A SEMINAR ON

“INVASIVE WEED OPTIMIZATION ALGORITHM”

BY ABDUR RASID MULLAH ; ROLL NO-163551

RAHUL KUMAR ; ROLL NO-163565

OUTLINES Introduction What weed is, and why it is important Invasive Weed Optimization Algorithm Fundamentals of Invasive Weed Optimization Algorithm Steps of implementing the IWO algorithm Application Of In Invasive Weed Optimization Multi-Objective Job Shop Scheduling Problems

Introduction Engineering design problems and applications always

involve optimization problems Many engineering problems do not have explicit

presentation of control variables and/or do not have continuity , which are necessary for applying gradient-based optimization techniques.

Direct optimization methods that onlyuse objective function and constrain values to steer towards the solution

Many algorithms inspired from natural processes or events in order to solve optimization problems.

For example:- genetic algorithms (GAs) , Ant colony optimization (ACO) , particle swarm optimization (PSO) etc..

What weed is, and why it is important ?

Weed - is any plant growing where it is not wanted.

The most robust and troublous plant in agriculture.

“The weeds always win” ,because weeds have some strong properties-

Adaptation Robustness Vigorousness invasive

Invasive Weed Optimization Algorithm(IWO)

The IWO algorithm was proposed by A.R. Mehrabian and C. Lucas in 2006

An evolutionary algorithm inspired from colonizing weeds.

Is capable of solving general multi-dimensional,linear and non-linear optimization problem.

IWO is capable of finding desired minima very fast comparing to GA,SA and PSO.

Fundamentals of Invasive Weed Optimization Algorithm

Initialization:- a finite number of seeds are being dispread over the search area.

Reproduction:- every seed grows to a flowering plant and produces seedsdepending on its fitness.

Spatial distribution: the produced seeds are being randomly dispread over the search area and grow to new plants.

Where,itermax = the maximum number of iterations, σiter =the SD at the present time step andn = the nonlinear modulation index Competitive exclusion: this process continues until maximum

number of plants is reached; now only the plants with better fitness can survive and produce seeds, others are being eliminated .

Steps of implementing the IWO algorithm

• Step 1: Initialize randomly generated weeds in the entire search space.• Step 2: Evaluate fitness of the whole population members.• Step 3: Allow each population member to produce a number of seeds with better population members produce more seeds (i.e. reproduction).• Step 4: The generated seeds are distributed over the search space by normally distributed random numbers with mean equal to zero but varying variance (i.e.,spatial dispersal).• Step 5: When the weed population exceeds the upper limit, perform competitive exclusion.• Step 6: Check the termination criteria.

Flow Chart of IWO

Solving Traveling Salesman Problem

Multi-Objective Job Shop Scheduling Problems

Optimization Technique for Antenna Configurations

Solving nonlinear equations systems

No-idle flow shop scheduling problem

Application Of Invasive Weed Optimization

OBJECTIVE :- Minimize the 1. Maximum completion time (make span),2. The total workload of machines and 3. The workload of the critical machine.

The problem of flexible job shop scheduling belongs to the NP-hard family.

Multi-Objective Job Shop Scheduling Problems

Difficulties:-

1. Assignment of each operation to a machine

2. Scheduling of this set of operations for optimization.

Input Data

For solving JSSP using IWO, the following inputs are required:• Number of jobs• Number of Machines• Machine order for all the jobs• Processing Times of all the operations• Due dates for all the jobs• Number of iterations to be carried out• Nonlinear modulation index for finding out standard deviation in each iteration.

Constraints

Machines are independent of one another.

A machine can be unavailable during the scheduling (case of machine breakdown).

Jobs are independent of one another.

Each operation is start at t=0

PROBLEM

The 1st and 2nd halves of the 1st row of the weed represent operations as repetition of jobs.

The 2nd row of represents weed’s position. Smallest Position Value (SPV) rule to find the permutation of

jobs. The 3rd row (L.H.S.) indicates the sequence of jobs in the

ordering 3rd row (R.H.S.) indicates the machines corresponding to

their job. Last row (L.H.S.) indicates operations in the order The operation O(1,1) of job J1 is executed by the machine M1

at time t = 0 , and then the operation O(2,1) of job J(2) is executed by the machine 1 M at time t = 1, and so on.

Begin{• Initialize population of weeds, set parameters;• Current_iteration=1;While (Current_iteration< Max_iteration)do{ • Compute the best and worst fitness in the population • Compute the standard deviation std depending on iteration For each weed w in the population W { • Compute the number of seeds for w depending on its fitness • Select the seeds from the feasible solutions around the parent weed w in a neighborhood with normal distribution having mean=0 and standard deviation=std;

Pseudo code for solving FJSSP

• Add seeds produced to the population W If (|W|>Max_SizePopulation) { • Sort the population W according to their fitness • W=SelectBetter(weed,seed,Max_SizePopulation) }End if }End for Current_iteration=Current_iteration+1;}End while}End

Contd.

REFERANCES Mehrabian, A. R. and Lucas, C. 2006. A novel numerical optimization algorithm inspired from

weed colonization.Ecological Informatics 1 (2006), 355–366.

Rao,C.S.P. and Madivada, H. 2012 . AN INVASIVE WEED OPTIMIZATION (IWO) APPROACH FOR MULTI-OBJECTIVE JOB SHOP SCHEDULING PROBLEMS (JSSPs).

Siddharth Pal, Anniruddha Basak and Swagatam Das “Linear Antenna Array Synthesis with Invasive Weed Optimization”,International Conference of Soft Computing and Pattern recognition, 2009.

Yongquan Zhou , Huan Chen , Guo Zhou . Invasive weed optimization algorithm for optimization no-idle fl ow shop scheduling problem . Neurocomputing 137 (2014) 285–292.

THANK YOU