First working version of LDSDA

[ZedongPeng]

Fixes # .

Summary/Motivation:

Succeed with small batch example.

Log:

Starting GDPopt version 22.5.13 using LDSDA algorithm
iterlim: None
time_limit: None
tee: true
logger: <Logger pyomo.contrib.gdpopt (INFO)>
mip_solver: gurobi
mip_solver_args:
nlp_solver: ipopt
nlp_solver_args:
minlp_solver: gams
minlp_solver_args:
local_minlp_solver: bonmin
local_minlp_solver_args:
small_dual_tolerance: 1.0e-08
integer_tolerance: 1.0e-05
constraint_tolerance: 1.0e-06
variable_tolerance: 1.0e-08
subproblem_initialization_method: <function restore_vars_to_original_values at 0x1049b1ab0>
call_before_subproblem_solve: !!python/name:pyomo.contrib.gdpopt.util._DoNothing ''
call_after_subproblem_solve: !!python/name:pyomo.contrib.gdpopt.util._DoNothing ''
call_after_subproblem_feasible: !!python/name:pyomo.contrib.gdpopt.util._DoNothing ''
force_subproblem_nlp: false
subproblem_presolve: true
tighten_nlp_var_bounds: false
round_discrete_vars: true
max_fbbt_iterations: 3
bound_tolerance: 1.0e-06
direction_norm: L2
starting_point: [3, 3, 3]
logical_constraint_list: ['lim[mixer]', 'lim[reactor]', 'lim[centrifuge]']

If you use this software, you may cite the following:
            - Implementation:
            Chen, Q; Johnson, ES; Bernal, DE; Valentin, R; Kale, S;
            Bates, J; Siirola, JD; Grossmann, IE.
            Pyomo.GDP: an ecosystem for logic based modeling and optimization
            development.
            Optimization and Engineering, 2021.

- LDSDA algorithm:
        Bernal DE, Ovalle D, Liñán DA, Ricardez-Sandoval LA, Gómez JM, Grossmann IE.
        Process Superstructure Optimization through Discrete Steepest Descent Optimization: a GDP Analysis and Applications in Process Intensification.
        Computer Aided Chemical Engineering 2022 Jan 1 (Vol. 49, pp. 1279-1284). Elsevier.
        https://doi.org/10.1016/B978-0-323-85159-6.50213-X
Original model has 34 constraints (1 nonlinear) and 9 disjunctions, with 37 variables, of which 18 are binary, 0 are integer, and 19 are continuous.
=============================================================================================
Iteration |   Search Type   | Lower Bound | Upper Bound |   Gap    | Time(s)

        0     Initial point          -inf   239960.01118       inf%      0.39  *
        1   Neighbor search          -inf   239960.01118       inf%      0.60  
        1   Neighbor search          -inf   239960.01118       inf%      0.81  
        1   Neighbor search          -inf   210580.83835       inf%      1.02  *
        1       Line search          -inf   181201.66551       inf%      1.25  *
Line search finished.
        2   Neighbor search          -inf   178545.19584       inf%      1.48  *
        2   Neighbor search          -inf   178545.19584       inf%      1.69  
Line search finished.
        3   Neighbor search          -inf   167427.65710       inf%      2.14  *
        3   Neighbor search          -inf   167427.65710       inf%      2.36  
Line search finished.
        4   Neighbor search          -inf   167427.65710       inf%      3.04  
Optimal solution (2, 2, 1)

Solved in 4 iterations and 3.04212 seconds
Optimal objective value 167427.6570965372
Relative optimality gap inf%

Problem: 
- Name: unknown
  Lower bound: -inf
  Upper bound: 167427.6570965372
  Number of objectives: 1
  Number of constraints: 34
  Number of variables: 37
  Number of binary variables: 18
  Number of integer variables: 0
  Number of continuous variables: 19
  Number of nonzeros: None
  Sense: 1
  Number of disjunctions: 9
Solver: 
- Name: GDPopt (22, 5, 13) - LDSDA
  Status: ok
  User time: 3.042007731000922
  Wallclock time: 3.042007731000922
  Termination condition: unknown
  Iterations: 4
  Timing: main_timer_start_time: 13558.79707101
total: 3.042007731000922

Changes proposed in this PR:

Legal Acknowledgement

By contributing to this software project, I have read the contribution guide and agree to the following terms and conditions for my contribution:

1. I agree my contributions are submitted under the BSD license.
2. I represent I am authorized to make the contributions and grant the license. If my employer has rights to intellectual property that includes these contributions, I represent that I have received permission to make contributions and grant the required license on behalf of that employer.

[ZedongPeng]

Updates:

1. Add reformulation summary into the log.
2. Report the value of external variables in each step.

Starting GDPopt version 22.5.13 using LDSDA algorithm
iterlim: None
time_limit: None
tee: true
logger: <Logger pyomo.contrib.gdpopt (INFO)>
mip_solver: gurobi
mip_solver_args:
nlp_solver: ipopt
nlp_solver_args:
minlp_solver: gams
minlp_solver_args:
local_minlp_solver: bonmin
local_minlp_solver_args:
small_dual_tolerance: 1.0e-08
integer_tolerance: 1.0e-05
constraint_tolerance: 1.0e-06
variable_tolerance: 1.0e-08
subproblem_initialization_method: <function restore_vars_to_original_values at 0x101f85ab0>
call_before_subproblem_solve: !!python/name:pyomo.contrib.gdpopt.util._DoNothing ''
call_after_subproblem_solve: !!python/name:pyomo.contrib.gdpopt.util._DoNothing ''
call_after_subproblem_feasible: !!python/name:pyomo.contrib.gdpopt.util._DoNothing ''
force_subproblem_nlp: false
subproblem_presolve: true
tighten_nlp_var_bounds: false
round_discrete_vars: true
max_fbbt_iterations: 3
bound_tolerance: 1.0e-06
direction_norm: L2
starting_point: [3, 3, 3]
logical_constraint_list: ['lim[mixer]', 'lim[reactor]', 'lim[centrifuge]']

If you use this software, you may cite the following:
            - Implementation:
            Chen, Q; Johnson, ES; Bernal, DE; Valentin, R; Kale, S;
            Bates, J; Siirola, JD; Grossmann, IE.
            Pyomo.GDP: an ecosystem for logic based modeling and optimization
            development.
            Optimization and Engineering, 2021.

- LDSDA algorithm:
        Bernal DE, Ovalle D, Liñán DA, Ricardez-Sandoval LA, Gómez JM, Grossmann IE.
        Process Superstructure Optimization through Discrete Steepest Descent Optimization: a GDP Analysis and Applications in Process Intensification.
        Computer Aided Chemical Engineering 2022 Jan 1 (Vol. 49, pp. 1279-1284). Elsevier.
        https://doi.org/10.1016/B978-0-323-85159-6.50213-X
Original model has 34 constraints (1 nonlinear) and 9 disjunctions, with 37 variables, of which 18 are binary, 0 are integer, and 19 are continuous.
Reformulation Summary:
┌─────────────────┬──────┬──────┬───────────────────────────────────────────────────────────┐
│   Ext Var Index │   LB │   UB │ Associated Boolean Vars                                   │
├─────────────────┼──────┼──────┼───────────────────────────────────────────────────────────┤
│               0 │    1 │    3 │ ['Y[1,mixer]', 'Y[2,mixer]', 'Y[3,mixer]']                │
│               1 │    1 │    3 │ ['Y[1,reactor]', 'Y[2,reactor]', 'Y[3,reactor]']          │
│               2 │    1 │    3 │ ['Y[1,centrifuge]', 'Y[2,centrifuge]', 'Y[3,centrifuge]'] │
└─────────────────┴──────┴──────┴───────────────────────────────────────────────────────────┘
=====================================================================================================
Iteration |   Search Type   |  External Variables  | Lower Bound | Upper Bound |   Gap    | Time(s)

        0     Initial point              (3, 3, 3)          -inf   239960.01118       inf%      0.69  *
        1   Neighbor search              (2, 3, 3)          -inf   239960.01118       inf%      1.03  
        1   Neighbor search              (3, 2, 3)          -inf   239960.01118       inf%      1.39  
        1   Neighbor search              (3, 3, 2)          -inf   210580.83835       inf%      1.74  *
        1       Line search              (3, 3, 1)          -inf   181201.66551       inf%      2.06  *
        2   Neighbor search              (2, 3, 1)          -inf   178545.19584       inf%      2.39  *
        2   Neighbor search              (3, 2, 1)          -inf   178545.19584       inf%      2.95  
        3   Neighbor search              (2, 2, 1)          -inf   167427.65710       inf%      4.07  *
        3   Neighbor search              (2, 3, 2)          -inf   167427.65710       inf%      4.63  
        4   Neighbor search              (2, 2, 2)          -inf   167427.65710       inf%      6.23  

Solved in 4 iterations and 6.22624 seconds
Optimal objective value 167427.6570965372
Relative optimality gap inf%

Problem: 
- Name: unknown
  Lower bound: -inf
  Upper bound: 167427.6570965372
  Number of objectives: 1
  Number of constraints: 34
  Number of variables: 37
  Number of binary variables: 18
  Number of integer variables: 0
  Number of continuous variables: 19
  Number of nonzeros: None
  Sense: 1
  Number of disjunctions: 9
Solver: 
- Name: GDPopt (22, 5, 13) - LDSDA
  Status: ok
  User time: 6.2260024060014985
  Wallclock time: 6.2260024060014985
  Termination condition: unknown
  Iterations: 4
  Timing: main_timer_start_time: 53578.926211638
total: 6.2260024060014985