User mip start did not produce a new incumbent solution

When working with Julia, it is common to encounter situations where the user mip start does not produce a new incumbent solution. This can be frustrating, but there are several ways to solve this issue. In this article, we will explore three different approaches to tackle this problem.

Approach 1: Adjusting MIP Start Parameters

One possible solution is to adjust the MIP start parameters. By tweaking these parameters, we can potentially improve the chances of obtaining a new incumbent solution. Here is an example of how to do this:

using JuMP, Gurobi

model = Model(Gurobi.Optimizer)
@variable(model, x, Bin)

# Set MIP start parameters
set_optimizer_attribute(model, "MIPGap", 0.01)
set_optimizer_attribute(model, "MIPStart", 1, [x], [0.5])

# Solve the model
optimize!(model)

# Check if a new incumbent solution was found
if termination_status(model) == MOI.INFEASIBLE_OR_UNBOUNDED
    println("No new incumbent solution found.")
else
    println("New incumbent solution found.")
end

This approach involves adjusting the MIPGap parameter, which controls the tolerance for finding new incumbent solutions. Additionally, we set the MIPStart parameter to provide an initial solution for the solver to start from. By experimenting with different values for these parameters, you can potentially improve the chances of obtaining a new incumbent solution.

Approach 2: Modifying the Model Constraints

Another approach is to modify the model constraints to encourage the solver to find a new incumbent solution. By adding or adjusting constraints, we can guide the solver towards exploring different regions of the solution space. Here is an example:

using JuMP, Gurobi

model = Model(Gurobi.Optimizer)
@variable(model, x, Bin)

# Add additional constraints
@constraint(model, x <= 0.5)

# Solve the model
optimize!(model)

# Check if a new incumbent solution was found
if termination_status(model) == MOI.INFEASIBLE_OR_UNBOUNDED
    println("No new incumbent solution found.")
else
    println("New incumbent solution found.")
end

In this approach, we add an additional constraint to the model to restrict the possible values of the decision variable. By doing so, we force the solver to explore different regions of the solution space, potentially leading to a new incumbent solution.

Approach 3: Adjusting Solver Parameters

The third approach involves adjusting the solver parameters to improve the chances of finding a new incumbent solution. Solver parameters control various aspects of the optimization process, such as the search strategy and the level of exploration. Here is an example:

using JuMP, Gurobi

model = Model(Gurobi.Optimizer)
@variable(model, x, Bin)

# Set solver parameters
set_optimizer_attribute(model, "Heuristics", 0.5)
set_optimizer_attribute(model, "MIPFocus", 2)

# Solve the model
optimize!(model)

# Check if a new incumbent solution was found
if termination_status(model) == MOI.INFEASIBLE_OR_UNBOUNDED
    println("No new incumbent solution found.")
else
    println("New incumbent solution found.")
end

In this approach, we adjust the Heuristics and MIPFocus parameters to control the solver's search strategy and level of exploration. By experimenting with different values for these parameters, you can potentially improve the chances of finding a new incumbent solution.

After exploring these three approaches, it is difficult to determine which one is the best option. The effectiveness of each approach may vary depending on the specific problem and the characteristics of the model. It is recommended to try different combinations of these approaches and evaluate their performance on your specific problem to determine the most effective solution.