Heuristic Optimization

Transcription

1 Heuristic Optimization Thomas Stützle RDA, CoDE Université Libre de Bruxelles 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 146(?) breweries in Belgium during his one week stay s this feasible? f yes, which route to take? The shortest certainly helps at brewery No. 49 your friend o ers to pay all beers you take on the trip if you solve the following riddle Last week my friends Anne, Carl, Eva, Gustaf and went out for dinner every night, Monday through Friday. missed the meal on Friday because 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, asushibar,apizzeria,agreekrestaurant,andthebrauhaus.evatook 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,

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, 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 di erent 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,

3 .. an easy one find the best (most valuable) element from the set of alternatives Heuristic Optimization, a more di cult (but still easy ) one find best (shortest) route from A to B in an edge-weighted graph Heuristic Optimization,

4 .. a harder one find best (shortest) round trip through some cities, aka Traveling Salesman Problem (TSP) Heuristic Optimization, find best (shortest) round trip through some cities, aka Traveling Salesman Problem (TSP) (see also Heuristic Optimization,

5 Practical applications of the TSP Heuristic Optimization, and a large instance Heuristic Optimization,

6 A more real-life like problem TSP arises as sub-problem, e.g., in vehicle routing problems (VRPs) Heuristic Optimization, realistic problems can involve many complicating details examples in VRP case are time windows, access restrictions, priorities, split delivery,... capacity restrictions, di erent 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,

7 Optimization problems arise everywhere! Most such problems are computationally very hard (NP-hard!) Heuristic Optimization, Solving (combinatorial) optimization problems systematic enumeration problem specific, dedicated algorithms generic methods for exact optimization heuristic methods Heuristic Optimization,

8 Heuristic methods Heuristic methods intend to compute e ciently, 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, Goals of this course Provide answers to these questions: Which heuristic methods are available and what are their features? How can heuristic methods be used to solve computationally hard problems? How should heuristic methods be studied and analysed empirically? How can heuristic algorithms be designed, developed, and implemented? Heuristic Optimization,

9 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 configuration complex problem features Heuristic Optimization, Heuristic Optimization field Operations Research SLS HO Computer Science Applications Statistics Heuristic Optimization,

10 Organizational matters webpages iridia.ulb.ac.be/~stuetzle/teaching/ho lectures and exercises Wednesday, 08:10 to 09:40 and 10:00 to 11:30 in RDA s seminar room (C.5.130) lecture dates (preliminary schedule; check for updates) February 28 (two) March 7 (one), 14 (one), 21 (one), 28 (one) April 18 (one), 25 (two) May 2 (two), 9 (one) Heuristic Optimization, exercises and implementation tasks five exercise sessions exercise dates (preliminary schedule; check for updates) Mar 7, 21, 28, April 25, May 9 two implementation exercises (second builds on first one) First: March 14 with short introductory lecture Second: April 18 Heuristic Optimization,

11 evaluation precondition for passing course: successful completion of both implementation tasks ( 10 for each; if necessary corrections) oral exam at the end of semester (counts 60%) implementation exercises (counts 40%) final mark: weighted average of implementation exercises and oral exam (0.4 mark impl +0.6 mark oral ) course material, literature slides H. H. Hoos and T. Stützle. Stochastic Local Search: Foundations and Applications. Morgan Kaufmann Publishers, additional literature will be given during the course Heuristic Optimization,