Biased Random-key Genetic Algorithm Research Articles

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.

Unsupervised feature selection based on bio-inspired approaches

In recent years, the scientific community has witnessed an explosion in the use of pattern recognition algorithms. However, little attention has been paid to the tasks preceding the execution of these algorithms, the preprocessing activities. One of these tasks is dimensionality reduction, in which a subset of features that improves the performance of the mining algorithm is located and algorithm's runtime is reduced. Although there are many methods that address the problems in pattern recognition algorithms, effective solutions still need to be researched and explored. Hence, this paper aims to address three of the issues surrounding these algorithms. First, we propose adapting a promising meta-heuristic called biased random-key genetic algorithm, which considers a random initial population construction. We call this algorithm as unsupervised feature selection by biased random-key genetic algorithm I. Next, we propose an approach for building the initial population partly in a deterministic way. Thus, we applied this idea in two algorithms, named unsupervised feature selection by particle swarm optimization and unsupervised feature selection by biased random-key genetic algorithm II. Finally, we simulated different datasets to study the effects of relevant and irrelevant attributes, and of noisy and missing data on the performance of the algorithms. After the Wilcoxon rank-sum test, we can state that the proposed algorithms outperform all other methods in different datasets. It was also observed that the construction of the initial population in a partially deterministic way contributed to the better performance. It should be noted that some methods are more sensitive to noisy and missing data than others, as well as to relevant and irrelevant attributes. • Particle swarm optimization and biased random-key genetic algorithms are proposed. • It is investigated how the construction of the initial population, as well as the missing and noisy data, implies the performance of the algorithms. • Ten simulated data sets are used containing relevant and irrelevant attributes, as well as different percentages of missing and noisy data. • An exhaustive computational and statistical evaluation is carried out. • The proposed approaches outperformed other methods.

The multicommodity traveling salesman problem with priority prizes: a mathematical model and metaheuristics

The classic Traveling Salesman Problem (TSP) only considers the costs involved in the routes and does not differentiate products or customers. Logistic companies face conflict between operational costs, customers with different categories of products, and customer satisfaction, which is directly related to delivery time. This paper presents a new mathematical model for a TSP with variable costs and priority prizes, taking into account the customer’s product and preference values. This problem is denoted as the Multicommodity Traveling Salesman Problem with Priority Prizes (MTSPPP). Two versions of the Biased Random-Key Genetic Algorithm (BRKGA) are proposed to solve medium and large instances of the MTSPPP. Computational tests were performed, using modified instances based on classical TSP instances. The proposed methods have proved to be efficient in solving the MTSPPP.

Order acceptance and scheduling with sequence-dependent setup times: A new memetic algorithm and benchmark of the state of the art

The Order Acceptance and Scheduling (OAS) problem describes a class of real-world problems such as in smart manufacturing and satellite scheduling. This problem consists of simultaneously selecting a subset of orders to be processed as well as determining the associated schedule. A common generalization includes sequence-dependent setup times and time windows. We propose a novel memetic algorithm for this problem, called Sparrow. It comprises a hybridization of biased random key genetic algorithm (BRKGA) and adaptive large neighbourhood search (ALNS). Sparrow integrates the exploration ability of BRKGA and the exploitation ability of ALNS. On a set of standard benchmark instances, this algorithm obtains better-quality solutions with runtimes comparable to state-of-the-art algorithms. To further understand the strengths and weaknesses of these algorithms, their performance is also compared on a set of new benchmark instances with more realistic properties. We conclude that Sparrow is distinguished by its ability to solve difficult instances from the OAS literature, and that the hybrid steady-state genetic algorithm (HSSGA) performs well on large instances in terms of optimality gap, although taking more time than Sparrow.

Evolutionary Algorithm for Optimization Regarding the Planning of Topological Facilities in Layout of a Shipyard

The purpose of this study is to contribute the approach to the problem of optimization regarding the planning of topological facilities in layout of a shipyard, with the objective of finding a robust solution to the problem by improving the solution space search through refining the genetic operators. For this, the computational results of the evolutionary algorithm proposed by Choi with changes made by the authors, being: 1) the use of the Partially-Matched Crossover (PMX) genetic operator; 2) the use of a recursive expression in the topological optimization step in addition to implementing the Biased Random-Key Genetic Algorithm (BRKGA) for the purpose of comparing the results. As a plan of the computational experiments two groups of experiments were performed: 1) with the parameters and variables of the work of Choi, in order to validate the efficiency and effectiveness of the AE proposed in this work and; 2) with the parameters and variables of the work of Choi with Department 03 fixed in the position of the best solution found in the 1st group of experiments (position 11 of the topological Grid). Each group contains 50 experiments with 100 iterations and variation of the number of individuals from 100 to 80,000 individuals. As a result, a better solution characterized by the reduction of material handling costs, of 11,816 presented by Choi, for 11,489 monetary units of cost, found from the changes made by the authors of the original proposal of the evolutionary algorithm and the use of BRKGA.

Decomposition heuristics for parallel-machine multiple orders per job scheduling problems with a common due date

Scheduling problems for identical parallel machines with earliness-tardiness objective are studied that are motivated by manufacturing processes in 300-mm wafer fabs. Wafers are transferred by front opening unified pods (FOUPs) in such fabs. Only a limited number of FOUPs is allowed since a large number of FOUPs results in a highly congested automated material handling system. A FOUP can contain a group of orders. A nonrestrictive common due date is assumed for all orders. Only orders of the same family can be grouped together in a FOUP. The lot and the item processing mode are differentiated in this article. Mixed integer linear programming (MILP) models are provided for both modes. It is shown that the two scheduling problems are NP-hard. Simple decomposition heuristics based on list scheduling and bin packing procedures are proposed. Biased random-key genetic algorithm (BRKGA)-based decomposition schemes are designed for the two scheduling problems. The BRKGAs are hybridised with the simple heuristics and an integer programming-based job formation approach in the lot processing mode. Results of computational experiments based on randomly generated problem instances are analysed and discussed for both scheduling problems. The results show that the proposed heuristics perform well with respect to solution quality and computing time. The BRKGA-type approaches clearly outperform the other heuristics.

Scheduling software updates for connected cars with limited availability

The current and the new generation of Internet of Things (IoT) devices present several challenges, among them the software update of legacy and new devices using wireless connections. In this paper, we study a problem of scheduling massive Firmware-Over-The-Air updates for millions of connected cars. We model this problem as a new generic problem called Time- and Machine-Dependent Scheduling Problem (TMDSP) that resembles project scheduling problems with variable-intensity activities. In the TMDSP, jobs, machine utilization, and production rates vary over time. In each period, a given job can be executed by a subset of machines with different capacities and production rates. The objective is to deploy a feasible schedule with minimum total completion time. We explore solving the problem using several approaches among than Biased Random-Key Genetic Algorithm (BRKGA), Iterated Local Search (ILS), Simulating Annealing (SA), two variations of Tabu Search (TB), and traditional genetic algorithms (TGA), in addition to a Mixed Integer Programming (MIP) model. We test the proposed approaches on a synthetic benchmark and very large real instances in IoT space. While using a commercial solver and the MIP model, we are able to solve only a few real instances (with, at most, 1,976 cars and 9,116 sectors); on the other hand, BRKGA presents significantly better results when compared to ILS, MIP solver and a simple multi-start heuristic.

Hybrid algorithms for placement of virtual machines across geo-separated data centers

Cloud computing has emerged as a new paradigm for hosting and supplying services over the Internet. This technology has brought many benefits, such as eliminating the need for maintaining expensive computing hardware. With an increasing demand for cloud computing, providing performance guarantees for applications that run over cloud become important. Applications can be abstracted into a set of virtual machines with certain guarantees depicting the quality of service of the application. In this paper, we consider the placement of these virtual machines across multiple data centers (VMPlacement), meeting the quality of service requirements while minimizing the bandwidth cost of the data centers. This problem is a generalization of the NP-hard generalized quadratic assignment problem (GQAP). In this paper, we present a greedy randomized adaptive search procedure and a biased random-key genetic algorithm, both hybridized with a path-relinking strategy and a local search based on variable neighborhood descent for solving this problem. The hybrid heuristics are also tested on instances of the GQAP. We show that both algorithms are effective in quickly solving small and large instances of VMPlacement problem, especially when the path-relinking is used. For GQAP, the results outperform the previous state-of-the-art algorithms.

Solving the open vehicle routing problem with capacity and distance constraints with a biased random key genetic algorithm

This paper presents a biased random-key genetic algorithm designed to solve the open vehicle routing problem with capacity and distance constraints. Consider a depot from which vehicles depart to deliver goods demanded by clients. Every client is served by one vehicle that is part of a homogeneous fleet. The vehicles initiate their routes at the depot and finish them after servicing the last client without returning to the depot. The problem’s objective function is to minimize the total distance traveled by the vehicles while respecting the capacity and maximum distance constraints. The potential applications in real life scenarios make this problem relevant among other vehicle routing problems. Three sets of benchmark problems from the literature are used to test the proposed algorithm. The obtained results show the algorithm’s good performance since the best-known solutions for 16 of the 30 instances were improved.

Minimizing flowtime in a flowshop scheduling problem with a biased random-key genetic algorithm

In this paper, we advance the state of the art for solving the Permutation Flowshop Scheduling Problem with total flowtime minimization. For this purpose, we propose a Biased Random-Key Genetic Algorithm (BRKGA) introducing on it a new feature called shaking. With the shaking, instead to full reset the population to escape from local optima, the shaking procedure perturbs all individuals from the elite set and resets the remaining population. We compare results for the standard and the shaking BRKGA with results from the Iterated Greedy Search, the Iterated Local Search, and a commercial mixed integer programming solver, in 120 traditional instances. For all algorithms, we use warm start solutions produced by the state-of-the-art Beam-Search procedure. Computational experiments show the efficiency of proposed BRKGA, in addition to identify lower and upper bounds, as well as some optimal values, among the solutions.

Model and methods to address urban road network problems with disruptions

AbstractDisruptions in urban road networks can quickly and significantly reduce the quality of the whole transportation network, and impact urban mobility for light vehicles, public transportation, etc. In this study, we consider both unidirectional and multidirectional road network problems with disruptions and connecting requirements. These problems aim at reconfiguring the urban network in terms of road direction in order to maintain a path among all points of the network (strong connectivity). The former is defined on simple graphs, mainly modeling part of a city such as historical centers, while the latter relies on multigraphs, modeling more general networks. Restoring the network (strong connectivity) after some disruptions may require the modification of the orientation of some streets, that is, arc reversals. Such actions can disturb users' driving habits. Thus, two objectives are considered separately: minimizing the total travel distance and minimizing the number of arc reversals. We define formally both problems and propose two metaheuristics, a biased random key genetic algorithm and an iterated local search. Numerical experiments have been performed on a set of generated instances and on the urban network of Troyes (France).

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.

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.