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.

This article in its entirety was written by a human being. No machine intelligence was involved in any way.

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:

First Aid for Painful Meetings

The foundation of any team meeting is its agenda. A crisply focused agenda can make the difference between a long, painful affair and finishing early. If you're the meeting organizer, develop and manage the agenda for maximum effectiveness.

Excuses, Excuses

When a goal remains unaccomplished, we sometimes tell ourselves that we understand why. And sometimes we do. But at other times, we're just fooling ourselves.

Guidelines for Sharing "Resources"

Often, team members belong to several different teams. The leaders of teams whose members have divided responsibilities must sometimes contend with each other for the efforts and energies of the people they share. Here are some suggestions for sharing people effectively.

You Might Be Stressed If…

A little stress once in a while keeps us sharp, but chronic intense stress shortens lives. Stress can build gradually, out of our awareness. Here are some indicators of chronic intense stress.

Problem-Solving Preferences

When people solve problems together, differences in preferred approaches can surface. Some prefer to emphasize the goal or objective, while others focus on the obstacles. This difference is at once an asset and annoyance.

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

Forthcoming issues of Point Lookout

Coming December 11: White Water Rafting as a Metaphor for Group Development

Tuckman's model of small group development, best known as "Forming-Storming-Norming-Performing," applies better to development of some groups than to others. We can use a metaphor to explore how the model applies to Storming in task-oriented work groups. Available here and by RSS on December 11.

And on December 18: Subgrouping and Conway's Law

When task-oriented work groups address complex tasks, they might form subgroups to address subtasks. The structure of the subgroups and the order in which they form depend on the structure of the group's task and the sequencing of the subtasks. Available here and by RSS on December 18.

Coaching services

I offer email and telephone coaching at both corporate and individual rates. Contact Rick for details at rbrenyrWpTxHuyCrjZbUpner@ChacnoFNuSyWlVzCaGfooCanyon.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, )
• Get 2003-4 in Why Dogs Wag (PDF, )
• Get 2005-6 in Loopy Things We Do (PDF, )
• Get 2007-8 in Things We Believe That Maybe Aren't So True (PDF, )
• Get 2009-10 in The Questions Not Asked (PDF, )
• Get all of the first twelve years (2001-2012) in The Collected Issues of Point Lookout (PDF, )

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 500-1000 words in your inbox in one hour. License any article from this Web site. More info