Solving multiobjective optimization instances from literature using Modolib.jl:

using Modolib

Biobjective assignment problems:

instance, true_frontier = read_boap_hadi(10)

@time solutions = fpbh(instance, lp_solver=ClpSolver(), timelimit=10.0)

nondominated_frontier = wrap_sols_into_array(solutions)

Computing quality of the frontier w.r.t. true frontier without normalization

hg, c, mc, ac, u = compute_quality_of_apprx_frontier(nondominated_frontier, true_frontier)
println("
    Hypervolume Gap = $hg % 
    Cardinality = $c % 
    Maximum Coverage = $mc 
    Average Coverage = $ac 
    Uniformity = $u")

Computing quality of the frontier w.r.t. true frontier with normalization

hg, c, mc, ac, u = compute_quality_of_norm_apprx_frontier(nondominated_frontier, true_frontier)
println("
    Hypervolume Gap = $hg % 
    Cardinality = $c % 
    Maximum Coverage = $mc 
    Average Coverage = $ac 
    Uniformity = $u")

Comparing the nondominated frontier of FPBH with the true frontier

plt_discrete_non_dom_frntr([true_frontier, nondominated_frontier], ["True Frontier", "FPBH(Clp)"], false, "Plot2.png")

Biobjective 1-D knapsack problems:

instance, true_frontier = read_bokp_xavier1("2KP150-1A")

@time solutions = fpbh(instance, lp_solver=ClpSolver(), timelimit=10.0)

nondominated_frontier = wrap_sols_into_array(solutions)

Comparing the nondominated frontier of FPBH with the true frontier

plt_discrete_non_dom_frntr([true_frontier, nondominated_frontier], ["True Frontier", "FPBH(Clp)"], false, "Plot3.png")

Biobjective 2-D knapsack problems:

instance, true_frontier = read_bokp_hadi(1)

@time solutions = fpbh(instance, lp_solver=ClpSolver(), timelimit=10.0)

nondominated_frontier = wrap_sols_into_array(solutions)

Comparing the nondominated frontier of FPBH with the true frontier

plt_discrete_non_dom_frntr([true_frontier, nondominated_frontier], ["True Frontier", "FPBH(Clp)"], false, "Plot4.png")

Biobjective set covering problems:

instance, true_frontier = read_boscp_xavier(100, 10, "a")

@time solutions = fpbh(instance, lp_solver=ClpSolver(), timelimit=10.0)

nondominated_frontier = wrap_sols_into_array(solutions)

Comparing the nondominated frontier of FPBH with the true frontier

plt_discrete_non_dom_frntr([true_frontier, nondominated_frontier], ["True Frontier", "FPBH(Clp)"], false, "Plot5.png")

Biobjective set packing problems:

instance, true_frontier = read_bospp_xavier("2mis100_300A")

@time solutions = fpbh(instance, lp_solver=ClpSolver(), timelimit=10.0)

nondominated_frontier = wrap_sols_into_array(solutions)

Comparing the nondominated frontier of FPBH with the true frontier

plt_discrete_non_dom_frntr([true_frontier, nondominated_frontier], ["True Frontier", "FPBH(Clp)"], false, "Plot6.png")

Biobjective mixed binary problems:

instance, true_frontier = read_bomip_hadi(6)

@time solutions = fpbh(instance, lp_solver=ClpSolver(), timelimit=10.0)

nondominated_frontier = wrap_sols_into_array(solutions)

Quality of the frontier w.r.t. true frontier without normalization

hg, c, mc, ac, u = compute_quality_of_apprx_frontier(nondominated_frontier, true_frontier, true)
println("
    Hypervolume Gap = $hg % 
    Cardinality = $c % 
    Maximum Coverage = $mc 
    Average Coverage = $ac 
    Uniformity = $u")

Quality of the frontier w.r.t. true frontier with normalization

hg, c, mc, ac, u = compute_quality_of_norm_apprx_frontier(nondominated_frontier, true_frontier, true)
println("
    Hypervolume Gap = $hg % 
    Cardinality = $c % 
    Maximum Coverage = $mc 
    Average Coverage = $ac 
    Uniformity = $u")

Comparing the nondominated frontier of FPBH with the true frontier

plt_non_dom_frntr_bomip([true_frontier, nondominated_frontier], ["True Frontier", "FPBH(Clp)"], "Plot7.png")

Biobjective uncapacitated facility location problems:

instance, true_frontier = read_bouflp_hadi(12)

@time solutions = fpbh(instance, lp_solver=ClpSolver(), timelimit=10.0)

nondominated_frontier = wrap_sols_into_array(solutions)

Comparing the nondominated frontier of FPBH with the true frontier

plt_non_dom_frntr_bomip([true_frontier, nondominated_frontier], ["True Frontier", "FPBH(Clp)"], "Plot8.png")

Triobjective assignment problems:

instance, true_frontier = read_moap_kirlik(3, 5, 1)

@time solutions = fpbh(instance, lp_solver=ClpSolver(), timelimit=10.0)

nondominated_frontier = wrap_sols_into_array(solutions)

Computing quality of the frontier w.r.t. true frontier without normalization

hg, c, mc, ac, u = compute_quality_of_apprx_frontier(nondominated_frontier, true_frontier)
println("
    Hypervolume Gap = $hg % 
    Cardinality = $c % 
    Maximum Coverage = $mc 
    Average Coverage = $ac 
    Uniformity = $u")

Computing quality of the frontier w.r.t. true frontier with normalization

hg, c, mc, ac, u = compute_quality_of_norm_apprx_frontier(nondominated_frontier, true_frontier)
println("
    Hypervolume Gap = $hg % 
    Cardinality = $c % 
    Maximum Coverage = $mc 
    Average Coverage = $ac 
    Uniformity = $u")

Comparing the nondominated frontier of FPBH with the true frontier

plt_discrete_non_dom_frntr([true_frontier, nondominated_frontier], ["True Frontier", "FPBH(Clp)"],  false, "Plot9.png")

Triobjective 1-D knapsack problems:

instance, true_frontier = read_mokp_kirlik(3, 10, 1)

@time solutions = fpbh(instance, lp_solver=ClpSolver(), timelimit=10.0)

nondominated_frontier = wrap_sols_into_array(solutions)

Comparing the nondominated frontier of FPBH with the true frontier

plt_discrete_non_dom_frntr([true_frontier, nondominated_frontier], ["True Frontier", "FPBH(Clp)"], false, "Plot10.png")

Triobjective mixed binary problems:

instance, true_frontier = read_mombp_aritra(3, 320, 1)

@time solutions = fpbh(instance, lp_solver=ClpSolver(), timelimit=10.0)

nondominated_frontier = wrap_sols_into_array(solutions)

Comparing the nondominated frontier of FPBH with the reference frontier

plt_discrete_non_dom_frntr([true_frontier, nondominated_frontier], ["True Frontier", "FPBH(Clp)"], false, "Plot11.png")