A biased random‐key genetic algorithm for the minimization of open stacks problem

A biased random-key genetic algorithm (BRKGA) is a general search procedure for finding optimal or near-optimal solutions to hard combinatorial optimization problems. It is derived from the random-key genetic algorithm of Bean (1994), differing in the way solutions are combined to produce offspring. BRKGAs have three key features that specialize genetic algorithms: A fixed chromosome encoding using a vector of N random keys or alleles over the real interval [0, 1), where the value of N depends on the instance of the optimization problem; A well-defined evolutionary process adopting parameterized uniform crossover to generate offspring and thus evolve the population; The introduction of new chromosomes called mutants in place of the mutation operator usually found in evolutionary algorithms. Such features simplify and standardize the procedure with a set of self-contained tasks from which only one is problem-dependent: that of decoding a chromosome, i.e. using, the keys to construct a solution to the underlying optimization problem, from which the objective function value or fitness can be computed. BRKGAs have the additional characteristic that, under a weak assumption, crossover always produces feasible offspring and, therefore, a repair or healing procedure to recover feasibility is not required in a BRKGA. In this tutorial we review the basic components of a BRKGA and introduce an Application Programming Interface (API) for quick implementations of BRKGA heuristics. We then apply the framework to a number of hard combinatorial optimization problems, including 2-D and 3-D packing problems, network design problems, routing problems, scheduling problems, and data mining. We conclude with a brief review of other domains where BRKGA heuristics have been applied.

This work proposes a hybrid genetic algorithm (GA) to address the unit commitment (UC) problem. In the UC problem, the goal is to schedule a subset of a given group of electrical power generating units and also to determine their production output in order to meet energy demands at minimum cost. In addition, the solution must satisfy a set of technological and operational constraints. The algorithm developed is a hybrid biased random key genetic algorithm (HBRKGA). It uses random keys to encode the solutions and introduces bias both in the parent selection procedure and in the crossover strategy. To intensify the search close to good solutions, the GA is hybridized with local search. Tests have been performed on benchmark large-scale power systems. The computational results demonstrate that the HBRKGA is effective and efficient. In addition, it is also shown that it improves the solutions obtained by current state-of-the-art methodologies.

The two-dimensional cutting problem has a direct relationship with industry problems. There are several proposals to solve these problems. In particular, solution proposals using metaheuristics are the focus of this research. Thus, in this paper, we present a specialized biased random key genetic algorithm. Several tests were performed using known instances in the specific literature, and the results found by the metaheuristics proposed were, in many cases, equal or superior to the results already published in the literature. Another comparison of results presented in this paper is related to the results obtained by specialized metaheuristics and the results found by a mathematical model using commercial software. Once again, in this case, the genetic algorithm presented results equal to or very close to the optimum found by the mathematical model. In addition, the optimization proposal was extended to two-dimensional non-guillotine cutting without parts orientation.

This paper describes libbrkga, a GNU-style dynamic shared Python/C++ library of the biased random-key genetic algorithm (BRKGA) for bound constrained global optimization. BRKGA (J Heuristics 17:487---525, 2011b) is a general search metaheuristic for finding optimal or near-optimal solutions to hard optimization problems. It is derived from the random-key genetic algorithm of Bean (ORSA J Comput 6:154---160, 1994), differing in the way solutions are combined to produce offspring. After a brief introduction to the BRKGA, including a description of the local search procedure used in its decoder, we show how to download, install, configure, and use the library through an illustrative example.

This research is focused on solving the Cutting Stock with Limited Open Stacks Problem (CS-LOSP). The CS-LOSP is an optimization problem which consists of the classical Cutting Stock Problem (CSP) paired with the additional constraint that the maximum number of open stacks from the sequencing of the cutting patterns obtained from the CSP solution is equal or lower than a preset limit. Despite being a problem with great practical importance, the literature lacks models for this problem, and only one-dimensional problems are addressed. In this paper, we propose two integer linear programming formulations for the CS-LOSP that are valid for solving instances of the CSP of any dimension. In order to eliminate symmetrical solutions to the problem, the proposed formulations sequence sets of cutting patterns instead of sequencing the cutting patterns individually, thus, the search space for solutions is reduced. A set of randomly generated instances for the two-dimensional problem is used to perform computational experiments in order to validate the proposed mathematical formulations.

Obtaining the Grundy chromatic number: How bad can my greedy heuristic coloring be?

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).

O problema de geração de padrões de corte (ou problema de corte de estoque) consiste em determinar o conjunto de padrões em que unidades demandadas (itens) são cortadas de unidades maiores (objetos) tal que, por exemplo, o custo ou a perda de material é minimizado. O problema de seqüenciamento de padrões de corte consiste em determinar a seqüência em que os padrões são cortados tal que, por exemplo, o número máximo de pilhas abertas (pilhas de itens com demanda apenas parcialmente produzida, que ainda serão cortados de um ou mais padrões seguintes nessa seqüência) é minimizado. Em geral, uma boa solução para o problema de geração de padrões não corresponde a uma boa solução para o problema de seqüenciamento de padrões e vice-versa. Esses dois problemas são freqüentemente resolvidos, tanto na prática como na literatura, de forma independente e sucessiva. Este trabalho apresenta três abordagens heurísticas para resolver de forma integrada os problemas de geração e seqüenciamento de padrões, considerando o trade-off entre os objetivos envolvidos. Embora essas abordagens possam ser aplicadas para problemas de corte e empacotamento de qualquer dimensão, neste trabalho elas são analisadas e comparadas apenas para o caso de corte unidimensional.

Neste artigo é tratado o clássico problema de corte de estoque bidimensional, cuja solução consiste em um conjunto de padrões de corte que otimiza uma função objetivo, por exemplo, a perda de material. Porém, os padrões de corte podem ser seqüenciados de modo que um outro objetivo também seja otimizado, como, por exemplo, o número máximo de pilhas abertas de itens (uma pilha é aberta quando um tipo de item é cortado pela primeira vez e fechada quando todos os itens deste tipo foram cortados). Uma boa solução para o problema de geração de padrões de corte freqüentemente não resulta numa boa solução para o problema de sequenciamento de padrões de corte, e vice-versa. Em geral, esses dois problemas são abordados, tanto na prática como na literatura, de forma independente e sucessiva. Pileggi et al. (2005) propuseram abordagens heurísticas para resolver esses dois problemas de forma integrada, considerando o trade-off entre os objetivos envolvidos, e analisaram o caso de corte unidimensional (p.e., corte de barras). No presente trabalho estas abordagens são estendidas e aplicadas para analisar o caso de corte bidimensional guilhotinado (p.e., corte de chapas). Resultados computacionais são apresentados para exemplos gerados aleatoriamente e para um exemplo real de uma fábrica de móveis.

The parallel batch processing machine scheduling problem with two-dimensional bin packing constraints (PBS-2D) has appeared in many industrial environments, but the research on this problem is still not sufficient. In this article, we use the 2-D rectangular packing constraints to describe the spatial geometric layout of jobs more accurately, and propose a mixed integer linear programming (MILP) model to minimize the makespan of PBS-2D. According to the in-depth analysis of the problem properties, PBS-2D is separated into three subproblems, which are job-machine assignment, 2-D job placement, and job sequence optimization. An improved biased random key genetic algorithm (OBRKGA) is proposed to solve job-machine assignment and job sequence optimization. This algorithm generates the initial population based on the idea of orthogonal experimental design, so that the whole solution space can be scanned evenly when generating the initial solution, making the algorithm be more likely to find better solutions for subsequent evolution. At the same time, a bin packing algorithm based on best fit is designed to handle 2-D job placement problem. Finally, the algorithms are tested on a large number of randomly generated instances, the results show that OBRKGA outperformed the original BRKGA, the classical moth-flame optimization algorithm, particle swarm optimization algorithm, gravity search algorithm, and MILP.

Optimizing Automated Manufacturing Processes Using a Hybrid BRKGA Algorithm: A Case Study on Flexible Job-Shop Scheduling

The environmental concerns are having a significant impact on the operation of power systems. The traditional Unit Commitment problem, which to minimizes the fuel cost is inadequate when environmental emissions are also considered in the operation of power plants. This paper presents a Biased Random Key Genetic Algorithm (BRKGA) approach combined with non-dominated sorting procedure to find solutions for the unit commitment multiobjective optimization problem. In the first stage, the BRKGA solutions are encoded by using random keys, which are represented as vectors of real numbers in the interval [0,1]. In the subsequent stage, a nondominated sorting procedure similar to NSGA II is employed to approximate the set of Pareto solution through an evolutionary optimization process. The GA proposed is a variant of the random key genetic algorithm, since bias is introduced in the parent selection procedure, as well as, in the crossover strategy. Test results with the existent benchmark systems of 10 units and 24 hours scheduling horizon are presented. The comparison of the obtained results with those of other Unit Commitment (UC) multiobjective optimization methods reveal the effectiveness of the proposed method.

Metaheuristic hybridizations for the regenerator placement and dimensioning problem in sub-wavelength switching optical networks

Improving Additive Manufacturing production planning: A sub-second pixel-based packing algorithm

In this study, an ABC-Local Search (ABC-Ls) method was proposed by including a new local search procedure into the standard artificial bee colony (ABC) algorithm to perform the parameter estimation of photovoltaic systems (PV). The aim of the proposed ABC-Ls method was to improve the exploration capability of the standard ABC with a new local search procedure in addition to the exploitation and exploration balance of the standard ABC algorithm. The proposed ABC-Ls method was first tested on 15 well-known benchmark functions in the literature. In the results of the Friedman Mean Rank test used for statistical analysis, ABC-Ls method successfully ranked first with a value of 1.300 in benchmark functions. After obtaining successful results on the benchmark tests, the proposed ABC-Ls method was applied to the single diode, double diode and Photowatt-PWP-201 PV modules of PV systems for parameter estimations. In addition, the proposed ABC-Ls method has been applied to the KC200GT PV module for parameter estimation under different temperature and irradiance conditions of the PV modules. The success of ABC-Ls method was compared with genetic algorithm (GA), particle swarm optimization (PSO) algorithm, ABC algorithm, tree seed algorithm (TSA), Jaya, Atom search optimization (ASO). The comparison results were presented in tables and graphics in detail. The RMSE values for the parameter estimation of single diode, double diode and Photowatt-PWP-201 PV module of the proposed ABC-LS method were found as 9.8602E−04, 9.8257E−04 and 2.4251E−03, respectively. In this context, the proposed ABC-LS method has been compared with the literature for parameter estimation of single diode, double diode and Photowatt-PWP-201 PV module and it has been found that it provides a parameter estimation similar or better than other studies. The proposed ABC-Ls method for parameter estimation of the KC200GT PV module under different conditions is shown in convergence graphs and box plots, where it achieves more successful, effective and stable results than GA, PSO, ABC, TSA, Jaya and ASO algorithms.