources

In this paper, we investigate a resource-constrained project scheduling problem with flexible resources. This is an $$\mathcal {NP}$$ -hard combinatorial optimization problem that consists of scheduling a set of activities requiring specific resource units of several skills. The goal is to minimize the makespan of the project. We propose a biased random-key genetic algorithm for computing feasible solutions for the referred problem. We study different decoding mechanisms: an already existing method in the literature, a new adapted serial scheduling generation scheme, and a combination of both. The new procedure is tested using a set of benchmark instances of the problem. The results provide strong evidence that the new heuristic is robust and yields high-quality feasible solutions.

BRKGA/VND Hybrid Algorithm for the Classic Three-dimensional Bin Packing Problem

The classic bin packing problem consists of packing a set of boxes with fixed orientation into the minimum number of bins. In this work we present a variable neighborhood descent (VND) inspired algorithm which improves the state-of-art biased random-key genetic algorithm (BRKGA), proposed in [6], for the three-dimensional bin packing problem. The constructive greedy heuristic method to pack the boxes uses an integer sequence to establish the order of boxes to be packed. The presented BRKGA/VND variant fills the initial and mutant population based on sorted box sequences. The devised hybrid method shows significantly superior average fitness through the generations, therefore, solutions with high quality are found faster. The novel approach is tested with a standard set of 320 instances. The computational experiment demonstrate that BRKGA/VND produces equal or better results compared to other state-of-art algorithms proposed in the literature. The empirical data shows that BRKGA/VND hybrid variant systematically produces high quality solutions at fewer iterations compared to the results attained by BRKGA.

A biased random key genetic algorithm for the protein–ligand docking problem

Molecular docking is a valuable tool for drug discovery. Receptor and flexible Ligand docking is a very computationally expensive process due to a large number of degrees of freedom of the ligand and the roughness of the molecular binding search space. A molecular docking simulation starts with receptor and ligand unbound structures, and the algorithm tests hundreds of thousands of ligand conformations and orientations to find the best receptor–ligand binding affinity by assigning and optimizing an energy function. Although the advances in the conception of methods and computational strategies for searching the best protein–ligand binding affinity, the development of new strategies, the adaptation, and investigation of new approaches and the combination of existing and state-of-the-art computational methods and techniques to the molecular docking problem are needed. We developed a Biased Random Key Genetic Algorithm as a sampling strategy to search the protein–ligand conformational space. We use a different method to discretize the search space. The proposed method (namely, BRKGA-DOCK) has been tested on a selection of protein–ligand complexes and compared to existing tools AUTODOCK VINA, DOCKTHOR, and a multiobjective approach (jMETAL). Compared to other traditional docking software, the proposed method shows best average Root-Mean-Square Deviation. Structural results were also statistically analyzed. The proposed method proved to be efficient and a good alternative for the molecular docking problem.

Methods for solving road network problems with disruptions

In this study, we provide two approximate methods for solving both Unidirectional and Multidirectional Road Network problems with Disruptions and connecting requirements. These problems aim at defining alternative paths to deviate traffic flows, allowing the arc orientation to be reversed, such that the network remains strongly connected. The objectives are set to minimize the total travel cost and the number of reversed arcs. Two methods, a Biased Random Key Genetic Algorithm and an Iterated Local Search, are proposed. Numerical experiments with single objective and bi-objective versions are performed and results are hence compared to the exact method studied in previous works.

Integrating pricing and capacity decisions in car rental: A matheuristic approach

Pricing and capacity decisions in car rental companies are characterized by high flexibility and interdependence. When planning a selling season, tackling these two types of decisions in an integrated way has a significant impact.This paper tackles the integration of capacity and pricing problems for car rental companies. These problems include decisions on fleet size and mix, acquisitions and removals, fleet deployment and repositioning, as well as pricing strategies for the different rental requests.A novel mathematical model is proposed, which considers the specific dynamics of rentals on the relationship between inventory and pricing as well as realistic requirements from the flexible car rental business, such as upgrades. Moreover, a solution procedure that is able to solve real-sized instances within a reasonable time frame is developed. The solution procedure is a matheuristic based on the decomposition of the model, guided by a biased random-key genetic algorithm (BRKGA) boosted by heuristically generated initial solutions. The positive impact on profit, of integrating capacity and pricing decisions versus a hierarchical/sequential approach, is validated.

Model-based view planning for building inspection and surveillance using voxel dilation, Medial Objects, and Random-Key Genetic Algorithm

Abstract Model-based view planning is to find a near-optimal set of viewpoints that cover the surface of a target geometric model. It has been applied to many building inspection and surveillance applications with Unmanned Aerial Vehicle (UAV). Previous approaches proposed in the past few decades suffer from several limitations: many of them work exclusively for 2D problems, generate only a sub-optimal set of views for target surfaces in 3D environment, and/or generate a set of views that cover only part of the target surfaces in 3D environment. This paper presents a novel two-step computational method for finding near-optimal views to cover the surface of a target set of buildings using voxel dilation, Medial Objects (MO), and Random-Key Genetic Algorithm (RKGA). In the first step, the proposed method inflates the building surfaces by voxel dilation to define a sub-volume around the buildings. The MO of this sub-volume is then calculated, and candidate viewpoints are sampled using Gaussian sampling around the MO surface. In the second step, an optimization problem is formulated as (partial) Set Covering Problem and solved by searching through the candidate viewpoints using RKGA and greedy search. The performance of the proposed two-step computational method was measured with several computational cases, and the performance was compared with two previously proposed methods: the optimal-scan-zone method and the randomized sampling-based method. The results demonstrate that the proposed method outperforms the previous methods by finding a better solution with fewer viewpoints and higher coverage ratio compared to the previous methods. Highlights A two-step “generate-test” view planning method is proposed. Voxel dilation, Medial Objects and Gaussian sampling are used to generate viewpoints. Random-Key GA and Greedy search are combined to solve the Set Covering Problem. The proposed method is benchmarked and outperforms two existing methods.

A Metaheuristic Approach to the Multi-Objective Unit Commitment Problem Combining Economic and Environmental Criteria

We consider a Unit Commitment Problem (UCP) addressing not only the economic objective of minimizing the total production costs—as is done in the standard UCP—but also addressing environmental concerns. Our approach utilizes a multi-objective formulation and includes in the objective function a criterion to minimize the emission of pollutants. Environmental concerns are having a significant impact on the operation of power systems related to the emissions from fossil-fuelled power plants. However, the standard UCP, which minimizes just the total production costs, is inadequate to address environmental concerns. We propose to address the UCP with environmental concerns as a multi-objective problem and use a metaheuristic approach combined with a non-dominated sorting procedure to solve it. The metaheuristic developed is a variant of an evolutionary algorithm, known as Biased Random Key Genetic Algorithm. Computational experiments have been carried out on benchmark problems with up to 100 generation units for a 24 h scheduling horizon. The performance of the method, as well as the quality, diversity and the distribution characteristics of the solutions obtained are analysed. It is shown that the method proposed compares favourably against alternative approaches in most cases analysed.

Single batch processing machine scheduling with two-dimensional bin packing constraints

We study the problem of minimizing the makespan for jobs on a single batch processing machine (BPM). A BMP can process several jobs as a batch simultaneously. Unlike the classic batch processing machine scheduling problems in which the capacity of a machine is modeled as one-dimensional knapsack constraints, in this research, the machine's capacity is represented by a two-dimensional rectangle and a job occupies a rectangle of its dimensions, i.e., width and height, while being processed on the machine. The processing time and the dimensions of the jobs are non-identical. A batch's processing time equals to the longest processing time of jobs in the batch. A batch is feasible only if the jobs can be placed in the machine without overlapping with each other. Arising from practical industrial applications such as advanced manufacturing and wafer fabrication, this problem is a generalization of both the classic single BPM scheduling problem and the two-dimensional bin packing problem (2D-BPP), which are both proven to be NP-hard. Thus, it is NP-hard as well. We present a mixed integer programming (MIP) model for this problem. We also develop heuristic algorithms to tackle this problem, including four single-sequence based heuristics, a biased random-key genetic algorithm (BRKGA), and a hybrid bin loading (HBL) algorithm. The performances of the MIP model and proposed algorithms are compared based on a set of random generated instances.

Heuristics for a flowshop scheduling problem with stepwise job objective function

In this work, we introduce the Flowshop Scheduling Problem with Delivery Dates and Cumulative Payoffs. This problem is a variation of the flowshop scheduling problem with job release dates that maximizes the total payoff with a stepwise job objective function. This paper contributes towards proposing a mathematical formulation for this new problem and an original constructive heuristic. Additionally, we develop a new benchmark of 300 hard instances which are available in a public repository. Besides, we provide primal and dual bounds for them. Extensive computational experiments were carried out taking into account classical constructive heuristics and hybrid local searches. Results show the merit of the FF heuristic when compared to other classical heuristics for flowshop scheduling problems. Additionally, we compare an Iterated Local Search (ILS), an Iterated Greedy Search (IGS), and a Biased Random-Key Genetic Algorithm (BRKGA), both customized for the studied problem, and a commercial mixed integer programming solver. The comparison between these methods showed that the BRKGA starting with a solution from FF heuristic is able to find the best solutions in a very short period of time. Iterated local Search and the commercial solver presented significantly worse results than the aforementioned methods.

A new load balance methodology for container loading problem in road transportation

The load balance aspect of the Container Loading Problem (CLP) has been handled in an simplified way in the literature. Either load balance has been treated as a soft constraint or the geometrical centre of the container has been assumed to be the ideal location for the centre of gravity of the cargo, or both, which does not meet regulatory directives and transportation legislation. In this paper, we treat load balance as a hard constraint and adopt vehicle specific diagrams that define the feasibility domain for the location of the centre of gravity of the cargo, according to the vehicle specific technical characteristics, thus fulfilling and complying with real-world regulations and legislation. We propose a multi-population biased random-key genetic algorithm (BRKGA), with a new fitness function that takes static stability and load balance into account. Extensive computational experiments were performed with different variants of the proposed approach. Also solutions taken from the literature were evaluated in terms of load balance. The computational results show that it is possible to obtain stable and load balanced solutions without compromising the performance in terms of container volume utilization, and demonstrate also the advantage in incorporating load balance in the packing generation algorithm.