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

A hybrid algorithm based on particle swarm and chemical reaction optimization for multi-object problems

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.

As demonstrated in Chap. 3, different evolutionary algorithms, including genetic algorithm (GA), simulated annealing (SA) algorithm, hybrid GASA algorithm, particle swarm optimization (PSO) algorithm, continuous ant colony optimization (CACO) algorithm, artificial bee colony (ABC) algorithm, and immune algorithm (IA), are employed to determine suitable for parameter combination of an SVR-based electric load forecasting model. These forecasting results indicate that almost all SVR-based models with different evolutionary algorithms are superior to other competitive forecasting models (including ARIMA, HW, GRNN, and BPNN models); however, these algorithms almost lack knowledge memory or storage mechanisms which would be neither time-consuming nor inefficient in searching the suitable parameters, that is, premature convergence (being trapped in local optimum). For example, for SVRGA model, in GA processing, new individuals are generated by the following operators, selection, crossover, and mutation. For all types of objective functions, the generation begins with a binary coding for the parameter set. Based on this special binary coding process, GA is able to solve some specified problems which are not easily to be solved by traditional algorithms. GA can empirically provide a few best fitted offsprings from the whole population; however, after some generations, due to low diversity of the population, it might lead to a premature convergence [1]. For SVRSA model, SA algorithm is a generic probabilistic search technique that simulates the material physical process of heating and controlled cooling. Each step of SA attempts to replace the current state by a random move. The new state may then be accepted with a probability that depends both on the difference between the corresponding function values and also on a global parameter, temperature. Thus, SA has some institution to reach more ideal solutions. However, SA algorithm requires the subtle and skillful adjustment in the annealing schedule; therefore, the settings of the size of the temperature steps during annealing, the temperature range, the number of restarts, and the redirection of the search will be taken into account carefully [1]; in addition, its Monte Carlo scheme and lack of knowledge memory mechanism will also lead to time-consuming and inefficient searching in annealing process.

This paper presents a comparison between the performance of Chemical Reaction Optimization algorithm and Genetic algorithm in solving maximum flow problem with the performance of Ford-Fulkerson algorithm in that. The algorithms have been implemented sequentially using JAVA programming language, and executed to find maximum flow problem using different network size. Ford-Fulkerson algorithm which is based on the idea of finding augmenting path is the most popular algorithm used to find maximum flow value but its time complexity is high. The main aim of this study is to determine which algorithm will give results closer to the Ford-Fulkerson results in less time and with the same degree of accuracy. The results showed that both algorithms can solve Max Flow problem with accuracy results close to Ford Fulkerson results, with a better performance achieved when using the genetic algorithm in term of time and accuracy.

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.

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.

Vehicle Routing Problem with Simultaneous Delivery and Pickup (VRPSDP) is a variant of Vehicle Routing Problem (VRP). VRPSDP has special constraints, namely requests and returns are carried out simultaneously. In this article we will use the Variable Neighborhood Descent (VND) algorithm to solve VRPSDP problems. There are two steps taken to use the VND algorithm on VRPSDP, namely finding an initial solution with the Insertion Heuristic algorithm and improving the position of the customer by using the neighborhood operator on the VND algorithm. The implementation of the VND algorithm on VRPSDP has been successfully made using the Borland Delphi 7.0 programming language. Inputs contained in the program are point position, distance between points, customer requests and returns and vehicle capacity. The output contained in the program in the form of routes that have been completed using an algorithm and output in the form of images of the final solution that has been obtained. Based on the results obtained, an example with 6 customers produces 3 routes with a total distance of 266 km, while an example with 10 customers produces 4 routes with a total distance of 100 km.

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.

This paper presents a novel combined algorithm based on particle swarm optimization (PSO) and simulated annealing algorithm(SA) for power system reactive optimization. According to the characteristics of PSO and SA, the proposed method which combined PSO and SA efficiently makes good use of easily implementing performance and fast convergence performance of PSO and global convergence performance of SA, and makes them search in phase. This paper detailed explains coding of control variables, selecting of parameters and material steps of combined algorithm for optimizing reactive power. Taking the IEEE 14-bus system, IEEE 57-bus system and IEEE 118-bus system for example, the simulation results demonstrate that the proposed method is simple and easy to implement, and has high computing efficiency and comparing with conventional PSO it can obtain higher quality solutions.

Layout exploration for three-dimensional Networks-on-Chip: Chemical equilibrium simulation approach

The bin packing problem is a classical problem widely existing in practical applications, such as shipping, warehousing and manufacturing industries. Whereas current research mainly focuses on reducing packing costs by optimizing the packing scheme, this study explores a novel approach by redesigning the bin sizes to fit the items ready to be packed. Specifically, this study considers a general three-dimensional open dimension problem (3D-ODP) where all dimensions, i.e. length, width and height, of a number of heterogeneous bin types are unknown and need to be decided. Based on the designed bin types, the corresponding packing scheme with minimal total costs is optimized, which is referred to as a three-dimensional multiple-bin-size bin packing problem (3D-MBSBPP). The combination of 3D-ODP and 3D-MBSBPP is redefined as a three-dimensional bin design and packing problem (3D-BDPP), for which a two-layer heuristic is developed. It consists of an outer heuristic framework (i.e. genetic algorithm or differential evolution algorithm) to design bin types, and an inner deterministic constructive heuristic (i.e. placement algorithm) to generate an effective solution for the 3D-MBSBPP. Extensive simulation tests on the classical benchmark and a case study derived from an e-commerce company are conducted to verify the algorithms and deduce managerial insights.

Oil production from tight oil reservoirs has become economically feasible because of the combination of horizontal drilling and multistage hydraulic fracturing. Optimal fracture design plays a critical role in successful economical production from a tight oil reservoir. However, many complex parameters such as fracture spacing and fracture half-length make fracturing treatments costly and uncertain. To improve fracture design, it is essential to determine reasonable ranges for these parameters and to evaluate their effects on well performance and economic feasibility. In traditional analytical and numerical simulation methods, many simplifications and assumptions are introduced for artificial fracture characterization and gas percolation mechanisms, and their implementation process remains complicated and computationally inefficient. Most previous studies on big data-driven fracturing parameter optimization have been based on only a single output, such as expected ultimate recovery, and few studies have integrated machine learning with evolutionary algorithms to optimize fracturing parameters based on time-series production prediction and economic objectives. This study proposed a novel approach, combining a data-driven model with evolutionary optimization algorithms to optimize fracturing parameters. We established a significant number of static and dynamic data sets representing the geological and developmental characteristics of tight oil reservoirs from numerical simulation. Four production-prediction models based on machine-learning methods—support vector machine, gradient-boosted decision tree, random forest, and multilayer perception—were constructed as mapping functions between static properties and dynamic production. Then, to optimize the fracturing parameters, the best machine-learning-based production predictive model was coupled with four evolutionary algorithms—genetic algorithm, differential evolution algorithm, simulated annealing algorithm, and particle swarm optimization—to investigate the highest net present value (NPV). The results show that among the four production-prediction models established, multilayer perception (MLP) has the best prediction performance. Among the evolutionary algorithms, particle swarm optimization (PSO) not only has the fastest convergence speed but also the highest net present value. The optimal fracturing parameters for the study area were identified. The hybrid MLP-PSO model represents a robust and convenient method to forecast the time-series production and to optimize fracturing parameters by reducing manual tuning.

Three-dimensional (3D) cooperative time- difference-of-arrival (TDOA) location model aims to solve the 3D location information of unmanned air vehicles (UAV) in complex environment without GPS. This paper uses a singlechain coding quantum wind driven optimization combined with Chan algorithm (Chan-QWDO) to solve the non-linear optimization problem in 3D cooperative TDOA location model. QWDO algorithm uses quantum rotation angle combined with chaotic equation and quantum rotation gate strategy on population evolution. Compared with Chan algorithm (Chan), particle swarm optimization (PSO) and genetic algorithms (GA), the Chan-QWDO algorithm shows better performance in 3D cooperative TDOA location problem. The simulation results show that if the parameters are assumed reasonably, Chan- QWDO algorithm has stable performance, fast convergence speed and strong adaptability. And the mean square error (MSE) is lower than other algorithms which means Chan-QWDO algorithm has higher positioning accuracy.