Assignment1: Heuristic Search

Second Draft

Due: 10/5/04 in class; problem 5 is due 10/16/04, 11p using electronic submission; submit your report and other material to Yan Wang prior to the deadline! Submit a hardcopy of your report and other materials in the class on Tu., October 19, 2004.

Approximate Problem Weights: 1:** 2:** 3:** 4:* 5:********** 6:*

(a) Formulate this problem as a state-space search problem Give a precise definition of a state, the start state, the goal state or goal condition, and the operators. Operators should be specified as "schemas" that indicate for a given state, when the operator is legal (i.e., a set of constraints on when the operator can be applied to an arbitrary state) and the description of the successor state after the operator is applied. In other words, each operator should be specified in a way that it would easily implemented in a program to solve this problem.

(b) Show the State Space

Draw the complete state-space graph that includes all nodes (and legal directed arcs
connecting these nodes) for this problem. Inside each node show the state description, and
label each arc with its associated operator. Highlight a path that gives a solution to the
problem.

(i) For each of the search strategies listed below,
(a) indicate which goal state is
reached if any, (b) list, in order, the states expanded,
and (c) show the final contents of the OPEN and CLOSED lists. (Recall that a
state is *expanded* when it is *removed* from the OPEN list.)
When all else is equal, nodes should be expanded in alphabetical order.

- breadth-first

- depth-first

*best-first*(using*f = h*)

*A**(using*f = g + h*)

*RBFS (using f=g+h)***--- due to the fact that RBFS is a recursive algorithm give the search tree as your answer for RBFS!***SMA* (using f=g+h and limiting the open-list to just 3 elements)*

OPEN = { startNode } // Nodes under consideration. CLOSED = { } // Nodes we're done with. while OPEN is not empty { remove an item from OPEN based on search strategy used - call it X if goalState?(X) return the solution found otherwise // Expand node X. { 1) add X to CLOSED 2) generate the immediate neighbors (ie, children of X) 3) eliminate those children already in OPEN or CLOSED 4) add REMAINING children to OPEN } } return FAILURE // Failed if OPEN exhausted without a goal being found.The following is the basic outline of the search strategy used for the A* and SMA* search algorithms.

OPEN = { startNode } // Nodes under consideration. CLOSED = { } // Nodes we're done with. while OPEN is not empty { remove an item from OPEN based on search strategy used - call it X if goalState?(X) return the solution found otherwise // Expand node X. { 1) add X to CLOSED 2) generate the immediate neighbors (ie, children of X) 3) add all children to OPEN } } return FAILURE // Failed if OPEN exhausted without a goal being found.

Remark: RBFS is a recursive algorithm and does not use open- and close-lists in the way the other five algorithm do.

(b) Outline an "informed", depth-first, backtracking-style approach to solve TSP. Propose, heuristics, if helpful to enhance the performance of the algorithm. Explain your approach!

(c) Either outline how evolutionary computing could be used to solve TSP or propose a third algorithm on your own to solve TSP. Either explain the proposed EC-approach or the "third" algorithm you propose.

(d) Implement 2 of the algorithms you proposed in steps a-c.

(e) Evaluate the performance of the two algorithm using a Benchmark of TSP-problems involving 3 different distance functions.

(f) Enhance the two algorithms based on the running of the benchmark, if feasible.

(g) Rerun the modified algorithms for the benchmark.

(f) Write a 4-6 page report that summarizes your solutions and results with respect to problems a-g. Also submit the source code of your program (no documentation required) and be prepared to demo the two programs you wrote.

(v1) enumerating leaf nodes from left to right

(v2) enumerating leaf nodes from right to left

Will versions v1 and v2 always select the same move, if there is a single best move? Will version v1 and v2 always have the same runtime? Give reasons for your answers!

(b) Most game-playing programs do not save search results from one move to the next. Instead, they usually start completely over whenever it is the machine's turn to move. Why?