Heuristic Optimization Thomas St¨ utzle IRIDIA, CoDE Universit´ e Libre de Bruxelles stuetzle@ulb.ac.be iridia.ulb.ac.be/ ∼ stuetzle iridia.ulb.ac.be/ ∼ stuetzle/Teaching/HO Example problems ◮ imagine a very good friend from Germany visits you and he wants to visit all 239 breweries in Belgium during his one week stay Is this feasible? If yes, which route to take? The shortest certainly helps ◮ at brewery No. 49 your friend offers to pay all beers you take on the trip if you solve the following riddle ‘Last week my friends Anne, Carl, Eva, Gustaf and I went out for dinner every night, Monday through Friday. I missed the meal on Friday because I was visiting my sister and her family. But otherwise, every one of us had selected a restaurant for a particular night and served as a host for that dinner. Overall, the following restaurants were selected: a French bistro, a sushi bar, a pizzeria, a Greek restaurant, and the Brauhaus. Eva took us out on Wednesday. The Friday dinner was at the Brauhaus. Carl, who doesn’t eat sushi, was the first host. Gustaf had selected the bistro for the night before one of the friends took everyone to the pizzeria. Tell me, who selected which restaurant for which night? Heuristic Optimization, 2012 2
How to solve it? ◮ many possible approaches ◮ systematic enumeration is probably not realistic ◮ some people may eliminate certain assignments or partial tours through careful reasoning ◮ other intuitive approach: start with some good guess and then try to improve it iteratively The latter is an example of a heuristic approach to optimization Heuristic Optimization, 2012 3 Optimization Optimization refers to choosing the best element from some set of available alternatives. Optimization problems . . . ◮ arise in a wide variety of applications ◮ arise in many different forms, e.g., continuous, combinatorial, multi-objective, stochastic, etc. ◮ here we focus mainly on combinatorial problems ◮ range from quite easy to hard ones ◮ here we focus on the hard ones! Heuristic Optimization, 2012 4
.. an easy one find the best (most valuable) element from the set of alternatives Heuristic Optimization, 2012 5 .. a more difficult (but still “easy”) one find best (shortest) route from A to B in an edge-weighted graph Heuristic Optimization, 2012 6
.. a harder one find best (shortest) round trip through some cities, aka Traveling Salesman Problem (TSP) Heuristic Optimization, 2012 7 find best (shortest) round trip through some cities, aka Traveling Salesman Problem (TSP) (see also http://www.tsp.gatech.edu//maps/ ) Heuristic Optimization, 2012 8
Practical applications of the TSP Heuristic Optimization, 2012 9 .. and a large instance Heuristic Optimization, 2012 10
A more real-life like problem TSP arises as sub-problem, e.g., in vehicle routing problems (VRPs) Customers Depot Heuristic Optimization, 2012 11 vehicle routes Customers Depot Heuristic Optimization, 2012 12
◮ realistic problems can involve many complicating details ◮ examples in VRP case are ◮ time windows, access restrictions, priorities, split delivery, . . . ◮ capacity restrictions, different costs of vehicles, . . . ◮ working time restrictions, breaks, . . . ◮ stochastic travel times or demands, incoming new requests, . . . ◮ in lecture: focus on simplified models of (real-life) problems ◮ useful for illustrating algorithmic principles ◮ they are “hard” and capture essence of more complex problems ◮ are treated in research to yield more general insights Heuristic Optimization, 2012 13 Solving (combinatorial) optimization problems ◮ systematic enumeration ◮ problem specific, dedicated algorithms ◮ generic methods for exact optimization ◮ heuristic methods Heuristic Optimization, 2012 14
Heuristic methods Heuristic methods intend to compute efficiently, good solutions to a problem with no guarantee of optimality ◮ range from rather simple to quite sophisticated approaches ◮ inspiration often from ◮ human problem solving ◮ rules of thumb, common sense rules ◮ design of techniques based on problem-solving experience ◮ natural processes ◮ evolution, swarm behaviors, annealing, . . . ◮ usually used when there is no other method to solve the problem under given time or space constraints ◮ often simpler to implement / develop than other methods Heuristic Optimization, 2012 15 Heuristic methods are the method of choice for solving many computationally hard problems. Recent Progress & Successes: ◮ Ability of solving hard combinatorial problems has increased significantly ◮ Solution of large travelling salesman problems ◮ Solution of large graph coloring problems ◮ Excellent results in many application areas Heuristic Optimization, 2012 16
Goals of this course Provide answers to these questions: ◮ How can heuristic methods be used to solve computationally hard problems? ◮ Which heuristic methods are available and what are their features? ◮ How should heuristic methods be studied and analysed empirically? ◮ How can heuristic algorithms be designed, developed, and implemented? Heuristic Optimization, 2012 17 Contents Basics: ◮ introduction, SLS framework ◮ iterative improvement algorithms ◮ simple SLS methods ◮ hybrid and population-based SLS methods ◮ empirical analysis of SLS algorithms ◮ search space analysis Additional topics: ◮ tuning, algorithm portfolios ◮ complex problem features ◮ SLS methods for continuous optimization Heuristic Optimization, 2012 18
Heuristic Optimization field Appli- cations Operations Computer SLS HO Research Science Statis- tics Heuristic Optimization, 2012 19 Organizational matters ◮ webpages iridia.ulb.ac.be/ ∼ stuetzle/Teaching/HO http://www.sls-book.net/ ◮ lectures and exercises ◮ Monday, 14:00 to 16:00, P.Forum.H (except Mar 12, P.Forum.E) ◮ Wednesday, 10:00 to 12:00, P.OF.2070 (Feb 15, 22), S.C5.130–IRIDIA (Feb 29, Mar 7), P.Forum.B (Mar 14), P.OF.2072 (Rest) ◮ lecture dates (preliminary schedule; check for updates) ◮ February 13, 15, 20, 22 ◮ March 5, 12, 26, 28 ◮ April 16, 23, 25, 30 Heuristic Optimization, 2012 20
◮ exercises and implementation tasks ◮ five exercise sessions ◮ exercise dates (preliminary schedule; check for updates) ◮ Feb 29, Mar 7, 14, April 18, May 2 ◮ two implementation exercises (second builds on first one) ◮ First: Feb 27 with short introductory lecture ◮ Second: March 28 Heuristic Optimization, 2012 21 ◮ evaluation ◮ precondition for passing course: successful completion of the implementation tasks ( ≥ 10 for both) ◮ oral exam at the end of semester (counts 75%) ◮ implementation exercises (counts 25%) ◮ final mark: weighted average of implementation exercises and oral exam ◮ course material, literature ◮ slides ◮ H. H. Hoos and T. St¨ utzle. Stochastic Local Search: Foundations and Applications . Morgan Kaufmann Publishers, 2005. ◮ additional literature will be given during the course Heuristic Optimization, 2012 22
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