Efficient modelling via Gurobi

Question

I would like to model the following constraint set in gurobi-java.

\begin{equation} t^n_{ij} \geq t^n_{(i-1)j}+S_{(i-1)j} - (1 - \sum_{\substack{m \in \mathcal{M} \\ G_{ijm} = 1}}\sum_{k \in \mathcal{K}} x^n_{ijmk}) \times \Omega \hspace{1cm} \forall j \in \mathcal{J}; i \in \mathcal{I}_j/1; n \in \mathcal{N}_j \end{equation}

where $t^n_{ij} \in \mathbb{R}_{\geq0}$ and $x^n_{ijmk} \in \{0,1\}$ are decision variables. I have modeled this constraint set in gurobi-java as follows:

GRBVar[][][][][] x = new GRBVar[i_idx][j_idx][n_idx][m_idx][k_idx];
for (int j : j_set) {
    for (int i : i_set[j]) {
        for (int n : n_set[j]) {
            for (int m : m_set) {
                if (G[i][j][m] == true) {
                    for (int k : k_set) {
                        x[i][j][n][m][k] = model.addVar(0, 1, 1, GRB.BINARY,
                                i + "_" + j + "_" + n + "_" + m + "_" + k);
                    }
                }
            }
        }
    }
}

GRBVar[][][] t = new GRBVar[i_idx][j_idx][n_idx];
for (int j : j_set) {
    for (int i : i_set[j]) {
        for (int n : n_set[j]) {
            t[i][j][n] = model.addVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS,
                    i + "_" + j + "_" + n);
        }
    }
}

GRBVar[][][] auxvar1 = new GRBVar[i_idx][j_idx][n_idx];
for (int j : j_set) {
    for (int i : i_set[j]) {
        for (int n : n_set[j]) {
            auxvar1[i][j][n] = model.addVar(0, 1, 1, GRB.BINARY,
                    i + "_" + j + "_" + n);

            GRBLinExpr lhs = new GRBLinExpr();
            GRBLinExpr rhs = new GRBLinExpr();

            lhs.addTerm(1, auxvar1[i][j][n]);
            rhs.addConstant(1);
            for (int m : m_set) {
                if (G[i][j][m] == true) {
                    for (int k : k_set) {
                        rhs.addTerm(-1, x[i][j][n][m][k]);
                    }
                }
            }

            model.addConstr(lhs, GRB.EQUAL, rhs, "auxiliary_" + i + "_" + j + "_" + n);
        }
    }
}


for (int j : j_set) {
    for (int i = 1; i < i_set[j].length; i++) {
        for (int n : n_set[j]) {
            GRBLinExpr lhs = new GRBLinExpr();
            GRBLinExpr rhs = new GRBLinExpr();

            lhs.addTerm(1, t[i][j][n]);

            rhs.addTerm(1, t[i-1][j][n]);
            rhs.addConstant(S[j][i-1]);
            rhs.addTerm(-Omega, auxvar1[i][j][n]);

            model.addConstr(lhs, GRB.GREATER_EQUAL, rhs, "time_flow_" + i + "_" + j + "_" + n);
        }
    }
}

In comparison to docplex-python, it is much less readable and requires much more lines of code.

mdl.add_constraints(t[i, j ,n] >= t[i-1, j, n] + S[i-1, j] - (1 - mdl.sum(x[i, j, n, m, k] for m in m_set if G[i, j, m] == 1 for k in k_set) * Omega for j in j_set for i in i_set[j] if i > 0 for n in n_set[j]))

I am new to gurobi-java. Are there any better ways to model this constraint set.

Answer 1

Probably not the answer you want, but Gurobi has a very nice Python interface. I'd be surprised if there was anything you liked from docplex that you wouldn't find to be at least as good or better in gurobipy.

When porting Python code to Java code, as a rule, there will probably a loss in readability/brevity. That's why Python is far more popular for data science, and now, for even general purpose programming.