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121 lines
3.7 KiB
121 lines
3.7 KiB
# This file extends some JuMP functions so that decision variables can be safely
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# replaced by (constant) floating point numbers.
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using Printf
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using JuMP
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import JuMP: value, fix, set_name
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function value(x::Float64)
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return x
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end
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function fix(x::Float64, v::Float64; force)
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return abs(x - v) < 1e-6 || error("Value mismatch: $x != $v")
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end
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function set_name(::Number, ::String)
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# nop
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end
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function _init(model::JuMP.Model, key::Symbol)::OrderedDict
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if !(key in keys(object_dictionary(model)))
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model[key] = OrderedDict()
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end
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return model[key]
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end
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function _set_names!(model::JuMP.Model)
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@info "Setting variable and constraint names..."
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time_varnames = @elapsed begin
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_set_names!(object_dictionary(model))
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end
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@info @sprintf("Set names in %.2f seconds", time_varnames)
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end
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function _set_names!(dict::Dict)
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for name in keys(dict)
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dict[name] isa AbstractDict || continue
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for idx in keys(dict[name])
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if dict[name][idx] isa AffExpr
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continue
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end
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idx_str = join(map(string, idx), ",")
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set_name(dict[name][idx], "$name[$idx_str]")
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end
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end
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end
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"""
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_add_pwl_constraints(model, xvar, yvars, xpts, ypts)
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Add piecewise-linear constraints to a JuMP model for multiple y variables.
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Creates constraints y_i = f_i(x) where each f_i is a piecewise-linear function
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defined by the breakpoints (xpts, ypts[:, i]).
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# Arguments
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- `model`: JuMP model
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- `xvar`: The x variable (JuMP variable)
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- `yvars`: Vector of y variables (JuMP variables)
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- `xpts`: Vector of x values for breakpoints (must be in non-decreasing order)
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- `ypts`: Matrix of y values where ypts[i, j] is the y value for the j-th variable
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at the i-th breakpoint
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# Example
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```julia
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@variable(model, y1)
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@variable(model, y2)
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ypts_matrix = [1.5 2.0; 0.0 1.5; 3.0 0.5] # 3 breakpoints, 2 y variables
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_add_pwl_constraints(model, x, [y1, y2], [0.0, 1.0, 2.0], ypts_matrix, name="multiPWL")
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```
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"""
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function _add_pwl_constraints(model, xvar, yvars, xpts, ypts)
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# Input validation
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ypts isa AbstractMatrix || throw(ArgumentError("ypts must be a matrix"))
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length(xpts) == size(ypts, 1) ||
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throw(ArgumentError("xpts length must match number of rows in ypts"))
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length(yvars) == size(ypts, 2) ||
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throw(ArgumentError("Number of y variables must match number of columns in ypts"))
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length(xpts) >= 1 || throw(ArgumentError("At least one breakpoint is required"))
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# Check that xpts is increasing
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for i = 2:length(xpts)
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xpts[i] > xpts[i-1] || throw(ArgumentError("xpts must be in increasing order"))
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end
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n_points = length(xpts)
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n_yvars = length(yvars)
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if n_points == 1
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# Single point case: y_j = ypts[1,j], x = xpts[1]
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@constraint(model, xvar == xpts[1])
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for j = 1:n_yvars
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@constraint(model, yvars[j] == ypts[1, j])
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end
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elseif n_points == 2
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# Two points case: single linear segment for each y variable
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x1, x2 = xpts[1], xpts[2]
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# Linear relationship for each y variable: y_j = y1_j + slope_j * (x-x1)
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for j = 1:n_yvars
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y1, y2 = ypts[1, j], ypts[2, j]
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slope = (y2 - y1) / (x2 - x1)
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@constraint(model, yvars[j] == y1 + slope * (xvar - x1))
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end
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else
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# Multiple segments case (3+ points): use SOS2 formulation
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λ = @variable(model, [1:n_points], lower_bound = 0, upper_bound = 1)
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@constraint(model, λ in SOS2())
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@constraint(model, sum(λ) == 1)
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@constraint(model, xvar == sum(xpts[i] * λ[i] for i = 1:n_points))
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for j = 1:n_yvars
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@constraint(model, yvars[j] == sum(ypts[i, j] * λ[i] for i = 1:n_points))
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end
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end
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return
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end
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