Copyright R. Weber Search in Problem Solving ISYS 370 Dr. R. Weber
Copyright R. Weber General Search Algorithm identify initial state expand (generate new states) choose option test goal function expand until goal not attained/no more states to expand
Copyright R. Weber General Search Algorithm search-tree := initial-node loop if there are no leaf nodes then return FAIL else choose a leaf node X according to "strategy" if X is a goal node then return X else expand X add the resulting new leaf node(s) to search-tree end loop
Copyright R. Weber Search strategies
Uninformed search strategies breadth-first search uniform cost search depth-first search depth-limited search iterative deepening search bidirectional search Informed /heuristic strategies best-first search A* Heuristic functions memory bounded search simulated annealing Hill-climbing
Copyright R. Weber Breadth-first search all nodes at depth d are expanded before the nodes at depth d+1 optimal and complete if there are more than one, it will find the shallowest planning puzzles; large memory requirements
Copyright R. Weber Depth-first search expands the deepest node to the deepest level of a tree only expands nodes at shallower levels after reaching the end it does not guarantee a solution (neither complete or optimal) less memory requirements may be faster than breadth-first, but it may get stuck exploring long (potentially infinite) paths, when there is a solution path of less steps
Copyright R. Weber Uniform cost search expands the lowest-cost node to find the best solution it requires that all operators have positive costs route-finding
Copyright R. Weber depth-limited search Improves from depth-first imposes a bound on the maximum depth of a path guarantees that a solution is found if it exists within the length of the chosen depth Not guaranteed to be the optimal iterative deepening search tries to bound the search iteratively (depth 1, 2, 3, till finds a solution) it is optimal and complete, like breadth-first search, but has memory requirements of depth-first search.
Copyright R. Weber bidirectional search start searching from the origin and from the goal and stop when searches meet
Copyright R. Weber Example problems toy problems –used to test search algorithms real world problems –used to solve real problems
Copyright R. Weber Toy problems
Copyright R. Weber The 8-puzzle (Russel&Norvig)
Copyright R. Weber Cryptarithmetic (Russel&Norvig)
Copyright R. Weber Real world problems
Copyright R. Weber Applications of route finding Routing in computer networks Automated travel advisory systems Airline travel planning Garbage collection/cleaning trucks Food/document delivery Does this mean that search is the only method to perform route planning??
Copyright R. Weber Traveling Salesperson Problems is a category of problems each city has to be visited once goal is to find the shortest tour
Copyright R. Weber Exams in university Nurses in hospitals Experts in call centers Crews in different organizations Scheduling NASA satellites NFL games Scheduling
Copyright R. Weber VLSI layout Very large scale integration Design of silicon chip Define the position and connections of a million gates in a chip Tasks: cell layout, channel routing Goal is to min area & connection length
Copyright R. Weber Robot navigation Generalization of route finding problem Any route can be chosen in a continuous space Possible actions and states in a continuous space are infinite The more actions a robot can perform the more dimensions are needed to describe states and actions To identify the result of an action, a robot must use vision
Copyright R. Weber Assembly sequencing Many industries use automatic assembly of objects Find an order to assemble parts of an object Find an order to submit parts to a given process Design for autoclave layout Layout Design
Copyright R. Weber General route finding algorithm 1.identify initial state as origin 2.expand to all possible locations 3.choose location with smallest cost/fastest route/favor highways 4.test goal function, is it the destiny? 5.if yes, return location else, return to 2
Copyright R. Weber General puzzles algorithm 1.identify initial state as origin 2.expand to all possible locations 3.the blank space changes place with tile on its right 4.test goal function, is it the destiny? 5.if yes, return configuration else, return to 2
Copyright R. Weber Constraint Satisfaction Problem 1.Initial is given by values of variables 2.Expand to all possible values 3.Variables change values 4.Do the variables’ values respect constraints? 5.if yes, return values else, return to 2 –Another class of problems –Design and scheduling problems –Algorithms designed specifically for CSP perform better than general ones
Copyright R. Weber Search strategies When do you solve a problem using a search strategy? When there is an algorithm to solve it when: it is guaranteed to find a solution when it finds a solution in a timely manner when the memory requirements are reasonable when it can find the best solution or at least one of the best sometimes, one can combine searches to improve the quality of a solution