Branch & Bound

(Guest article by user Mike, thanks for contributing) By common definition, Branch & Bound is a mathematical algorithm to solve integer optimization problems. But simplified versions of Branch & Bound are also applied to find best fitting technical solutions manually. It is a useful tool for making fundamental decisions, such as the selection of a synthesis route during the project development of a new chemical factory complex.

In the context of CalamarPark, the design of the underwater habitat is such a fundamental decision: Should it be small or large? To operate at what depth? Ambient or atmospheric pressure? A certain design might be perfect at one location, but only second choice at another.

A brute force method to find the right decision is to declare any combination as a valid option and to calculate the benefits for each option. Obviously, that turns out to become an awful lot of work. Two locations, two sizes, two pressure levels and two depths are already 2 x 2 x 2 x 2 = 16 combinations. And we did not talk about energy supply (land based, surface buoy with solar panels) and purpose (tourism, research) yet, save gas supply and much more.

When using Branch & Bound, you reduce the number of options to look at by putting the futile ideas aside and focusing on the promising ones. The catch is that you do not know upfront which idea is good and which one is not. Often, the so called ‘common sense’ is misleading. Many SCUBA divers made the experience that they were fully convinced of the quality of a piece of diving gear in the moment they bought it. But soon after they realized that the new piece of equipment did not perform as expected, or had some flaws in the design. The simplified Branch & Bound method helps avoiding these wrong decisions, by focusing on financial figures and numerical boundaries.

How do boundaries help? And what are numerical boudaries? Let’s assume CalamarPark get’s a call from a rich sponsor, who offers 1 Million Euros for a submarine habitat, provided it will be completed within three years time. This grateful offer contains two boundaries: Time and money. We can now search our database of historical submarine habitats and filter for those which are less expensive that 1 mln Euros at prices of today. In addition, we can filter places with little infrastructure and inefficient bureaucracy, since three years is not that much time when you have to request a permit including a scientific study of environmental impact on marine life.

Upon completion of this exercise, we would have identified a fully developed and feasible option to deliver the habitat in budget and in time. But it is quite likely that we are unhappy with what we have got so far: The subsea station is just a copy&paste from an outdated design, it is smaller than we would have hoped for, supposed for a boring place with little marine life and so on. This is the point where the branches come into play. Imagine a true green tree: It rests on a large trunk that forks into thick branches, then thinner branches and finally twigs. In this picture, our first option is one of the tallest branches in the middle. Now we vary some details and evaluate the impact on time and money. In the tree picture, we fork another branch from the thick one. If we are still within the boundaries (time & money), then we accept the modification and continue with another improvement, until we violate the boundaries (1 mln Euros, 3 years).

Just to give some examples how we get from the reasonable initial project plan to a better design:

  • Placement: Design the habitat to be flexible enough to fit into different environments. After a period at place A, it can be moved to place B.
  • Size: Try a modular approach, so it can expand when fresh money arrives.
  • High-Tech: Take proven and tested technology as basis and apply up-to-date equipment only in those areas, where you benefit the most.

Do not forget to calculate the price and the impact on the project schedule that is associated with each modification (or branch).

One might argue that Branch & Bound would prevent technological break-throughs and innovation. Could we find the Tesla car by means of this method? The answer is, as quite often: It depends. When you look for branches only at the treetop, then you probably would not invent a Tesla. You also have to look near the tree trunk. Without boundaries and guidance to make your way through the almost infinite number of options, chances are to loose yourself in details. The first NASA Space Shuttle seemed to triumph over conventional rockets. No-one cared that it came later and was more expensive than expected. Today the Space Shuttle is mothballed and the Space-X re-useable rocket is the better option, though it is still a rocket. Facts to think about.

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