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annealing's Introduction

Jacob Xu
C++
to run:
    cd anneal
    make
    ./anneal inputfile 13 -kempe -st
notes:

    the INITPROB parameter may not work well if set too low
        i suspect it to because the initial solution is not good enough
            more details in code comments
        T is set to 10.0 if first trial run has changes/trails > 0.5
    
    binary search was used to search for lowest k that FIXED_K finds
        a hard iteration limit is also set for fixed_k approach
        simulated annealing is run multiple times

    CUTOFF is supposed to be a double/float despite what is specified in the assignment i think
        the johnson part 2 paper sets it to 0.1 for fixed k

    binary search is used to set T based on INITPROB
        it is possible for a solution to be found during these trial runs

    inf looping was observed for some cases of kempe chain and fixed_k
        some simple checks were added to terminate early
            if same cost or same # of changes > 50 times then terminate

    a debug flag at top of anneal.cpp can be set true for more output

    the program was tested on the following
        run_sa("input1.txt"); // sanity benchmarks
        run_sa("input.txt");
        run_sa("input2.txt");
        run_sa("4-Insertions_3.col"); // medium size
        run_sa("2-FullIns_5.col"); // larger size

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