The Nesting of Two-Dimensional Shapes Using Genetic Algorithms

1995 ◽  
Vol 209 (2) ◽  
pp. 115-124 ◽  
Author(s):  
H S Ismail ◽  
K K B Hon
Keyword(s):  
Genetic Algorithms ◽  
Evolutionary Process ◽  
Search Space ◽  
Cutting Stock ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Spatial Constraints ◽  
Global Optimal ◽  
Optimum Solution ◽  
Rapid Conversion

The general two-dimensional cutting stock problem is concerned with the optimum layout and arrangement of two-dimensional shapes within the spatial constraints imposed by the cutting stock. The main objective is to maximize the utilization of the cutting stock material. This paper presents some of the results obtained from applying a combination of genetic algorithms and heuristic approaches to the nesting of dissimilar shapes. Genetic algorithms are stochastically based optimization approaches which mimic nature's evolutionary process in finding global optimal solutions in a large search space. The paper discusses the method by which the problem is defined and represented for analysis and introduces a number of new problem-specific genetic algorithm operators that aid in the rapid conversion to an optimum solution.

scholarly journals An Automated Structural Optimisation Methodology for Scissor Structures Using a Genetic Algorithm

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Aushim Koumar ◽  
Tine Tysmans ◽  
Rajan Filomeno Coelho ◽  
Niels De Temmerman
Keyword(s):  
Genetic Algorithms ◽  
Search Space ◽  
Optimal Solutions ◽  
Multiobjective Optimisation ◽  
Nsga Ii ◽  
Design Variables ◽  
Depth Analysis ◽  
Making Choices ◽  
Optimisation Methods ◽  
Number Of Individuals

We developed a fully automated multiobjective optimisation framework using genetic algorithms to generate a range of optimal barrel vault scissor structures. Compared to other optimisation methods, genetic algorithms are more robust and efficient when dealing with multiobjective optimisation problems and provide a better view of the search space while reducing the chance to be stuck in a local minimum. The novelty of this work is the application and validation (using metrics) of genetic algorithms for the shape and size optimisation of scissor structures, which has not been done so far for two objectives. We tested the feasibility and capacity of the methodology by optimising a 6 m span barrel vault to weight and compactness and by obtaining optimal solutions in an efficient way using NSGA-II. This paper presents the framework and the results of the case study. The in-depth analysis of the influence of the optimisation variables on the results yields new insights which can help in making choices with regard to the design variables, the constraints, and the number of individuals and generations in order to obtain efficiently a trade-off of optimal solutions.

Optimization of Bicycle Frames Using Genetic Algorithms

2007 ◽  
Author(s):  
Yuan Mao Huang ◽  
Kuo Juei Wang
Keyword(s):  
Genetic Algorithms ◽  
Factor Of Safety ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Dimensional Model ◽  
Equilibrium Equations ◽  
Fitness Value ◽  
Two Dimensional Model ◽  
Bicycle Frame ◽  
The Mean

A bicycle frame is optimized for the lightest weight by using genetic algorithms in this study. Stresses of five rods in the bicycle frame less than the material yielding strength with consideration of the factor of safety are the constraints. A two-dimensional model of the frame is created. Equilibrium equations are derived and loads acting on rods are determined. A known function is used to verify feasibility of the program generated. Effects of the mutation rate, the crossover rate and the number of generation on the mean and the standard deviation of the fitness value are studied. The optimal solutions with the outer diameters and the inner diameters of the front frame rods to be 0.040 m and 0.038 m, respectively, the outer diameters and the inner diameters of the rear frame rods to be 0.024 m and 0.021m, respectively, and the weight of the bicycle frame to be 0.896 kg are recommended for the bicycle frame.

scholarly journals 3-Phase Matheuristic Model in Two-Dimensional Cutting Stock Problem of Triangular Shape Items

2020 ◽  
Vol 5 (1) ◽  
pp. 23
Author(s):  
Putra Bahtera Jaya Bangun ◽  
Sisca Octarina ◽  
Sisca Puspita Sepriliani ◽  
Laila Hanum ◽  
Endro Sastro Cahyono
Keyword(s):  
Branch And Bound ◽  
Consumer Demand ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Two Dimensional ◽  
Triangular Shape ◽  
Optimum Cutting ◽  
Trim Loss ◽  
Cutting Pattern ◽  
Optimum Solution

Cutting Stock Problem (CSP) is a problem of cutting stocks with certain cutting rules. This study used the data of rectangular stocks, which cut into triangular shape items with various order sizes. The Modified Branch and Bound Algorithm (MBBA) was used to determine the optimum cutting pattern then formulated it into the 3-Phase Matheuristic model which consisted of constructive phase, improvement phase, and compaction phase. Based on the results, it showed that the MBBA produces three optimum cutting patterns, which was used six times, eight times, and four times respectively to fulfill the consumer demand. Then the cutting patterns were formulated into the 3-Phase Matheuristic model whereas the optimum solution was the minimum trim loss for the first, second and third patterns.

A Controlled Stability Genetic Algorithm With the New BLF2G Guillotine Placement Heuristic for the Orthogonal Cutting-Stock Problem

2021 ◽  
pp. 1471-1491
Author(s):  
Slimane Abou-Msabah ◽  
Ahmed-Riadh Baba-Ali ◽  
Basma Sager
Keyword(s):  
Genetic Algorithm ◽  
Orthogonal Cutting ◽  
Evolutionary Process ◽  
Search Space ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Data Sets ◽  
Item Order ◽  
Minimum Number ◽  
Qualified Individual

The orthogonal cutting-stock problem tries to place a given set of items in a minimum number of identically sized bins. Combining the new BLF2G heuristic with an advanced genetic algorithm can help solve this problem with the guillotine constraint. According to the item order, the BLF2G heuristic creates a direct placement of items in bins to give a cutting format. The genetic algorithm exploits the search space to find the supposed optimal item order. Other methods try to guide the evolutionary process. A new enhancement guides the evolutionary process, enriching the population via qualified individuals, without disturbing the genetic phase. The evolution of the GA process is controlled, and when no improvements after some number of iterations are observed, a qualified individual is injected to the population to avoid premature convergence to a local optimum. A generated set of order-based individuals enriches the evolutionary process with qualified chromosomes. The proposed method is compared with other heuristics and metaheuristics found in the literature on existing data sets.

A Controlled Stability Genetic Algorithm With the New BLF2G Guillotine Placement Heuristic for the Orthogonal Cutting-Stock Problem

2019 ◽  
Vol 13 (4) ◽  
pp. 91-111
Author(s):  
Slimane Abou-Msabah ◽  
Ahmed-Riadh Baba-Ali ◽  
Basma Sager
Keyword(s):  
Genetic Algorithm ◽  
Orthogonal Cutting ◽  
Evolutionary Process ◽  
Search Space ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Local Optimum ◽  
Data Sets ◽  
Item Order ◽  
Minimum Number

The orthogonal cutting-stock problem tries to place a given set of items in a minimum number of identically sized bins. Combining the new BLF2G heuristic with an advanced genetic algorithm can help solve this problem with the guillotine constraint. According to the item order, the BLF2G heuristic creates a direct placement of items in bins to give a cutting format. The genetic algorithm exploits the search space to find the supposed optimal item order. Other methods try to guide the evolutionary process. A new enhancement guides the evolutionary process, enriching the population via qualified individuals, without disturbing the genetic phase. The evolution of the GA process is controlled, and when no improvements after some number of iterations are observed, a qualified individual is injected to the population to avoid premature convergence to a local optimum. A generated set of order-based individuals enriches the evolutionary process with qualified chromosomes. The proposed method is compared with other heuristics and metaheuristics found in the literature on existing data sets.

A New Genetic Algorithm Based on Optimal Solution Orientation

2010 ◽  
Vol 139-141 ◽  
pp. 1779-1784
Author(s):  
Quan Wang ◽  
Jin Chao Liu ◽  
Pan Wang ◽  
Juan Ying Qin
Keyword(s):  
Genetic Algorithm ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Search Space ◽  
Local Domain ◽  
Local Search Algorithm ◽  
Global Optimal Solution ◽  
Global Optimal ◽  
Optimum Solution ◽  
Standard Genetic Algorithm

Many researchers have indicated that standard genetic algorithm suffers from the dilemma---premature or non-convergence. Most researchers focused on finding better search strategies, and designing various new heuristic methods. It seemed effective. From another view, we can transform search space with a samestate-mapping. A special genetic algorithm applied to the new search space would achieve better performance. Thus, we present a new genetic algorithm based on optimal solution orientation. In this paper, a new genetic algorithm based on optimum solution orientation is presented. The algorithm is divided into "optimum solution orientation" phase and "highly accurately searching in local domain of global optimal solution" phase. Theoretical analysis and experiments indicate that OSOGA can find the "optimal" sub domain effectively. Cooperating with local search algorithm, OSOGA can achieve highly precision solution with limited computing resources.

Hybrid Multi-Population and Adaptive Search Range Strategy With Particle Swarm Optimization for Multimodal Optimization

2021 ◽  
Vol 12 (4) ◽  
pp. 146-168
Author(s):  
Shiqi Wang ◽  
Zepeng Shen ◽  
Yao Peng
Keyword(s):  
Particle Swarm Optimization ◽  
Optimal Solution ◽  
Search Space ◽  
Multimodal Optimization ◽  
Adaptive Search ◽  
Optimal Solutions ◽  
Search Range ◽  
Global Optimal Solution ◽  
Swarm Optimization ◽  
Global Optimal

This paper proposes an algorithm named hybrid multi-population and adaptive search range strategy with particle swarm optimization (ARPSO) for solving multimodal optimization problems. The main idea of the algorithm is to divide the global search space into multiple sub-populations searching in parallel and independently. For diversity increasing, each sub-population will continuously change the search area adaptively according to whether there are local optimal solutions in its search space and the position of the global optimal solution, and in each iteration, the optimal solution in this area will be reserved. For the purpose of accelerating convergence, at the global and local levels, when the global optimal solution or local optimal solution is found, the global search space and local search space will shrink toward the optimal solution. Experiments show that ARPSO has unique advantages for solving multi-dimensional problems, especially problems with only one global optimal solution but multiple local optimal solutions.

Comparative Analysis of Genetic Algorithms and Particle Swarm Optimization Algorithms for Optimal Reservoir Operation

2011 ◽  
Vol 90-93 ◽  
pp. 2727-2733
Author(s):  
Ruan Yun
Keyword(s):  
Genetic Algorithms ◽  
Particle Swarm Optimization ◽  
Comparative Analysis ◽  
Population Size ◽  
Reservoir Operation ◽  
Particle Swarm ◽  
Optimization Techniques ◽  
Optimal Solutions ◽  
Swarm Optimization ◽  
Global Optimal

Apart from traditional optimization techniques, modern heuristic optimization techniques, like genetic algorithms (GA), particle swarm optimization algorithm (PSO) have been widely used to solve optimization problems. This paper deals with comparative analysis of GA and PSO and their applications in a reservoir operation problem. Extensive component analysis, parameter sensitivity analysis of GA and PSO show that both GA and PSO can be used for optimal reservoir operation, but they display different features. GA can obtain very high approximate global optimal solutions of the problem with a high stability and a high computing efficiency, but it can’t obtain the problem’s accurate global optimal solutions. For GA, population size and mutation rate are two main parameters affect its solution qualities. Comparative to GA, PSO can obtain the accurate global optimal solutions of the problem with a higher computing efficiency, but with a less stability. For PSO, population size and velocity parameter are two main parameters affect its solution qualities.

Scheduling of Water Distribution System Rehabilitation Using Structured Messy Genetic Algorithms

1999 ◽  
Vol 7 (3) ◽  
pp. 311-329 ◽  
Author(s):  
Driss Halhal ◽  
Godfrey A. Walters ◽  
Dragan A. Savic ◽  
Driss Ouazar
Keyword(s):  
Genetic Algorithms ◽  
Distribution System ◽  
Water Distribution ◽  
Inflation Rate ◽  
Evolutionary Process ◽  
Distribution Networks ◽  
Optimal Solutions ◽  
Costs And Benefits ◽  
Programming Technique ◽  
Artificial Network

A methodology is presented for the optimal design and scheduling of investment for the rehabilitation of water distribution networks. Based on the evolutionary programming technique known as Structured Messy Genetic Algorithms, the methodology utilizes a multi-objective formulation which improves the evolutionary process and provides non-dominated optimal solutions over a range of costs and benefits. The model is applied to an example—a small artificial network of fifteen pipes. The effects on the optimal solutions of varying parameters such as interest rate and inflation rate are also investigated.

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