Jan2015-Real Optimization-Lakshmibai College-University of Delhi

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Real Optimization

Vikas Jain

vikas.jain@iAdhyan.com

Founder, Adhyan Innovative Learning

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Intuitive Approach towards Optimization

There are two ways of understanding any concept. One is Specialized which is well researched, accurate and uses sophisticated language. Other method is more intuitive where meaning of the concept can be explained in a layman language. To understand this better one can recall the definition of “Machine” in the Movie “Three Idiots”. Benefit of understanding a concept in intuitive way is that one doesn’t have to remember the concept. They just know it.

Formal/Specialized meaning of Optimization:

In mathematics, computer science, economics, or management science, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.

Source: en.wikipedia.org/wiki/Mathematical_optimization

As discussed earlier, although this is a formal definition, but lets focus on understanding the intuitive meaning of Optimization so that we can apply it in Professional as well as Personal Life.

Best approach to understand the intuitive meaning of any concept is to know the Etymology of that word. Etymology helps us to understand the root of the word and thus understand the meaning better.

Optimization roots :-

Hence intuitive meaning of Optimization is getting best out of available resources. Lets connect with its different aspects.

Functional is first step towards Optimization:

Functional means that the Approach is correct, and it would yield expected results.

Optimized means let’s try to improve the “Approach” to get results in best possible manner.

 

Let’s take a simple example of Counting to understand this better:

Problem: Count total number of balls in 10 jars where we know that each jar has 5 balls.

Approach 1

If this task is given to a Class 1 student who has not studied addition, we expect the child to count each and every ball in all the jars by picking each and every ball.

  • Is this Solution Functional? -> Yes
  • Is this Optimized? -> No.

Approach 2

A Class 2 student having knowledge of Addition, would like to solve the problem by 5+5.. 10 times. = 50.

  • Is this Solution Functional? -> Yes
  • Is this Optimized? -> No

With the understanding of Multiplication, we can easily say that there are better ways of doing it. Hence optimization is an ongoing process. All the solutions may be functional. But there is always a scope of improvement for better optimization.

Approach 3

A Class 5 student with knowledge of Multiplication, would like to solve the problem by 5X10=50.

  • Is this Solution Functional? -> Yes
  • Is this Optimized? -> Yes

Please note that for most of the people this would be an optimized Solution. But a true Mathematician would always strive to improve the solution further.

Hence we can have multiple Functional Solutions and we need to make them optimized. Thus, all of the below mentioned solutions are functional but not optimized.

Count them -> Add them -> Multiply them

 

Real Life Scenario in Profession – True Optimization

With understanding of Functional and Optimized solution, lets take a real life scenario from Information Technology field. Most of the average IT companies expect just a Functional Solution from Candidate during Interview. On the other hand, top IT companies expect sound knowledge of Optimized Solution from Candidate. They first look for a functional solution from candidate. Once he has provided a Functional Solution, they would further expect from him to optimize the solution.

Here is my interview experience with Microsoft in the year 2013 that I was able to clear.

I was asked to write a program to find all prime numbers between 1 to n. As per Microsoft standard this is a very easy program, but I am quoting this here to make you understand the importance of Optimization and undergraduate audience of Mathematics students.

My first Solution was

Main()

{

Take input “n” from user

For each number starting from 2 to n

{

call IsPrime(number)

If <it is a prime number, print that number>

else<Skip that number and don’t print it.>

}

}

IsPrime(number)

{

For each number say num1 from 2 to number-1

if num1 divides number completely without any remainder then

Return false this is not a prime number

Loop completes

Return True is this is a prime number

}

Now lets evaluate the Solution:

  • Is this a functional Solution? -> Yes
  • Is this optimized? -> No

 

During further discussion, below mentioned are few optimization that are possible:

  1. In function Main, we need not take every number from 2 to n. As we can easily skip Even numbers from this sequence. Hence beside checking, 2,3,4,… n, we should ideally check only 3,5,7 ..n etc.
  2. In function IsPrime, we need not check till number-1. We can just take till square_root(number).

Every business, is looking for Functional and Optimized Solution. If you can provide those answers then you will get tremendous success in life.

 

Relate this concept to Real Life

Most of the students have a lifestyle like this: Coming to college, Attending the Classes, Preparing for Exam, Getting score. Having fun in College.

  • Is this approach Functional? -> Yes, it is working for most people
  • Is this approach Optimized? -> May not be, as there are people who have optimized this approach and achieved great results.

There are B.Tech. Students who are struggling to get a software job of even 10K per month and land up in some BPO call center job. On the other hand there are students who have not even graduated from well known colleges, but followed the optimized approach and getting more than a lakh per month.

This is not Luck. This is not IQ. This is not Family Background. This is just by following an Optimized (getting best out of available resources) approach in life called “Secret of Success”.

Few examples:

  • Jack Ma from China, founder of Alibaba.com was an English Teacher. In year 1999 someone introduced him to Internet. He built Alibaba.com and now he is Richest man in China and Second Richest in Asia.
  • Sandeep Maheshwari, average student from North Delhi area who struggled to get a basic job in 2000. He is now a successful entrepreneur. He built imagesbazaar.com and earned crores of rupees by 2007. He now delivers Motivational Seminars all over India and that too for FREE.

These people did not accept “Functional” approach towards life and worked hard to get it Optimized (getting best out of available resources)

 

 

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