如何在 OR 工具中将惩罚性覆盖约束从仅限超额更改为目标？

Question

我正在 OR Tools (Python) 上的 CP-Sat 中开发调度程序，并且我正在尝试扩展 这个约束

// Cover constraints
    foreach (int s in Range(1, numShifts))
    {
        foreach (int w in Range(numWeeks))
        {
            foreach (int d in Range(7))
            {
                var works = new BoolVar[numEmployees];
                foreach (int e in Range(numEmployees))
                {
                    works[e] = work[e, s, w * 7 + d];
                }

                // Ignore off shift
                var minDemand = weeklyCoverDemands[d][s - 1];
                var worked = model.NewIntVar(minDemand, numEmployees, "");
                model.Add(LinearExpr.Sum(works) == worked);

                var overPenalty = excessCoverPenalties[s - 1];
                if (overPenalty > 0)
                {
                    var name = $"excess_demand(shift={s}, week={w}, day={d}";
                    var excess = model.NewIntVar(0, numEmployees - minDemand, name);
                    model.Add(excess == worked - minDemand);
                    obj.AddTerm(excess, overPenalty);
                }
            }
        }

据我了解，每天轮班次数过多会受到惩罚。

我如何扩展/编辑它，以便它尝试达到目标（

minDemand

）？换句话说：我如何惩罚过度和不足？理想情况下，采用某种成本乘法，因此距离目标越远，成本就越高。 我所有的努力都以“不可行”或“未知”状态结束。

Answer 1

它在这里实现：https://github.com/google/or-tools/blob/d37317b17ca16658451cafe05085fc22c39dd6c8/examples/python/shift_scheduling_sat.py#L131

    cost_variables = []
    cost_coefficients = []
    sum_var = model.NewIntVar(hard_min, hard_max, "")
    # This adds the hard constraints on the sum.
    model.Add(sum_var == sum(works))

    # Penalize sums below the soft_min target.
    if soft_min > hard_min and min_cost > 0:
        delta = model.NewIntVar(-len(works), len(works), "")
        model.Add(delta == soft_min - sum_var)
        # TODO(user): Compare efficiency with only excess >= soft_min - sum_var.
        excess = model.NewIntVar(0, 7, prefix + ": under_sum")
        model.AddMaxEquality(excess, [delta, 0])
        cost_variables.append(excess)
        cost_coefficients.append(min_cost)

    # Penalize sums above the soft_max target.
    if soft_max < hard_max and max_cost > 0:
        delta = model.NewIntVar(-7, 7, "")
        model.Add(delta == sum_var - soft_max)
        excess = model.NewIntVar(0, 7, prefix + ": over_sum")
        model.AddMaxEquality(excess, [delta, 0])
        cost_variables.append(excess)
        cost_coefficients.append(max_cost)