**Problem Statements are the fundamental unit of design and innovation.**

However, the art of writing effective problem statements has been lost and forgotten over the years. None of the design and innovation programs focus on this important aspect leading to elongated *cycle time** to solutions in the best case to ineffective and poor solutions in the worst case.

**The time taken to traverse across the design space from the problem to the solution is called cycle time. For prolific innovators, the cycle time is very short. For most of us, the cycle time is elongated or perpetual/never ending.*

I have spoken to many innovation professors, design engineers and practitioners over time and except one octogenarian engineer, no one could explain why problem statements are key to innovation, invention and design.Worse, most could not tell me how to write an effective problem statement. It soon dawned on me that the design engineers of the 1800’s era that created the industrial revolution either did not pass down the skill or the incoming generation somehow decided against their value and importance.

Before we can write effective and powerful problem statements, we need to understand their impact on the design space and how they incorporate objective functions and constraints.

**Note :** *The recent trending phenomenon of using “How Might We” statements borrowed from CPS (Creative Problem Solving) techniques are not problem statements, not widely used in the innovation and design industry. I have found them to be cool and trendy, but largely ineffective in real world innovation problem solving.*

**What is a Design Space ?**

Design Space is an abstract space in which problems and solutions reside or cues to problems and solutions reside. Our unconscious mind finds solutions in the space automatically and mostly without our conscious awareness.

As discussed in “Understanding the Unconscious Mind“, the unconscious mind is formed of the 100 billion odd neurons combined with the chemical and analog embodied mind. It runs the principal pattern recognition processes and response modulation processes operating in our nervous system. Beneath our conscious awareness, neural drives remember and recognize patterns and act with logical precision. I would call these 24 X 7 drives unconscious search drives or *unconscious search (US)*.

These drives support our speech, respond to our feelings, organize an idea, find the right words, arrange them in order, check grammar and operate our vocal chords. Our conscious mind follows the system level unconscious mind with a little bit of delay. The unconscious mind and the Bayesian brain is adaptive in nature. Below the threshold of awareness, it keeps sensing the environment, creating responses, enabling adaption and survival in the environment. Relaying the problem to our unconscious mind allows the unconscious processes to maintain sustained laser focus on the problem to be solved. It continues to compute billions of possible solutions till a solution meets our requirements.

Relaying the problem to our unconscious mind allows the unconscious processes to maintain sustained laser focus on the problem to be solved. When our unconscious system has found the solution (s) to a problem, it will start pushing upward the solution set in our conscious mind as a series of insights in a precipitative manner, slowly synthesizing the bits and pieces allowing us enhanced and novel sense-making of the entire context . Our 100 billion of so neurons carry out detailed and comprehensive neural computations on digital, chemical and analog level to arrive at these solutions.

If it is already not clear, the designer or innovator is intuitively or formally using engineering optimization methods to solve problems as optimization computation is hard coded in our DNA and evolution.

**First Principles of Optimization**

Optimization is the art and science of making things better. At the core level, Optimization is problem solving. For Operations Research enthusiasts, Mathematicians and Programmers, **Optimization** *is a generic label for computational techniques which can utilize a given set of input data and provide recommendations for the most **Feasible** and **Optimal** solutions. The tallest hills are optimal solutions (global optima) and other hills are feasible solutions (local optima). It is possible and very easy to get stuck in local optima not knowing that a global optima may be nearby hidden from plain sight. *

Design and Innovation is not different as it is also a way of making daily use things better and searching for global optima. Look around you and it is easy to notice that every good product, widget or piece of software is optimized around one of two key functions. The lowly beverage can is optimized for ease of transportation, low cost and intuitive use.

Nature is always optimizing everything around us and human evolution is a perfect test case for optimization. Natural selection is the process by which living things that are most well suited to their environments adapt, survive and reproduce.

Let us use the example of the “*Saguaro Cactus*” plant. It is native to the Sonoran Desert in Arizona, the Mexican State of Sonora, the Whipple Mountains and Imperial County areas of California. The plant has the ability to survive under under harsh heat and water devoid conditions. As it stores water, it becomes a prime target for animals and it’s sharp thorns are optimized to keeps most of those animals at bay. The shape of the plant, it’s water absorption and storage capability and the evolution of thorns is is a perfect use case where the plant has optimized objective functions to survive in harsh conditions. In the field of optimization engineering, the core building blocks are functions, objectives and constraints. Even though one may not be solving an engineering problem, writing effective problem statements is almost impossible unless one has good intuitive understanding of objective functions and constraints.

**Objectives, Functions and Constraints**

**Objectives** – Objectives are basically outcomes about the design or innovation initiatives. They are desired attributes of a design functionality and have primary and secondary objectives bound together in a hierarchical manner. Objectives enable the designer to explore the design space so that the right alternatives can be selected from billions and trillions of possibilities. Objectives are almost always quantifiable i.e. minimize the time in which a user can beat the eggs, minimize the cost of running an equipment and, maximize the yield from flight bookings. Look at our daily life and we will be optimizing some objective function i.e. create time for ourselves and families, make maximum money that we can, achieve proficiency in our skills etc.

“I think frugality drives innovation just like other constraints do” ~ Jeff Bezos

**Constraints** – Constraints are strict limits that a design must meet in order to be acceptable. Constraints can be soft constrains or hard constraints. Hard constrains are unchangeable as they are limitations imposed by the environment on what can or cannot be achieved. Soft constrains can be changed by the designer or end user. Constraints almost always constrain and limit the size of the design space.

**Functions** – Functions are desired input-output transformations and focus on specifics of the objectives i.e. achieve so and so task in maximum 5 minutes. Functions are usually called objective functions as they are hierarchically interrelated.

Learning too soon our limitations, we never learn our powers ~ Mignon McLaughlin

**Design space** is an abstract space in which solutions, problems, objective functions and constraints reside. Our unconscious mind knows more than our conscious mind knows and over a lifetime, it diligently catalogs, files and categorizes our knowledge of others in our intuitive and unconscious filing cabinets. Inventors and Designers in the passionate pursuit of a problem diligently create an unconscious filing system of the context, articulated and un-articulated user needs and evolving trends in the eco-system. In a future post, I will show that a design space is more than an conceptual and abstraction frame. It is very much real in the realm of our unconscious filing catalogs.

While objective function can be changed or calibrated, the constraint is usually fixed or locked down. Hard constraints exist in the environment where design is unfolding or existing. As such,whenever constraints change in an ecosystem, new opportunities open up. Real innovation occurs, though, when designers can side-step the constraints to reduce dependency on them and yet achieve effective solutions.

**The Lifeguard Problem**

I will use an example of the Lifeguard Problem to explain the concept of functions, objectives and constraints. The case study has been used from Mark French’s writings and simplified to remove mathematical computations from it.

On the beach in the illustration below, there is a lifeguard, a swimmer and they are separated by an almost equal distance of water and beach sand. In this scenario, the life guard is scanning the horizon from the lifeguard station and she sees a swimmer drowning on the deep end of the water.

Alright, so, what would be the top level objective here in the given situation ?

It is obviously to rescue and extract the drowning swimmer alive. This being the top level objective, let us go down a step to see what is the most important element in this scenario. If there is only one thing the lifeguard has to do in such a situation, what would that be ?

Try to answer this before you progress and read the answer.

A good problem statement often includes what is known, what is unknown and what is sought ~ Edward Hodnett

If you said, reach the swimmer in the least possible time, you are right. To meet the top level objective of rescuing and extracting the swimmer alive, the lifeguard needs to reach the swimmer in the shortest time possible. The overall strategy of rescue will fail if the lifeguard takes longer than a hypothetical time (t) after which the rescue will convert to a recovery operation.

The formula for time is the speed of the lifeguard divided by amount of distance traveled. As distance is being traversed over two zones i.e distance over sand while running and distance over water while swimming, we can divide the time into t1 (sand) and t2 (water).

**Speed = Distance X Time**

What could possibly come in the way of rescuing the drowning swimmer in time t ?

The lifeguard can run faster over the beach sand than swim. The first problem is to is to find the shortest path to the swimmer that also minimizes time. Assuming that the distance remains constant both over land and sea, the only thing coming into the way of a successful rescue is the running speed and the swimming speed of the lifeguard.

Let us further assume that the lifeguard holds two world records for fastest runner and fastest swimmer, the fastest running and swimming speeds cannot be maximized more than the records established. These limitations come in the way of minimizing time beyond an established norm and are hard constraints.

It is easy to see in the above situation that to rescue the drowning swimmer alive (objective) , the lifeguard has to reach the swimmer in the least amount of time possible (function), but she is limited in minimizing time (t) due to her maximum running speed (constraint 1) and maximum swimming speed (constraint 2).

On a side note, when we move to actual solutions in these cases, the lifeguard minimizes time by running very fast and leaping into the sea reducing the time taken to traverse the distance as well as sidestepping her hard coded maximum swimming speed constraint. The time (t) can be divided into three parts, t1 as time taken to run over the beach sand, t2 as time in flight during the dive into the water and t3 as the time during conventional swimming in water.

“A clever person solves a problem. A wise person avoids it” ~ Albert Einstein

The above situation has been over-simplified to explain functions, objectives and constraints. However, this situation is actually very complex as the relationship between the function and constraints is non-linear.

In simple life situations, we are solving multi-objective problems, where there is more than one objective function to be achieved and many more constraints to be satisfied. To top it up, the relationship between these variables is usually non-linear creating a combinatorial explosion of possibilities. A small change in any of them over time leads to billions and trillions of permutation and combinations and soon, the inventor or designer can get lost. As we will see in Part II, problem statements come to