How do I parse optional arguments in a bash script if no order is given?

This article shows two different ways - shift and getopts (and discusses the advantages and disadvantages of the two approaches).

With shift your script looks at $1, decides what action to take, and then executes shift, moving $2 to $1, $3 to $2, etc.

For example:

while :; do
    case $1 in
        -a|--flag1) flag1="SET"            
        ;;
        -b|--flag2) flag2="SET"            
        ;;
        -c|--optflag1) optflag1="SET"            
        ;;
        -d|--optflag2) optflag2="SET"            
        ;;
        -e|--optflag3) optflag3="SET"            
        ;;
        *) break
    esac
    shift
done

With getopts you define the (short) options in the while expression:

while getopts abcde opt; do
    case $opt in
        a) flag1="SET"
        ;;
        b) flag2="SET"
        ;;
        c) optflag1="SET"
        ;;
        d) optflag2="SET"
        ;;
        e) optflag3="SET"
        ;;
    esac
done

Obviously, these are just code-snippets, and I've left out validation - checking that the mandatory args flag1 and flag2 are set, etc.

Which approach you use is to some extent a matter of taste - how portable you want your script to be, whether you can live with short (POSIX) options only or whether you want long (GNU) options, etc.

use an array.

#!/bin/bash

args=( --flag1 "$1" --flag2 "$2" )
[  "x$3" = xFALSE ] ||  args+=( --optflag1 "$3" )
[  "x$4" = xFALSE ] ||  args+=( --optflag2 "$4" )
[  "x$5" = xFALSE ] ||  args+=( --optflag3 "$5" )
[  "x$6" = xFALSE ] ||  args+=( --optflag4 "$6" )
[  "x$7" = xFALSE ] ||  args+=( --optflag5 "$7" )

program_name "${args[@]}"

this will handle arguments with spaces in them correctly.

[edit] I was using the roughly eqivalent syntax args=( "${args[@]}" --optflag1 "$3" ) but G-Man suggested a better way.