Discrete Optimization course begins today

Here is the instructor Pascal Van Hentenryck answer from the coursera forums:

"Thanks for pointing this out.

First, we obviously cover linear programming and mixed-integer programming in this course. These techniques are indeed very successful in practice and I hope that you will also enjoy these lectures. They make up a third of the class. The references

    Integer Programming by Laurence A. Wolsey
    Integer and Combinatorial Optimization by Laurence A. Wolsey, George L. Nemhauser
    Large Scale Linear and Integer Optimization: A Unified Approach by Richard Kipp Martin
    Introduction to Linear Optimization by Dimitris Bertsimas, John N. Tsitsiklis
    Understanding and Using Linear Programming by Jiri Matousek, Bernd Gärtner
    Theory of Linear and Integer Programming by Alexander Schrijver

are also provided in the additional material. The work mentioned in the introductory lectures include many applications that are based on mixed-integer programming. So I am not sure where this person is coming from with her/his comment.

This being said, constraint programming and local search are also very successful in practice, often for different types of problems. So this class aims at giving an introduction to a subset of the techniques that are successful in practice (there are other too) as an introduction to the field. My research group uses all three of these techniques to solve large-scale problems in logistics and supply-chains, energy, and disaster management. Some of the problems we solve require the three approaches together to achieve high-quality solutions. To paraphrase John von Neumann defending George Dantzig: "If this technique applies to your problem, use it; otherwise do not".

We also cover column generation and large neighborhood search in the advanced topics. I used to cover Lagrangian relaxation in my class at Brown and we may add a lecture on this. This class has almost all the material of my optimization class at Brown University but not all, since it is a shorter. We may still add an advanced lecture on this topic (I have an additional motivation now)

With respect to the job market, I would simply say: Go to the Informs conference and see how many people, both from academia, industry, and government, are recruiting. Companies such Google, IBM, Amazon, ... have outstanding groups in optimization. Follow Mike Trick's blog and tweeter accounts to get a sense of how lively this community is (see the community link on the page). I never had a student not find a job and most of them did not go to academia. One of them actually works for ... Fedex. My sense is that the opportunities for optimization keep growing and it is an exciting time for optimization. There are many startups, established companies, large multi-national organizations all doing optimization. Some focus on solvers, some on vertical products, some on dedicated applications, and some of several or all of these aspects. The field has progressed significantly.

There is a lot of work, and a lot of progress, in making optimization more reusable and the tools/solvers are now much better in being more generic. Unless P=NP, this will always be a challenge but there are more generic tools to solve classes of applications. There are also solvers that provide a lot more flexibility to build dedicated algorithms much more simply. Many people (including me) spent their research and academic careers trying to design such tools and some make a significant difference in practice.

Finally, optimization is a multi-disciplinary field. My group employs mathematicians, physicists, engineers, and computer scientists. What I personally find incredibly stimulating in this area right now, is that sometimes you need a physicist, a mathematician, and a computer scientist together to solve a complex problem. We all look at a problem from different angles and there is tremendous values in that. I am part of the INFORMS, artificial intelligence, and computer science communities, and some of the scientific contributions I am most proud of are typically those when I was able to bridge two fields. Many of the techniques in optimization come from a variety of fields and this is also what makes it exciting.

And, yes, I am exciting about the future of optimization,

I hope it helps."

The Indiana Jones take off is fine. Mentioning the knapsack problem is less good because it's not so important in practice. Saying that the knapsack problem is difficult to solve, e.g., encounters exponential algorithms because technically it's in NP-complete, is next to irrelevant for practice, misleading, and hype and not fine.

> it's also important to update how you state your value to others

On this, I outlined my suggestion: Own a little company and sell results based on how much money they save the customer. Make the sale about saving the customers money in ways that even an auditor can confirm are correct.

INFORMS is clearly an echo chamber, people in optimization looking for work and talking to themselves.

Broadly for optimization in business, there is a very serious problem: Optimization is not a 'profession' like law, medicine, or major parts of engineering. So, there is no licensing, certification such as the CPA, peer-review of practice, legal liability, etc. So, as I said, the field "don't get no respect". Also missing is a point the legal profession has: Any working lawyer must report only to a lawyer; the interface between the optimization guy and the business guy is nearly impossible.

> Is the point of your argument ...

I tried to make several points. One of the points was about 'optimal'. The mathematical definition is fine, but long that definition was taken as suggesting that what we should do in practice is look for such solutions, then strain to find them, etc. That turned out to be a grand mistake.

Why? Because maybe there is, compared with what the customers is doing now, $10 million to be saved with an optimal solution. But too commonly saving all $10 million is too difficult for the algorithms and computing. So, straining to save all the $10 million converts an important business problem into a much more difficult mathematical problem. It also turns out that commonly it's fairly easy to save, say, $9 million. The difficulty is saving the last of the money, and the most difficult money to save is the last, say, the last 10 cents.

'Optimal' was taken as a moral objective, as I said, as if saving the last 10 cents was worth much more than 10 cents.

Struggling over 'optimal' taken literally and, thus, making real problems much more difficult than necessary, was several torpedoes below the waterline of the ship of optimization.

Part of this mistake was the simplistic and excessive emphasis on NP-completeness -- for real problems the whole P versus NP question is next to irrelevant. One way to see this is the simplex algorithm -- it's the core of optimization and astoundingly fast in practice but worst case exponential. There is a polynomial algorithm for linear programming, but it's way too slow in practice. In practice, that an algorithm is worst case exponential is commonly just irrelevant.

I had to conclude that for business, optimization is a dead field. It got started due to WWII and US DoD funding, and maybe in places there is still some interest for US DoD problems.

Here is a little: A post above, in response to a post of mine, claimed that IBM had a good optimization group. If so, then good for IBM. But I was at IBM's Watson lab, published a paper on optimization, and off and on considered joining the optimization group there. Phil Wolfe, William Pulleyblank, Ellis Johnson. and others were in that group. At one point, Roger Wets was visiting. The group did the IBM Optimization Subroutine Library (OSL). Then in 3 years near 1994, IBM lost $16 billion. Johnson joined George Nemhauser at Georgia Tech. Pulleyblank became a professor at West Point. Basically the optimization group fell apart. Maybe they put a group back together, but losing Johnson and Pulleyblank were big mistakes.

E.g., again, with Pulleyblank at West Point, the US DoD remains interested in optimization.

Heck, I supported myself and my wife through our Ph.D. degrees by working in optimization for the US DoD.

In academics, the professors were to do research to get the field going, e.g., research in 'systems analysis', 'mathematical sciences', 'civil engineering', 'production', etc. Yes, if optimization problems were easy to solve, then optimization would have central roles in those fields. Alas, mostly important practical optimization problems are not so easy to solve, even approximately. So, the professors are still doing research -- maybe in some decades or centuries they will have something of serious importance for those fields. I doubt that the research is very well supported.

I tried to give a summary of essentially a 'cultural contradiction' expecting optimization to be a popular field in business: By the time computing is ready to make optimization easy enough, there are other things to do with the computing making much more money than with optimization.

It's not that optimization can't save money in business; there is money to be saved; in a lot of stable businesses, optimization can provide some of the highest ROI available to the business. So, there is some ground available there, what is in principle some fertile ground. So, there can be some optimization groups here and there. If the course prof has such a group in Australia, good for him. With some really impressive 'cases' published in, say, INFORMS, maybe mainline business will try optimization again. I doubt it, but maybe. Don't hold your breath waiting; there are lots of impressive cases long since published in INFORMS, and ORSA, Mangement Science, etc. The optimization literature is huge going back to the late 1940s, e.g., for Dantzig at Rand and Berkeley.

Here's a little on the difficulty: In the US there are college accrediting groups, and for some years they said that an undergraduate degree in business should have courses in optimization and statistics. So, for years each business school student, undergraduate or MBA, got a course in optimization. For some years, I taught such courses. Still the field didn't take off.

I can't recommend that anyone try to have a career in optimization in business. You stand to have an easier time supporting a family with a career as a plumber, literally. With software, do an information technology start up, sell out, and pocket, say, $10 million -- knocks the socks off optimization. With irony, if interested in 'optimization' of your career and financial security, then avoid optimization!

Optimization is like some item at Dunkin Donuts that doesn't sell. Lots of other stuff at Dunkin Donuts sells really well, but that one item just doesn't. They can do a good job getting the item ready to eat, put it out in the display cases, and wait, and what happens is the item just sits there and goes stale. Then they throw away the stale, unsold items. It was a waste. Finally, Dunkin Donuts just quits offering the item.

Dunkin Donuts doesn't go on and on about why the item really should sell. Instead, they just listen to the clear message they've gotten from the market and, thus, save having to figure out solid reasons it doesn't sell.

Similarly all across business -- some stuff doesn't sell or doesn't sell very well or sells only a little and then only into a tiny market. Optimization in business is like that -- at best, it's a super tough sale; usually it just doesn't sell.

Optimization, as a field, in business, is a dead duck. F'get about it and pursue something else.

If the course professor can have a flourishing, productive group in optimization in Australia, then good for him, his group, and the good judgment of his customers.

In the US, optimization was a field with lots of effort back at least to Dantzig at Rand in the late 1940s. The main push for the field was just the US DoD.

For US business, there have been some niche applications, but the overall situation has long been just as I described -- the field "gets no respect". With rare exceptions, people just don't want it. Elsewhere in this thread I've given nearly exhaustive reports of why basically in US business optimization is a dead duck.