Biased Random-key Genetic Algorithm Research Articles

Vehicle routing problem considering equity of demand satisfaction

Planning of distribution processes has been represented by vehicle routing problems (VRP), where objective functions are commonly related to the cost of routes and delivery times involved in those processes. However, other objectives, such as equity of demand satisfaction, are of particular interest in social or non-profit distribution systems. This study addresses a VRP focused on an egalitarian distribution among all demand centroids considering a heterogeneous fleet. In particular, our goal is to maximize the minimum fraction of fulfilled demand to foster the equity of demand satisfaction while minimizing the delivery times as a secondary objective. We formulate our optimization problem as a mixed-integer linear program that is intractable by using a commercial solver for large instances. Therefore, we design three variants of the biased random-key genetic algorithm, and one of them can obtain near-optimal solutions for instances up to 120 demand points and 15 routes in less than one minute of computational time. Finally, we present an analysis of the trade-off between egalitarian demand satisfaction and total delivery time for a scenario based on an economically deprived region in Mexico.

Optimizing the artificial neural network parameters using a biased random key genetic algorithm for time series forecasting

Artificial Neural Networks (ANN) is one of the most used methods in time series forecasting. Mostly, it is hard to determine the design and weight parameters of ANNs by experience. For this reason, ANN optimization is considered to find the best network design and parameter sets. In this study, a novel hybrid algorithm based on biased random key genetic algorithms is proposed for ANN optimization. The algorithm, which is named as BRKGA–NN, determines the number of hidden neurons, bias values of hidden neurons and the connection weights between nodes. To test the performance of the BRKGA–NN, the algorithm is compared with genetic algorithm based ANN, ANN with back-propagation, Support Vector Regression and Autoregressive Integrated Moving Average on some of the most known time series datasets. According to the results of forecasts, BRKGA–NN algorithm can produce better forecasts than the compared methods. In addition to the time series datasets, the results and comparisons of the forecasts with the proposed algorithm using real-life data are also presented.

Failure risk of brazilian tailings dams: a data mining approach

Abstract This paper proposes the use of a hybrid method that combines Biased Random Key Genetic Algorithm (BRKGA) with a local search heuristic to separate Brazilian tailing dam data into groups. The goal was identifying dams similar to Fundao and B1 failed dams. The groups were created by solving the clustering problem by BRKGA. The clustering problem consists in separating a set of objects into groups such that members of each group are similar to each other. The data was composed by 427 dams, with the actual 425 dams of Brazilian Register of Tailing Dams and the two Brazilian failed dams from the last years. Computational experiments considering real data available are presented to demonstrate the efficacy of the proposed method producing feasible solutions. Thus, it is expected that the good results can be applied in the identification of tailings dams with risk potentials, assisting in the identification of these dams.

A BRKGA-based matheuristic for the maximum quasi-clique problem with an exact local search strategy

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 has a number of applications in data mining, e.g., in social networks or phone call graphs. We propose a matheuristic for solving the maximum cardinality quasi-clique problem, based on the hybridization of a biased random-key genetic algorithm (BRKGA) with an exact local search strategy. The newly proposed approach is compared with a pure biased random-key genetic algorithm, which was the best heuristic in the literature at the time of writing. Computational results show that the hybrid BRKGA outperforms the pure BRKGA.

A Hybrid Chemical Reaction Optimization Algorithm for Solving 3D Packing Problem

This paper combines the chemical reaction optimisation algorithm with the greedy algorithm to solve the three-dimensional bin packing problem (3D-BPP). Traditionally, the 3D-BPP is solved with algorithms based on particle swarm optimisation, genetic algorithm, or simulated annealing algorithm, etc. The chemical reaction optimisation algorithm is proposed in recent years, which has the advantages of traditional simulated annealing algorithm and has a faster convergence speed. After making appropriate adjustments to the chemical reaction optimisation algorithm, the experiment was performed on classic 320 examples. The results show that the proposed algorithm outperforms the existing algorithms such as greedy variable neighbourhood descent (GVND) and biased random key genetic algorithm (BRKGA).

Biased random-key genetic algorithm for cobot assignment in an assembly/disassembly job shop scheduling problem

Abstract Nowadays many manufacturing companies try to improve the performance of their processes by including innovative available technologies such as collaborative robots. Collaborative robots are robots where no safety distance is necessary, through cooperation with human workers they can increase production speed. In this paper we consider the collaborative robot assignment combined with the job shop scheduling problem. To solve this problem, we propose a genetic algorithm with a biased random-key encoding. The objective function for the optimization is a weighted function that factors in production cost and makespan that should be minimized. We propose a special encoding of the solution: the assignment of cobots to workstations, the assignment of tasks to different workstations and the priority of tasks. The results show how much the weighted objective function can be decreased by the deployment of additional collaborative robots in a real-world production line. Additionally, the biased random-key encoded results are compared to typical integer encoded solution. With the biased random-key encoding, we were able to find better results than with the standard integer encoding.

Hybrid metaheuristics to solve a multiproduct two‐stage capacitated facility location problem

AbstractThis paper presents two hybrid metaheuristics to solve a multiproduct two‐stage capacitated facility location problem (MP‐TSCFLP). In this problem, a set of different products must be transported from a set of plants to a set of intermediate depots (first stage) and from these depots to a set of customers (second stage). The objective is to minimize the cost related to open plants and depots plus the cost for transporting the products from the plants to the customers satisfying demand and capacity constraints. Recently, the methods clustering search (CS) and biased random‐key genetic algorithm (BRKGA) were successfully applied to solve a single‐product problem (SP‐TSCFLP). Therefore, in this paper we propose adaptations and implementations of these methods for handling with a multiproduct approach. To the best of our knowledge, CS and BRKGA presented the best results for the SP‐TSCFLP and both have not yet been applied to solve the problem with multiple products. Four sets of large‐sized instances with different characteristics are proposed and computational experiments compare the obtained results to those from a commercial solver.

A biased random-key genetic algorithm for the set orienteering problem

This paper addresses the Set Orienteering Problem which is a generalization of the Orienteering Problem where the customers are grouped in clusters, and the profit associated with each cluster is collected by visiting at least one of the customers in the respective cluster. The problem consists of finding a tour that maximizes the collected profit but, since the cost of the tour is limited by a threshold, only a subset of clusters can usually be visited. We propose a Biased Random-Key Genetic Algorithm for solving the Set Orienteering Problem in which three local search procedures are applied to improve the fitness of the chromosomes. In addition, we introduced three rules useful to reduce the size of the instances and to speed up the resolution of the problem. Finally, a hashtable is used to quickly retrieve the information that are required several times during the computation. The computational results, carried out on benchmark instances, show that our algorithm is significantly faster than the other algorithms, proposed in the literature, and it provides solutions very close to the best-known ones.

Iterated local search for single machine total weighted tardiness batch scheduling

This paper presents an iterated local search (ILS) algorithm for the single machine total weighted tardiness batch scheduling problem. To our knowledge, this is one of the first attempts to apply ILS to solve a batching scheduling problem. The proposed algorithm contains a local search procedure that explores five neighborhood structures, and we show how to efficiently implement them. Moreover, we compare the performance of our algorithm with dynamic programming-based implementations for the problem, including one from the literature and two other ones inspired in biased random-key genetic algorithms and ILS. We also demonstrate that finding the optimal batching for the problem given a fixed sequence of jobs is $$\mathcal {NP}$$ -hard, and provide an exact pseudo-polynomial time dynamic programming algorithm for solving such problem. Extensive computational experiments were conducted on newly proposed benchmark instances, and the results indicate that our algorithm yields highly competitive results when compared to other strategies. Finally, it was also observed that the methods that rely on dynamic programming tend to be time-consuming, even for small size instances.

Barrakuda: A Hybrid Evolutionary Algorithm for Minimum Capacitated Dominating Set Problem

The minimum capacitated dominating set problem is an NP-hard variant of the well-known minimum dominating set problem in undirected graphs. This problem finds applications in the context of clustering and routing in wireless networks. Two algorithms are presented in this work. The first one is an extended version of construct, merge, solve and adapt, while the main contribution is a hybrid between a biased random key genetic algorithm and an exact approach which we labeled Barrakuda. Both algorithms are evaluated on a large set of benchmark instances from the literature. In addition, they are tested on a new, more challenging benchmark set of larger problem instances. In the context of the problem instances from the literature, the performance of our algorithms is very similar. Moreover, both algorithms clearly outperform the best approach from the literature. In contrast, Barrakuda is clearly the best-performing algorithm for the new, more challenging problem instances.

A multistart biased random key genetic algorithm for the flexible job shop scheduling problem with transportation

AbstractThis work addresses the flexible job shop scheduling problem with transportation (FJSPT), which can be seen as an extension of both the flexible job shop scheduling problem (FJSP) and the job shop scheduling problem with transportation (JSPT). Regarding the former case, the FJSPT additionally considers that the jobs need to be transported to the machines on which they are processed on, while in the latter, the specific machine processing each operation also needs to be decided. The FJSPT is NP‐hard since it extends NP‐hard problems. Good‐quality solutions are efficiently found by an operation‐based multistart biased random key genetic algorithm (BRKGA) coupled with greedy heuristics to select the machine processing each operation and the vehicles transporting the jobs to operations. The proposed approach outperforms state‐of‐the‐art solution approaches since it finds very good quality solutions in a short time. Such solutions are optimal for most problem instances. In addition, the approach is robust, which is a very important characteristic in practical applications. Finally, due to its modular structure, the multistart BRKGA can be easily adapted to solve other similar scheduling problems, as shown in the computational experiments reported in this paper.

Microaggregation heuristic applied to statistical disclosure control

The dissemination of microdata by public institutions, especially National Statistical Offices (NSOs), and data sharing between public and private organizations and the academia are of undeniable importance today. However, very important ethical and legal aspects related to privacy protection, whether for an individual or a company, often restrict this cooperation. In this sense, the methods of Statistical Disclosure Control (SDC), or, more specifically, microaggregation techniques, offer an alternative to enable the dissemination and sharing of microdata through the control of disclosure risk. In this article, we propose a new heuristic method that adopts concepts from Biased Random Key Genetic Algorithm (BRKGA) metaheuristic and present a comparative study with well-known microaggregation methods. Computational simulations show that the proposed method consistently outperforms other methods in terms of simultaneously reducing information loss and disclosure risk. In addition, the proposed method allows the adopting or even combining of any information loss and disclosure risk metrics. This feature delivers great flexibility and much more control to the privacy protection process.

Timetabling with flexible frequencies to synchronise groups of bus lines at common stops

ABSTRACT In this study, we present a bi-objective partially-integrated optimisation approach for frequency setting and timetabling problems, assuming that buses' speed depends on the departure time of trips. Our goal is to synchronise groups of bus lines at common stops, minimising the average waiting time at synchronisation points and operational costs in terms of lines' frequencies. Our optimisation problem is formulated as a mixed-integer linear programme, which uses time-indexed variables to define a linear approximation of the average waiting time. Moreover, we present an experimental stage using the commercial solver CPLEX, a weighted sum method implementing a Biased Random-Key Genetic Algorithm (BRKGA) to solve the problem, and a BRKGA combined with the Hierarchical Non-dominated Sorting Algorithm to obtain an approximation of the Pareto front for bi-objective version. Numerical results show that our proposed metaheuristics are handy tools to obtain better solutions in short computational times than the solver of CPLEX.

The double traveling salesman problem with partial last‐in‐first‐out loading constraints

AbstractIn this paper, we introduce the double traveling salesman problem with partial last‐in‐first‐out loading constraints (DTSPPL). It is a pickup‐and‐delivery single‐vehicle routing problem, where all pickup operations must be performed before any delivery operation because the pickup‐and‐delivery areas are geographically separated. The vehicle collects items in the pickup area and loads them into its container, a horizontal stack. After performing all pickup operations, the vehicle begins delivering the items in the delivery area. Loading and unloading operations must obey a partial last‐in‐first‐out (LIFO) policy, that is, a version of the LIFO policy that may be violated within a given reloading depth. The objective of the DTSPPL is to minimize the total cost, which involves the total distance traveled by the vehicle and the number of items that are unloaded and then reloaded due to violations of the standard LIFO policy. We formally describe the DTSPPL through two integer linear programming (ILP) formulations and propose a heuristic algorithm based on the biased random‐key genetic algorithm (BRKGA) to find high‐quality solutions. The performance of the proposed solution approaches is assessed over a broad set of instances. Computational results have shown that both ILP formulations have been able to solve only the smaller instances, whereas the BRKGA obtained good‐quality solutions for almost all instances, requiring short computational times.

A non-dominated sorting based customized random-key genetic algorithm for the bi-objective traveling thief problem

In this paper, we propose a method to solve a bi-objective variant of the well-studied traveling thief problem (TTP). The TTP is a multi-component problem that combines two classic combinatorial problems: traveling salesman problem and knapsack problem. We address the BI-TTP, a bi-objective version of the TTP, where the goal is to minimize the overall traveling time and to maximize the profit of the collected items. Our proposed method is based on a biased-random key genetic algorithm with customizations addressing problem-specific characteristics. We incorporate domain knowledge through a combination of near-optimal solutions of each subproblem in the initial population and use a custom repair operator to avoid the evaluation of infeasible solutions. The bi-objective aspect of the problem is addressed through an elite population extracted based on the non-dominated rank and crowding distance. Furthermore, we provide a comprehensive study showing the influence of each parameter on the performance. Finally, we discuss the results of the BI-TTP competitions at EMO-2019 and GECCO-2019 conferences where our method has won first and second places, respectively, thus proving its ability to find high-quality solutions consistently.

A MIP model and a biased random-key genetic algorithm based approach for a two-dimensional cutting problem with defects

This paper addresses a two-dimensional (2D) non-guillotine cutting problem, where a set of small rectangular items of given types has to be cut from a large rectangular stock plate having defective regions so as to maximize the total value of the rectangles cut. The number of small items of each item type which can be cut from the large object is unrestricted. A novel MIP model and a hybrid approach combining a novel placement procedure with a biased random-key genetic algorithm (BRKGA) are presented. The parameters used by the novel placement procedure for the development of a cutting plan are evolved by the BRKGA. The management of the free spaces and of the defects uses a maximal-space representation. The approach is evaluated and compared to other approaches by means of a series of detailed numerical experiments using 5414 benchmark instances taken from the literature. The experimental results validate the quality of the solutions and the effectiveness of the proposed algorithm.

Biased random-key genetic algorithm for scheduling identical parallel machines with tooling constraints

We address the problem of scheduling a set of n jobs on m parallel machines, with the objective of minimizing the makespan in a flexible manufacturing system. In this context, each job takes the same processing time in any machine. However, jobs have different tooling requirements, implying that setup times depend on all jobs previously scheduled on the same machine, owing to tool configurations. In this study, this NP-hard problem is addressed using a parallel biased random-key genetic algorithm hybridized with local search procedures organized using variable neighborhood descent. The proposed genetic algorithm is compared with the state-of-the-art methods considering 2,880 benchmark instances from the literature reddivided into two sets. For the set of small instances, the proposed method is compared with a mathematical model and better or equal results for 99.86% of instances are presented. For the set of large instances, the proposed method is compared to a metaheuristic and new best solutions are presented for 93.89% of the instances. In addition, the proposed method is 96.50% faster than the compared metaheuristic, thus comprehensively outperforming the current state-of-the-art methods.

Robust meter placement for state estimation considering Distribution Network Reconfiguration for annual energy loss reduction

This paper proposes a methodology to allocate meters in distribution networks oriented to state estimation. The proposed approach considers that the meter placement is carried out simultaneously with the Distribution Network Reconfiguration (DNR) for annual energy loss reduction. This formulation of the allocation problem prevents the State Estimator Accuracy (SEA) from being degraded when the topology is changed and that an excessive number of meters is installed to obtain acceptable accuracy. These objectives were achieved using a multi-objective formulation that minimizes resistive losses, the risk of violating SEA and the number of meters installed in the network. The problem of meter placement formulated in this paper is solved through the Multi-Objective Biased Random-Key Genetic Algorithm (MOBRKGA). The tests results demonstrate that MOBRKGA can generate high quality solutions with significant reduction in annual energy losses and metering system with good accuracy and low installation cost.

A genetic algorithm applied to optimal allocation in stratified sampling

Over the last decades, many researchers have studied and proposed new methods for the solution of the multivariate optimal allocation problem, which can be performed by choosing one of the following goals: (i) minimizing the weighted combination of relative variances, considering the sample size fixed or (ii) minimizing the sample size in a way that the coefficients of variation are lower or equal to the previously fixed coefficients of variation. Taking each goal into account, the present article proposes two heuristic algorithms that were developed by studying the optimization technique called biased random key genetic algorithm. The computational experiments reported in the end of this work indicate that the proposed algorithms can be a good alternative for the solution of this problem, when compared with the two methods from literature.

A biased random-key genetic algorithm for routing and wavelength assignment under a sliding scheduled traffic model

The problem of routing and wavelength assignment in optical networks consists in minimizing the number of wavelengths that are needed to route a set of demands, such that demands routed using lightpaths that share common links are assigned to different wavelengths. We present a biased random-key genetic algorithm for approximately solving the problem of routing and wavelength assignment of sliding scheduled lightpath demands in optical networks. In this problem variant, each demand is characterized not only by a source and a destination, but also by a duration and a time window in which it has to be met. Computational experiments show that the numerical results obtained by the proposed heuristic improved upon those obtained by a multistart constructive heuristic. In addition, the biased random-key genetic algorithm obtained much better results than an existing algorithm for the problem, finding solutions that use roughly 50% of the number of wavelengths determined by the latter.