mathematical modelling in research

Jan 19, 2023Download as pptx, pdf0 likes34 views

Mathematical modeling is used in research to predict phenomena like climate change. There are static and dynamic models. Static modeling creates diagrams of reservoir characteristics while dynamic modeling simulates airflows over time. Integrated static and dynamic modeling was used to study CO2 storage. Optimization techniques like genetic algorithms, simulated annealing, and particle swarm optimization are used to find optimal solutions to problems. Genetic algorithms evolve populations toward optimal solutions, simulated annealing finds global optima like metals cooling, and particle swarm optimization mimics flock behavior.

https://ibmathsresources.com/2017/01/29/maths-of-global-warming-
modeling-climate-change/
Mathematical modelling for prediction

Dyanamic modelling diagrams
Refer - /100arab/dynamic-and-static-modeling

Static modelling
3D static modelling of Reservoir characteristics
Static modelling diagrams

Computational fluid dynamic (CFD) modelling of airflows and velocities
during cone sampling with head placement within the cone.
Dynamic modelling

Integrated static modeling and dynamic simulation framework for CO2
storage capacity in Upper Qishn Clastics, S1A reservoir, Yemen
Integrated static and Dynamic modelling

System simulation &research lab in IIT kanpur

Genetic algorithm
Refer - https://www.generativedesign.org/02-deeper-dive/02-04_genetic-algorithms/02-04-01_what-is-a-genetic-
algorithm
The genetic algorithm is a method for solving both constrained and
unconstrained optimization problems that is based on natural
selection, the process that drives biological evolution. The genetic
algorithm repeatedly modifies a population of individual solutions.
At each step, the genetic algorithm selects individuals from the
current population to be parents and uses them to produce the
children for the next generation. Over successive generations, the
population "evolves" toward an optimal solution.

Simulated annealing
Simulated Annealing (SA) is an effective and general form of optimization. It is useful in
finding global optima in the presence of large numbers of local optima. “Annealing” refers
to an analogy with thermodynamics, specifically with the way that metals cool and
anneal. Simulated annealing uses the objective function of an optimization problem instead
of the energy of a material.
Simulated annealing searching for a
maximum. The objective here is to get to
the highest point. In this example, it is
not enough to use a simple hill climb
algorithm, as there are many local
maxima. By cooling the temperature
slowly the global maximum is found.

Particle swarm optimization (PSO) is a population-based optimization technique
inspired by the motion of bird flocks and schooling fish. PSO shares many
similarities with evolutionary computation techniques. The system is initialized with a
population of random solutions, and the search for the optimal solution is performed
by updating generations.
Particle swarm optimization

The document discusses various optimization techniques and algorithms including genetic algorithms, artificial neural networks, and data analytics. Specifically, it covers genetic algorithms in more detail including the basic concepts of populations of chromosomes evolving over generations using processes like crossover, mutation, and selection to optimize an objective function. It also discusses other metaheuristic algorithms like simulated annealing, particle swarm optimization, and ant colony optimization which are inspired by natural processes and use stochastic components to find robust solutions.

H012225053IOSR Journals

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This document provides a review of non-traditional optimization algorithms that have been used to solve simultaneous scheduling problems in industrial and production environments. It discusses several metaheuristic algorithms such as genetic algorithms, simulated annealing, particle swarm optimization, artificial immune systems, differential evolution, and ant colony optimization. These algorithms are able to find good solutions to combinatorial optimization problems like scheduling that are NP-complete and cannot be solved optimally in polynomial time using traditional methods. The review concludes that these non-traditional techniques can yield global optimal solutions and efficiently explore solution spaces, making them useful approaches for simultaneous scheduling problems.

Artificial Intelligence in Robot Path Planningiosrjce

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IOSR Journal of Computer Engineering (IOSR-JCE) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of computer engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in computer technology. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.

T01732115119IOSR Journals

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This document discusses various artificial intelligence techniques for robot path planning, including ant colony optimization. It provides background on particle swarm optimization, genetic algorithms, tabu search, simulated annealing, reactive search optimization, and ant colony algorithms. It then proposes a solution for robotic path planning that uses ant colony optimization. The proposed solution involves defining a source and destination point for the robot, moving it forward one step at a time while checking for obstacles, having it take three steps back if an obstacle is encountered, and applying ant colony optimization algorithms to help the robot find an optimal path to bypass obstacles and reach the destination point.

L018147377IOSR Journals

��

This document proposes an improved genetic algorithm called DGA that combines genetic algorithm and differential evolution. DGA uses adaptive differential evolution as its mutation operator instead of simple genetic algorithm's crossover and mutation. It also adds strategies of optimal reservation and worst elimination. Simulation results show DGA has stronger global optimization ability, faster convergence speed and better stability compared to simple genetic algorithm.

Cuckoo Search: Recent Advances and ApplicationsXin-She Yang

��

This document summarizes recent advances and applications of the cuckoo search algorithm, a nature-inspired metaheuristic optimization algorithm developed in 2009. Cuckoo search mimics the brood parasitism breeding behavior of some cuckoo species. It uses a combination of local and global search achieved through random walks and Levy flights to efficiently explore the search space. Studies show cuckoo search often finds optimal solutions faster than genetic algorithms and particle swarm optimization. The algorithm has been applied to diverse optimization problems and continues to be improved and extended to multi-objective optimization.

Sca a sine cosine algorithm for solving optimization problemslaxmanLaxman03209

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The document proposes a new population-based optimization algorithm called the Sine Cosine Algorithm (SCA) for solving optimization problems. SCA creates multiple random initial solutions and uses sine and cosine functions to fluctuate the solutions outward or toward the best solution, emphasizing exploration and exploitation. The performance of SCA is evaluated on test functions, qualitative metrics, and by optimizing the cross-section of an aircraft wing, showing it can effectively explore, avoid local optima, converge to the global optimum, and solve real problems with constraints.

Bat Algorithm: Literature Review and ApplicationsXin-She Yang

��

This document provides a review of the bat algorithm, which is a bio-inspired optimization algorithm developed in 2010 based on the echolocation behavior of microbats. The paper summarizes the basic behavior and formulation of the bat algorithm, reviews variants that have been developed, and highlights diverse applications that have been studied. It also discusses the essence of algorithms and links between algorithms and self-organization, noting that optimization algorithms can be viewed as complex dynamical systems that self-organize to select optimal solutions.

ComparisonTomasz Waszczyk

��

The document compares five evolutionary optimization algorithms: genetic algorithms, memetic algorithms, particle swarm optimization, ant colony systems, and shuffled frog leaping. It provides a brief description of each algorithm, including how they are inspired by natural processes and behaviors. It also includes pseudocode to facilitate implementing each algorithm. The document then presents benchmark comparisons of the five algorithms on continuous and discrete optimization problems in terms of processing time, convergence speed, and solution quality. It discusses the performance of evolutionary algorithms and provides guidelines for determining the best parameters for each.

VET4SBO Level 2 module 2 - unit 2 - v1.0 enKarel Van Isacker

��

This document provides an introduction to several metaheuristic optimization algorithms including genetic algorithms, ant colony optimization, simulated annealing, and particle swarm optimization. It describes the basics of each algorithm, including how they were inspired by natural processes and how they can be applied to optimization problems. As an example, it discusses how genetic algorithms and ant colony optimization have been used to optimize municipal waste collection vehicle routing.

VET4SBO Level 2 module 2 - unit 1 - v1.0 enKarel Van Isacker

��

This document provides an introduction to optimization methods and strategies. It defines optimization as selecting the best solution from available alternatives according to some criteria. Traditional gradient-based algorithms can find local optima but not global optima. Gradient-free methods avoid limitations of gradient methods but are less efficient. Metaheuristic methods like genetic algorithms and particle swarm optimization are inspired by nature and can find global optima without derivatives. Engineering optimization applies these techniques to achieve design goals. Nature-inspired metaheuristics use randomization and local search to find high-quality solutions without guaranteeing optimality.

Engineering Optimization_Introduction-guest lecture.pptxMohDedyIndraSetiawan

��

The document provides an introduction to engineering optimization, outlining various problem types and methods as well as challenges. It discusses single and multi-objective optimization problems, constrained and unconstrained problems, and applications such as truss bridge structure optimization and microridged punch design optimization. The document emphasizes that engineering optimization is important for finding optimal designs that meet requirements while minimizing costs.

Metaheuristic Optimization: Algorithm Analysis and Open ProblemsXin-She Yang

��

This document analyzes metaheuristic optimization algorithms and discusses open problems in their analysis. It reviews convergence analyses that have been done for simulated annealing and particle swarm optimization. It also provides a novel convergence analysis for the firefly algorithm, showing that it can converge for certain parameter values but also exhibit chaos which can be advantageous for exploration. The document outlines the need for further mathematical analysis of convergence and efficiency in metaheuristics.

A Genetic Algorithm on Optimization Test FunctionsIJMERJOURNAL

��

ABSTRACT: Genetic Algorithms (GAs) have become increasingly useful over the years for solving combinatorial problems. Though they are generally accepted to be good performers among metaheuristic algorithms, most works have concentrated on the application of the GAs rather than the theoretical justifications. In this paper, we examine and justify the suitability of Genetic Algorithms in solving complex, multi-variable and multi-modal optimization problems. To achieve this, a simple Genetic Algorithm was used to solve four standard complicated optimization test functions, namely Rosenbrock, Schwefel, Rastrigin and Shubert functions. These functions are benchmarks to test the quality of an optimization procedure towards a global optimum. We show that the method has a quicker convergence to the global optima and that the optimal values for the Rosenbrock, Rastrigin, Schwefel and Shubert functions are zero (0), zero (0), -418.9829 and -14.5080 respectively

Parallel evolutionary approach paperPriti Punia

��

This paper proposes a parallel evolutionary algorithm to solve single variable optimization problems. Specifically: - It presents a genetic algorithm approach that runs in parallel using a master-slave model, where the master performs genetic operations and distributes individuals to slaves for evaluation. - The algorithm is tested on single variable optimization problems to find minimum/maximum values. - Experimental results show the parallel genetic algorithm is effective at finding optimal solutions to these problems and represents an efficient parallel approach for optimization.

Genetic AlgorithmsAlaa Khamis, PhD, SMIEEE

��

Lecture 2 Basic Concepts of Optimal Design and Optimization Techniques final1...Khalil Alhatab

��

This document provides an overview of optimization techniques and the process of formulating an optimal design problem. It begins with introducing optimization and defining it as finding the best solution under given circumstances by optimizing an objective function. It then contrasts conventional versus optimal design processes and discusses classifying optimization problems based on constraints, variables, objectives, and other factors. The document concludes by outlining the five steps to formulate an optimal design problem: project description, data collection, defining design variables, establishing an optimization criterion or objective function, and specifying constraints.

Nuclear_Reaction_Optimization_A_Novel_and_Powerful.pdfAmmarElSheikh4

��

Hakimi asiabar, m. 2009: multi-objective genetic local search algorithm using...ArchiLab 7

��

This document summarizes a research paper that proposes a new multi-objective genetic algorithm called SBMOCA. SBMOCA hybridizes genetic algorithms with Kohonen's self-organizing map and variable neighborhood search to improve genetic diversity and local search efficiency. The paper describes limitations of traditional genetic algorithms, such as slow convergence near optima and genetic drift. It then reviews literature on hybridizing genetic algorithms with local search methods. Finally, it introduces the SBMOCA algorithm and applies it to optimize reservoir operation management, a non-linear, multi-objective problem.

An Effective Improved Multi-Objective Evolutionary Algorithm (IMOEA) For Solv...Michele Thomas

��

This paper introduces a new multi-objective evolutionary algorithm (IMOEA) to solve constrained single-objective engineering optimization problems more efficiently. The algorithm considers constraints as a new objective function, converting problems into multi-objective optimization. Different mutations and crossovers are tested to avoid local optima, and the best operators are selected. Infeasible solutions can provide useful information to guide convergence, so they are defined based on optimization concepts. Dynamic interference of operators and a selection strategy are used to find optimal solutions faster. The IMOEA is tested on benchmark problems and engineering applications, showing powerful convergence to global optima compared to other algorithms.

SimulatedAnnealing.pptVivekChawla19

��

Simulated annealing is a local search algorithm that can find good approximations to global optimization problems. It is inspired by the physical process of annealing in solids. The algorithm starts with a random solution and uses the Metropolis algorithm to probabilistically accept moves to neighboring solutions based on a cooling schedule, allowing it to escape local optima. It has been applied successfully to problems like the traveling salesman problem, graph partitioning, and VLSI design placement and routing. The cost function and cooling schedule are important factors that affect its performance.

COMPARISON BETWEEN THE GENETIC ALGORITHMS OPTIMIZATION AND PARTICLE SWARM OPT...IAEME Publication

��

Close range photogrammetry network design is referred to the process of placing a set of cameras in order to achieve photogrammetric tasks. The main objective of this paper is tried to find the best location of two/three camera stations. The genetic algorithm optimization and Particle Swarm Optimization are developed to determine the optimal camera stations for computing the three dimensional coordinates. In this research, a mathematical model representing the genetic algorithm optimization and Particle Swarm Optimization for the close range photogrammetry network is developed. This paper gives also the sequence of the field operations and computational steps for this task. A test field is included to reinforce the theoretical aspects.

Comparison between the genetic algorithms optimization and particle swarm opt...IAEME Publication

��

The document compares the genetic algorithms optimization and particle swarm optimization methods for designing close range photogrammetry networks. It presents the genetic algorithm and particle swarm optimization as two popular meta-heuristic algorithms inspired by natural evolution and collective animal behavior, respectively. The document develops mathematical models representing the genetic algorithm and particle swarm optimization for close range photogrammetry network design and evaluates them in a test field to reinforce the theoretical aspects.

Optimum engineering design - Day 6. Classical optimization methodsSantiagoGarridoBulln

��

The document discusses various optimization methods for engineering design problems, including direct search methods, the Nelder-Mead algorithm, and simulated annealing. Direct search methods like Nelder-Mead, particle swarm optimization, and genetic algorithms solve optimization problems without gradients by evaluating the objective function. The Nelder-Mead algorithm finds the minimum within a simplex by reflecting, expanding, contracting, or shrinking it in each iteration. Simulated annealing models the physical annealing process and accepts worse solutions probabilistically to avoid local optima.

50120130406046IAEME Publication

��

The document discusses using genetic algorithms for financial forecasting. It begins with an abstract that notes genetic algorithms have been used extensively in various domains including finance to generate profitable trading rules. The document then provides background on genetic algorithms and their basic functions like selection, crossover and mutation. It explains how genetic algorithms can be used to develop a model for financial forecasting by evaluating trading rules based on historical data to determine which rules would have yielded the highest returns.

Review of Hooke and Jeeves Direct Search Solution Method Analysis Applicable ...ijiert bestjournal

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Role of optimization in engineering design is prominent one with the a dvent of computers. Optimization has become a part of computer aided design methodology. It is primarily being used in those design activities in which the goal is not only to achieve a feasible design,but als o a design objective. The paper reviews the optimization in detail followed by the literature review and b rief discussion of Hooks and Jeeves Method Analysis with an example.

Convergence tendency of genetic algorithms and artificial immune system in so...ijcsity

��

By the advances in the Evolution Algorithms (EAs) and the intelligent optimization metho ds we witness the big revolutions in solving the optimization problems. The application of the evolution algorithms are not only not limited to the combined optimization problems, but also are vast in domain to the continuous optimization problems. In this paper we analyze and study the Genetic Algorithm (GA) and the Artificial Immune System (AIS) algorithm which are capable in escaping the local optimization and also fastening reaching the global optimization and to show the efficiency of the GA and AIS th e application of them in Solving Continuous Optimization Functions (SCOFs) are studied. Because of the multi variables and the multi - dimensional spaces in SCOFs the use of the classic optimization methods, is generally non - efficient and high cost. In other words the use of the classic optimization methods for SCOFs generally leads to a local optimized solution. A possible solution for SCOFs is to use the EAs which are high in probability of succeeding reaching the local optimized solution. The results in pa per show that GA is more efficient than AIS in reaching the optimized solution in SCOFs.

Efficient evaluation of flatness error from Coordinate Measurement Data using...Ali Shahed

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mathematical modelling in research

1. Mathematical modelling in Research

2. Mathematical modelling

4. https://ibmathsresources.com/2017/01/29/maths-of-global-warming- modeling-climate-change/ Mathematical modelling for prediction

6. Mathematical modelling - example

7. Static model and dynamic model

8. Static modelling diagrams

9. Dyanamic modelling diagrams Refer - /100arab/dynamic-and-static-modeling

10. Static modelling 3D static modelling of Reservoir characteristics Static modelling diagrams

11. Computational fluid dynamic (CFD) modelling of airflows and velocities during cone sampling with head placement within the cone. Dynamic modelling

12. Integrated static modeling and dynamic simulation framework for CO2 storage capacity in Upper Qishn Clastics, S1A reservoir, Yemen Integrated static and Dynamic modelling

13. System simulation

14. System simulation &research lab in IIT kanpur

15. Optimization techniques

16. Genetic algorithm Refer - https://www.generativedesign.org/02-deeper-dive/02-04_genetic-algorithms/02-04-01_what-is-a-genetic- algorithm The genetic algorithm is a method for solving both constrained and unconstrained optimization problems that is based on natural selection, the process that drives biological evolution. The genetic algorithm repeatedly modifies a population of individual solutions. At each step, the genetic algorithm selects individuals from the current population to be parents and uses them to produce the children for the next generation. Over successive generations, the population "evolves" toward an optimal solution.

17. Genetic algorithm

18. Simulated annealing Simulated Annealing (SA) is an effective and general form of optimization. It is useful in finding global optima in the presence of large numbers of local optima. “Annealing” refers to an analogy with thermodynamics, specifically with the way that metals cool and anneal. Simulated annealing uses the objective function of an optimization problem instead of the energy of a material. Simulated annealing searching for a maximum. The objective here is to get to the highest point. In this example, it is not enough to use a simple hill climb algorithm, as there are many local maxima. By cooling the temperature slowly the global maximum is found.

19. GA – Genetic algorithm

20. Particle swarm optimization (PSO) is a population-based optimization technique inspired by the motion of bird flocks and schooling fish. PSO shares many similarities with evolutionary computation techniques. The system is initialized with a population of random solutions, and the search for the optimal solution is performed by updating generations. Particle swarm optimization

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