Hill Climbing and Its Limitations

Finding the extreme values of functions is a common problem in mathematics. For instance, one form of the famous "traveling salesman" problem involves finding the shortest path that a traveling salesman can follow to visit all customers in a given district. Algorithms for optimizing functions are called "hill climbing" algorithms if they work by gradually improving a solution, adjusting its attributes one at a time.

The hill climbing metaphor comes from imagining the function's value as being the altitude of a point in a geographical region. To find the highest point in the region, we take one step at a time, always uphill. By always climbing uphill, we hope that we'll find the highest point in the region. The metaphor is so powerful that hill climbing algorithms are called "hill climbing" even when we're minimizing something instead of maximizing.

There's just one problem: hill climbing doesn't always work. For example, suppose you're unlucky enough to start your optimizing on the shoulder of a hill that happens to be the second-highest hill in the region. By always "moving uphill" you will indeed find the peak of that second-highest hill, but you'll never find the highest hill. In effect, the algorithm is "captured" by the second-highest hill and it can't break free.

That's unfortunate, because we use hill climbing often without being aware of it. For instance, when we hire people, we look for attributes that we feel will ensure that we hire the best. One such attribute is experience in efforts exactly like the ones we anticipate. Even though identical experience doesn't necessarily ensure future success, we use experience because we believe that it will take us most steeply "uphill." It's possible, of course, that someone with a different experience background might be just what we need to achieve even better results. But we'll never know, because the current solution has captured us.

This In decision-making, we use hill
climbing often without being
aware of ithappens in problem solving too. When we're familiar with one solution, we tend to focus on filling out the rest of that solution, rather than seeking a completely new approach that might lead to a far better solution. Such new approaches are sometimes said to arise from "thinking out of the box."

And most tragically, hill climbing can lead to the downfall of an entire enterprise. A company that's dominant in its market can become captured by the particular way in which it meets customer needs. Even though it searches constantly for innovations, it seeks only those innovations that preserve certain attributes of its current offerings. When a competitor enters the market with a wholly different approach, that competitor can prevail if its solution gives the customer a path to a "higher hill." Think airlines and railroads, iTunes and record stores, or iPhone and Blackberry.

Is your enterprise captured by a hill climbing approach? Maybe it's not too late to do something about it.  Top    Next Issue

Are your projects always (or almost always) late and over budget? Are your project teams plagued by turnover, burnout, and high defect rates? Turn your culture around. Read 52 Tips for Leaders of Project-Oriented Organizations, filled with tips and techniques for organizational leaders. Order Now!

Your comments are welcome

About Point Lookout

Thank you for reading this article. I hope you enjoyed it and found it useful, and that you'll consider recommending it to a friend.

Point Lookout is a free weekly email newsletter. Browse the archive of past issues. Subscribe for free.

Support Point Lookout by joining the Friends of Point Lookout, as an individual or as an organization.

Do you face a complex interpersonal situation? Send it in, anonymously if you like, and I'll give you my two cents.

Related articles

More articles on Personal, Team, and Organizational Effectiveness:

Mudfights

When we steer the discussion away from issues to attack the credibility, motives, or character of our debate partners, we often resort to a technique known as the ad hominem attack. It's unfair, it's unethical, and it leads to bad, expensive decisions that we'll probably regret.

Organizing a Barn Raising

Once you find a task that you can tackle as a "barn raising," your work is just beginning. Planning and organizing the work is in many ways the hard part.

Clueless on the Concept

When a team member seems not to understand something basic and important, setting him or her straight risks embarrassment and humiliation. It's even worse when the person attempting the "straightening" is wrong, too. How can we deal with people we believe are clueless on the concept?

Office Automation

Desktop computers, laptop computers, and tablets have automation capabilities that can transform our lives, but few of us use them. Why not? What can we do about that?

Wacky Words of Wisdom: V

Adages, aphorisms, and "words of wisdom" are true often enough that we accept them as universal. They aren't. Here's Part V of some widely held beliefs that mislead us at work.

See also Personal, Team, and Organizational Effectiveness and Problem Solving and Creativity for more related articles.

Forthcoming issues of Point Lookout

Coming April 24: Big, Complicated Problems

Big, complicated problems can be difficult to solve. Even contemplating them can be daunting. But we can survive them if we get advice we can trust, know our resources, recall solutions to past problems, find workarounds, or as a last resort, escape. Available here and by RSS on April 24.

And on May 1: Full Disclosure

The term "full disclosure" is now a fairly common phrase, especially in news interviews and in film and fiction thrillers involving government employees or attorneys. It also has relevance in the knowledge workplace, and nuances associated with it can affect your credibility. Available here and by RSS on May 1.

Coaching services

I offer email and telephone coaching at both corporate and individual rates. Contact Rick for details at rbrenRYIbqLdPFomwcmAhner@ChacNtdTqKiJvkOqWFCroCanyon.com or (650) 787-6475, or toll-free in the continental US at (866) 378-5470.

Get the ebook!

Past issues of Point Lookout are available in six ebooks:

• Get 2001-2 in Geese Don't Land on Twigs (PDF, USD 11.95)
• Get 2003-4 in Why Dogs Wag (PDF, USD 11.95)
• Get 2005-6 in Loopy Things We Do (PDF, USD 11.95)
• Get 2007-8 in Things We Believe That Maybe Aren't So True (PDF, USD 11.95)
• Get 2009-10 in The Questions Not Asked (PDF, USD 11.95)
• Get all of the first twelve years (2001-2012) in The Collected Issues of Point Lookout (PDF, USD 28.99)

Are you a writer, editor or publisher on deadline? Are you looking for an article that will get people talking and get compliments flying your way? You can have 500 words in your inbox in one hour. License any article from this Web site. More info

Public seminars

The Power Affect: How We Express Our Personal Power

Many people who possess real organizational power have a characteristic demeanor. It's the way they project their presence. I call this the power affect. Some people — call them power pretenders — adopt the power affect well before they attain significant organizational power. Unfortunately for their colleagues, and for their organizations, power pretenders can attain organizational power out of proportion to their merit or abilities. Understanding the power affect is therefore important for anyone who aims to attain power, or anyone who works with power pretenders. Read more about this program.

• A recording of a program presented 6:00 PM June 29 (Eastern Time), Monthly Webinar, Technobility Webinar Series. You can earn 1.0 Category 'A' PDU by viewing this program. View this program now.