The document discusses multi-objective optimization and various techniques used to solve multi-objective problems. It introduces concepts like Pareto optimality and Pareto frontier. It then describes various solution methods like weighted sum, normal boundary intersection, goal programming, and Pareto genetic algorithms. Genetic algorithms use concepts like fitness, reproduction, and Pareto set filtering to evolve a population towards the Pareto optimal frontier while satisfying constraints.
Multi Objective Optimization and Pareto Multi Objective Optimization with cas...Aditya Deshpande
This gives basic idea of MOO ie. Multi Objective Optimization and also Pareto graph used for it.
Here i have done Ansys optimization on simple object to elaborate concept of MOO.
Thanks
Aditya D
deshadi805@gmail.com
Multi Objective Optimization and Pareto Multi Objective Optimization with cas...Aditya Deshpande
This gives basic idea of MOO ie. Multi Objective Optimization and also Pareto graph used for it.
Here i have done Ansys optimization on simple object to elaborate concept of MOO.
Thanks
Aditya D
deshadi805@gmail.com
Multi-Objective Optimization using Non-Dominated Sorting Genetic Algorithm wi...Ahmed Gad
When solving a problem, the goal is not only solving it but also optimizing such solution. There might be multiple solutions to a problem and the challenge is to find the best of them. The more metrics defining the solution goodness, the harder finding the best solution. This presentation discusses one of the multi-objective optimization techniques called non-dominated sorting genetic algorithm II (NSGA-II) explaining its steps including non-dominated sorting, crowding distance, tournament selection, and genetic algorithm. The presentation works through a numerical example step-by-step.
Artificial Intelligence: Introduction, Typical Applications. State Space Search: Depth Bounded
DFS, Depth First Iterative Deepening. Heuristic Search: Heuristic Functions, Best First Search,
Hill Climbing, Variable Neighborhood Descent, Beam Search, Tabu Search. Optimal Search: A
*
algorithm, Iterative Deepening A*
, Recursive Best First Search, Pruning the CLOSED and OPEN
Lists
Guest Lecture about genetic algorithms in the course ECE657: Computational Intelligence/Intelligent Systems Design, Spring 2016, Electrical and Computer Engineering (ECE) Department, University of Waterloo, Canada.
It is a selection of best element (with regard to some criteria) from some set of available alternatives. In the simplest case, an optimization problem consist of maximizing or minimizing a real function by choosing input values from within an allowed set and computing the value of function. The classical optimization techniques are useful in finding the optimum solution or unconstrained maxima or minima of continuous and differentiable functions. These are analytical methods and make use of differential calculus in locating the optimum solution. The classical methods have limited scope in practical applications as some of them involve objective functions which are not continuous and un-differentiable. Yet, the study of these classical techniques of optimization form a basis for developing most of the numerical techniques that have evolved into advanced techniques more suitable to today’s practical problems.
Evolutionary algorithms are stochastic search and optimization heuristics derived from the classic evolution theory, which are implemented on computers in the majority of cases.
Multiobjective optimization and Genetic algorithms in ScilabScilab
In this Scilab tutorial we discuss about the importance of multiobjective optimization and we give an overview of all possible Pareto frontiers. Moreover we show how to use the NSGA-II algorithm available in Scilab.
Mathematical Optimisation - Fundamentals and ApplicationsGokul Alex
My Session on Mathematical Optimisation Fundamentals and Industry applications for the Academic Knowledge Refresher Program organised by Kerala Technology University and College of Engineering Trivandrum, Department of Interdisciplinary Studies.
A presentation about NGBoost (Natural Gradient Boosting) which I presented in the Information Theory and Probabilistic Programming course at the University of Oklahoma.
Multi-Objective Optimization using Non-Dominated Sorting Genetic Algorithm wi...Ahmed Gad
When solving a problem, the goal is not only solving it but also optimizing such solution. There might be multiple solutions to a problem and the challenge is to find the best of them. The more metrics defining the solution goodness, the harder finding the best solution. This presentation discusses one of the multi-objective optimization techniques called non-dominated sorting genetic algorithm II (NSGA-II) explaining its steps including non-dominated sorting, crowding distance, tournament selection, and genetic algorithm. The presentation works through a numerical example step-by-step.
Artificial Intelligence: Introduction, Typical Applications. State Space Search: Depth Bounded
DFS, Depth First Iterative Deepening. Heuristic Search: Heuristic Functions, Best First Search,
Hill Climbing, Variable Neighborhood Descent, Beam Search, Tabu Search. Optimal Search: A
*
algorithm, Iterative Deepening A*
, Recursive Best First Search, Pruning the CLOSED and OPEN
Lists
Guest Lecture about genetic algorithms in the course ECE657: Computational Intelligence/Intelligent Systems Design, Spring 2016, Electrical and Computer Engineering (ECE) Department, University of Waterloo, Canada.
It is a selection of best element (with regard to some criteria) from some set of available alternatives. In the simplest case, an optimization problem consist of maximizing or minimizing a real function by choosing input values from within an allowed set and computing the value of function. The classical optimization techniques are useful in finding the optimum solution or unconstrained maxima or minima of continuous and differentiable functions. These are analytical methods and make use of differential calculus in locating the optimum solution. The classical methods have limited scope in practical applications as some of them involve objective functions which are not continuous and un-differentiable. Yet, the study of these classical techniques of optimization form a basis for developing most of the numerical techniques that have evolved into advanced techniques more suitable to today’s practical problems.
Evolutionary algorithms are stochastic search and optimization heuristics derived from the classic evolution theory, which are implemented on computers in the majority of cases.
Multiobjective optimization and Genetic algorithms in ScilabScilab
In this Scilab tutorial we discuss about the importance of multiobjective optimization and we give an overview of all possible Pareto frontiers. Moreover we show how to use the NSGA-II algorithm available in Scilab.
Mathematical Optimisation - Fundamentals and ApplicationsGokul Alex
My Session on Mathematical Optimisation Fundamentals and Industry applications for the Academic Knowledge Refresher Program organised by Kerala Technology University and College of Engineering Trivandrum, Department of Interdisciplinary Studies.
A presentation about NGBoost (Natural Gradient Boosting) which I presented in the Information Theory and Probabilistic Programming course at the University of Oklahoma.
Gradient-Based Multi-Objective Optimization TechnologyeArtius, Inc.
Multi-Gradient Analysis (MGA), and two multi-objective optimization methods based on MGA are presented: Multi-Gradient Explorer (MGE), and Multi Gradient Pathfinder (MGP) methods. Dynamically Dimensioned Response Surface Method (DDRSM) for dynamic reduction of task dimension and fast estimation of gradients is also disclosed.
MGE and MGP are based on the MGA’s ability to analyze gradients and determine the area of simultaneous improvement (ASI) for all objective functions. MGE starts from a
given initial point, and approaches Pareto frontier sequentially by stepping into the ASI area until a Pareto optimal point is obtained. MGP starts from a Pareto-optimal point, and steps along the Pareto surface in the direction that allows for improvement on a subset
of the objective functions with higher priority. DDRSM works for optimization tasks with virtually any number (up to thousands) of design variables, and requires just 5-7 model evaluations per Pareto optimal point for the MGE and MGP algorithms regardless of task
dimension. Both algorithms are designed to optimize computationally expensive models, and are able to optimize models with dozens, hundreds, and even thousands of design variables.
SEARN Algorithm is a search-based algorithm for structured prediction.
Most of the content is taken from http://users.umiacs.umd.edu/~hal/docs/daume06thesis.pdf. I just read the thesis and presented what's in there. Thus the credits of the content should go to the author of the thesis.
Lecture notes of the course Future Models I (AR1TWF030), The Why Factory, Directed by Prof. Winy Mass, TU Delft, Faculty of Architecture and Built Environment
A brief study on linear programming solving methodsMayurjyotiNeog
This small presentation includes a brief study on various linear programming solving methods. These methods (graphical & simplex) are used to solve industrial engineering related problems in practical use.
For a good business plan creative thinking is important. A business plan is very important and strategic tool for entrepreneurs. A good business plan not only helps entrepreneurs focus on specific steps necessary for them to make business ideas succeed, but it also helps them to achieve short-term and long-term objectives. As an inspiring entrepreneur who is looking towards starting a business, one of the businesses you can successfully start without much stress is book servicing café.
Importance:
Nowadays, network plays an important role in people’s life. In the process of the improvement of the people’s living standard, people’s demand of the life’s quality and efficiency is more higher, the traditional bookstore’s inconvenience gradually emerge, and the online book store has gradually be used in public. The online book store system based on the principle of providing convenience and service to people.
With the online book servicing café, college student do not need to blindly go to various places to find their own books, but only in a computer connected to the internet log on online book servicing café in the search box, type u want to find of the book information retrieval, you can efficiently know whether a site has its own books, if you can online direct purchase, if not u can change the home book store to continue to search or provide advice to the seller in order to supply. This greatly facilitates every college student saving time.
The online book servicing café’s main users are divided into two categories, one is the front user, and one is the background user. The main business model for Book Servicing Café relies on college students providing textbooks, auctions, classifieds teacher evaluations available on website. Therefore, our focus will be on the marketing strategy to increase student traffic and usage. In turn, visitor volume and transactions will maintain the inventory of products and services offered.
Online bookstore system i.e. Book Servicing Café not only can easily find the information and purchase books, and the operating conditions are simple, user-friendly, to a large extent to solve real-life problems in the purchase of the books.
When you shop in online book servicing cafe, you have the chance of accessing and going through customers who have shopped at book servicing café and review about the book you intend to buy. This will give you beforehand information about that book.
While purchasing or selling books at the book servicing café, you save money, energy and time for your favorite book online. The book servicing café will offer discount coupons which help college students save money or make money on their purchases or selling. Shopping for books online is economical too because of the low shipping price.
Book servicing café tend to work with multiple suppliers, which allows them to offer a wider variety of books than a traditional retail store without accruing a large, costly inventory which will help colle
Hybrid Multi-Gradient Explorer Algorithm for Global Multi-Objective OptimizationeArtius, Inc.
Hybrid Multi-Gradient Explorer (HMGE) algorithm for global multi-objective
optimization of objective functions considered in a multi-dimensional domain is presented. The proposed hybrid algorithm relies on genetic variation operators for creating new solutions, but in addition to a standard random mutation operator, HMGE
uses a gradient mutation operator, which improves convergence. Thus, random mutation helps find global Pareto frontier, and gradient mutation improves convergence to the
Pareto frontier. In such a way HMGE algorithm combines advantages of both
gradient-based and GA-based optimization techniques: it is as fast as a pure gradient-based MGE algorithm, and is able to find the global Pareto frontier similar to genetic algorithms
(GA). HMGE employs Dynamically Dimensioned Response Surface Method (DDRSM) for calculating gradients. DDRSM dynamically recognizes the most significant design variables, and builds local approximations based only on the variables. This allows one to
estimate gradients by the price of 4-5 model evaluations without significant loss of accuracy. As a result, HMGE efficiently optimizes highly non-linear models with dozens and hundreds of design variables, and with multiple Pareto fronts. HMGE efficiency is 2-10
times higher when compared to the most advanced commercial GAs.
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
See how to accelerate model training and optimize model performance with active learning
Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
👨🏫 Andras Palfi, Senior Product Manager, UiPath
👩🏫 Lenka Dulovicova, Product Program Manager, UiPath
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
4. Multi-Objective Optimization
•Involves the simultaneous optimization of several
incommensurable and often competing objectives.
•These optimal solutions are termed as Pareto optimal
solutions.
•Pareto optimal sets are the solutions that cannot be
improved in one objective function without
deteriorating their performance in at least one of the
rest.
•Problems usually Conflicting in nature (Ex: Minimize
cost, Maximize Productivity)
•Designers are required to resolve Trade-offs.
6. Typical Multi-Objective
Optimization Formulation
Minimize {f1(x),…….,fn(x)}T
where fi(x) = ith objective function to be minimized,
n = number of objectives
Subject to:
g(x) ≤ 0;
h(x) = 0;
x min ≤ (x) ≤ (x max)
7. Basic Terminology
Search space or design space is the set of all possible
combinations of the design variables.
Pareto Optimal Solution achieves a trade off. They are
solutions for which any improvement in one objective results in
worsening of atleast one other objective.
Pareto Optimal Set: Pareto Optimal Solution is not unique,
there exists a set of solutions known as the Pareto Optimal Set.
It represents a complete set of solutions for a Multi-Objective
Optimization (MOO).
Pareto Frontier: A plot of entire Pareto set in the Design
Objective Space (with design objectives plotted along each
axis) gives a Pareto Frontier.
8. Dominated & Non- Dominated points
A Dominated design point, is the one for which there
exists at least one feasible design point that is better
than it in all design objectives.
Non Dominated point is the one, where there does not
exist any feasible design point better than it. Pareto
Optimal points are non-dominated and hence are also
known as Non-dominated points.
9. Challenges in the Multi Objective
Optimization problem.
Challenge 1: Populate the Pareto Set
Challenge 2: Select the Best Solution
Challenge 3: Find the corresponding Design Variables
10. Solution methods for Challenge 1
Methods discusses in earlier lectures:
Random Sampling
Weighting Method
Distance Method
Constrained Trade-off method
11. Solution methods for Challenge 1
Methods discusses to be discussed today:
Random Sampling
Weighting Method
Distance Method
Constrained Trade-off method
Normal Boundary Intersection method
Goal Programming
Pareto Genetic Algorithm
13. Weighted Sum Approach
Uses weight functions to reflect the importance of each
objective.
Involves relative preferences.
Inter-criteria preference- Preference among several
objectives. (e.g. cost > aesthetique)
Intra-criterion preference- Preference within an objective.
(e.g. 100< mass <200)
14. Drawbacks of Weighted sum method
Finding points on the Pareto front by varying the weighting
coefficients yields incorrect outputs.
Small changes in ‘w’ may cause dramatic changes in the
objective vectors. Whereas large changes in ‘w’ may result in
almost unnoticeable changes in the objective vectors. This
makes the relation between weights and performance very
complicated and non-intuitive.
Uneven sampling of the Pareto front.
Requires Scaling.
15. Drawbacks of Weighted sum method..
For an even spread of the weights, the optimal solutions in the
criterion space are usually not evenly distributed
Weighted sum method is essentially subjective, in that a
Decision Maker needs to provide the weights.
This approach cannot identify all non-dominated solutions.
Only solutions located on the convex part of the Pareto front
can be found. If the Pareto set is not convex, the Pareto points
on the concave parts of the trade-off surface will be missed.
Does not provide the means to effectively specify intra-
criterion preferences.
17. Normal Boundary Intersections (NBI)
NBI is a solution methodology developed by Das and Dennis
(1998) for generating Pareto surface in non-linear
multiobjective optimization problems.
This method is independent of the relative scales of the
objective functions and is successful in producing an evenly
distributed set of points in the Pareto surface given an evenly
distributed set of parameters, which is an advantage compared
to the most common multiobjective approaches—weighting
method and the ε-constraint method.
A method for finding several Pareto optimal points for a
general nonlinear multi criteria optimization problem, aimed at
capturing the tradeoff among the various conflicting objectives.
18. Normal Boundary Intersections (NBI)
NBI is a solution methodology developed by Das and Dennis
(1998) for generating Pareto surface in non-linear
multiobjective optimization problems.
This method is independent of the relative scales of the
objective functions and is successful in producing an evenly
distributed set of points in the Pareto surface given an evenly
distributed set of parameters, which is an advantage compared
to the most common multiobjective approaches—weighting
method and the ε-constraint method.
A method for finding several Pareto optimal points for a
general nonlinear multi criteria optimization problem, aimed at
capturing the tradeoff among the various conflicting objectives.
21. Convex Hull of Individual Minima (CHIM)
The set of points in objective space that are convex
combinations of each row of payoff table, is referred to as the
Convex Hull of Individual Minima (CHIM).
22. Formulation of NBI Sub Problem
Where,
n : Normal Vector from CHIM towards the origin
D : Represents the set of points on the normal.
Beta : Weight
The vector constraint F(x) ensures that the point x is actually
mapped by F to a point on the normal, while the remaining
constraints ensure feasibility of x with respect to the original
problem (MOP).
24. Advantages of NBI
Finds a uniform spread of Pareto points.
NBI improves on other traditional methods like goal
programming in the sense that it never requires any prior
knowledge of 'feasible goals'.
It improves on multilevel optimization techniques from
the tradeoff standpoint, since multilevel techniques
usually can only improve only a few of the 'most
important' objectives, leaving no compromise for the rest.
26. History
Goal programming was first used by Charnes
and Cooper in 1955.
The first engineering application of goal
programming, was by Ignizio in 1962:
Designing and placing of the antennas on the
second stage of the Saturn V.
27. How this method works?
Requirements:
1) Choosing either Max or Min the objective
2) Setting a target or a goal value for each objective
3) Designer specifies -
WGP & WGP +
Therefore, indicate penalties for deviating from either sides
Basic principle:
Minimize the deviation of each
design objective from its target value
- +
Deviational variables dGP & dGP
30. Advantages and disadvantages
1) Simplicity and ease of use
2) It is better than weighted sum method because the
designer specify two different values of weights for
each objective on the two sides of the target value
1) Specifying weights for the designer preference is not
easy
2) What about…?
31. Testing for Pareto
Why the solution was not a Pareto optimal?
Because the designer set a pessimistic target value
32. Larbani & Aounini method
Goal programming method: (Program 1)
The output of Program 1 is X1
Pareto Method: (Program 2)
The output of Program 2 is X2
If X1 is a solution of program 2, therefore it is Pareto optimal
solution and vice versa
34. Genetic Algorithms (GAs) :
Adaptive heuristic search algorithm based on the
evolutionary ideas of natural selection.
Darvin’s Theory:
The individuals who best adapt to the environment are
the ones who will most likely survive.
35. Important Concepts in GAs
1. Fitness:
Each nondominated point in a model should be equally
important and considered an optimal goal.
Nondominated rank procedure.
36. 2. Reproduction
a. Crossover:
Produces new individuals in
combining the information
contained in two or more parents.
b. Mutation:
Altering individuals with low
probability of survival.
38. 4. Pareto Set Filter
Reproduction cannot guarantee that best characteristics of
the parents are inherited by their next generation.
Some of them maybe Pareto optimal points
Filter pools nondominated points ranked 1 at each
generation and drops dominated points.
41. Constrained Multiobjective Optimization via GAs
Transform a constrained optimization problem into an
unconstrained one via penalty function method.
Minimize F(x)
subject to,
g(x) <= 0
h(x) = 0
Transform to,
Minimize Φ(x) = F(x) + rp P(x)
A penalty term is added to the fitness of an infeasible
point so that its fitness never attains that of a feasible
point.
42. Fuzzy Logic (FL) Penalty Function Method
Derives from the fact that classes and concepts for
natural phenomenon tend to be fuzzy instead of crisp.
Fuzzy Set
A point is identified with its degree of membership in that set.
A fuzzy set A in X( a collection of objects) is defined as,
μ mapping from X to unit interval [0,1] called as membership
A :
function
0: worst possible case
1: best possible case
43. When treating a points violated amount for
constraints, a fuzzy quantity- such as the points
relationship to feasible zone as very close, close , far,
very far- can provide the information required for GA
ranking.
Fuzzy penalty function
For any point k,
KD value depends on membership function.
44. Entire search space is divided into zones.
Penalty value increases
from zone to zone.
Same penalty for points
in the same zone.
45. Advantages of GAs
Doesn’t require gradient information
Only input information required from the given problem is
fitness of each point in present model population.
Produce multiple optima rather than single local optima.
Disadvantages
Not good when Function evaluation is expensive.
Large computations required.