IMPROVED BIASED RANDOM KEY GENETIC ALGORITHM FOR THE TWO-DIMENSIONAL NON-GUILLOTINE CUTTING PROBLEM

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.

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.

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.

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).

The Two-Dimensional Cutting Problem has a direct relationship with problems of industries. There are several proposals for solving this problem. In particular, solution proposals using metaheuristics were the focus of this research. Thus, in this paper we present a specialized genetic algorithm of randomized random keys. Several tests were performed using known instances in the specific literature, and the results found by the metaheuristic proposed were in many cases, equal or superior, to the results already published in the literature. Another comparative of results presented in this paper is related to the results obtained by the metaheuristic expert and results found by mathematical modeling using commercial software. In this case, again 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 cut without parts orientation.

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.

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 paper describes a biased random‐key genetic algorithm (BRKGA) for the minimization of the open stacks problem (MOSP). The MOSP arises in a production system scenario, and consists of determining a sequence of cutting patterns that minimize the maximum number of open stacks during the cutting process. The proposed approach combines a BRKGA and a local search procedure for generating the sequence of cutting patterns. A novel fitness function for evaluating the quality of the solutions is also developed. Computational tests are presented using available instances taken from the literature. The high quality of the solutions obtained validate the proposed approach.

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

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

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 paper, cell loading and shipment method optimisation problem in a cellular manufacturing system are studied. A hierarchical methodology that consists of mathematical optimisation model, genetic algorithms (GAs) and artificial neural networks (ANNs) were proposed. The mathematical model is compared with the GA in terms of the optimisation performance. Next, ANN model was developed as decision support tool to study the impact of GA parameters on the solution quality. Several problem sizes were experimented with the proposed GA and the mathematical model, and compared. GA was run to make a total of 648 sample solutions for the 20-job problem. Next, ANN model was built based on the sample solutions' data and the optimal ANN model is identified out of 1,000 networks. The results were also coupled with sensitivity and statistical analyses, which indicated that type of crossover and mutation operators, had the greatest impact on the solution quality.

This chapter first presents job shop scheduling problems (JSSP) with fuzzy processing time and fuzzy trapezoid or doublet due-date. An efficient random key genetic algorithm (RKGA) is suggested, in which a random key representation and a new decoding strategy are proposed and two-point or discrete crossover are used. Performance analyses on random key representation are done and RKGA is compared with other algorithm. Computations results validate the effectiveness of random key representation and the promising advantage of RKGA on fuzzy scheduling.

The present work aims to find an efficient and fast method for the nesting of two-dimensional Irregular or regular parts in an irregular or regular sheet using genetic and heuristic algorithms, with a view to maximizing the utilization of the sheet material. The proposed genetic algorithm gives out the best sequence and orientation of parts, using which the given heuristic generates a nested pattern with bottom left strategy. The heuristic approach makes use of the positioning technique to find out the acceptable position of each part on the sheet. The application of the proposed approach is illustrated by considering both irregular parts and irregular sheets composed of line features.