First published version

Add readme and license.
Change the objective function of the example.

Author: otvam

LICENSE.md

@@ -0,0 +1,23 @@
+Copyright (c) 2020 Thomas Guillod.
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+1. Redistributions of source code must retain the above copyright notice, this
+   list of conditions and the following disclaimer.
+
+2. Redistributions in binary form must reproduce the above copyright notice,
+   this list of conditions and the following disclaimer in the documentation
+   and/or other materials provided with the distribution.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIEDi
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

README.md

@@ -0,0 +1,53 @@
+# MATLAB tool for multi-objective optimization (genetic or brute-force)
+
+This **MATLAB** tool offers different functionalities for multi-objective optimization:
+* Offer a **common interface** for different solvers
+    * **Brute force** grid search (exhaustive search)
+    * MATLAB **single-objective genetic** algoritm ('ga')
+    * MATLAB **multi-objective genetic** algoritm ('gamultiobj')
+* Offer an **abstraction layer** to the MATLAB solver
+    * Scaling the input variables
+    * Generating and filtering initial points
+    * Transforming high-level datastructures ('struct') to low-level ('matrix')
+    * Generating the low-level inputs required by the solvers
+* Allow **vectorized and parallel** evaluation of the functions
+    * Divide the number of points to be evaluated into chunks
+    * Evaluate the chunks with parallel computing ('parfor')
+    * The points inside a chunk are evaluated in a vectorized way
+
+Mathematically, the following optimization problem are solved:
+* Multiple variables
+* Integer variables
+* Upper and lower bounds
+* Inequality constraints
+* Equality constraints
+* Non continuous objective function
+* Single-objective or multi-objective goals
+
+Look at the example [run_example.m](run_example.m) which generates the following results:
+
+<p float="middle">
+    <img src="readme_img/input.png" width="400">
+    <img src="readme_img/output.png" width="400">
+</p>
+
+## Adding Solvers
+
+The code is made to take advantage of optimization methods using vectorized evaluation of the objective function.
+Therefore, it would be easy to add support for 'patternsearch', 'particleswarm', or 'paretosearch'.
+Adding support for non vectorized solvers ('fmincon', 'fminbnd', or 'fminsearch') is possible but less interesting.
+
+## Compatibility
+
+* Tested with MATLAB R2018b.
+* Required the gads_toolbox (for contour detection).
+* Required the optimization_toolbox (for contour simplification).
+* Compatibility with GNU Octave not tested but probably problematic.
+
+## Author
+
+**Thomas Guillod** - [GitHub Profile](https://github.com/otvam)
+
+## License
+
+This project is licensed under the **BSD License**, see [LICENSE.md](LICENSE.md).

get_data.m

@@ -9,15 +9,18 @@
 %      - Integer variables
 %      - Upper and lower bounds
 %      - Inequality constraints
-%      - Inequality constraints
+%      - Equality constraints
+%      - Non continuous objective function
 %      - Single-objective or multi-objective goals
 %
 %   Use the followig strategies:
 %      - brute force grid search (mixed integer)
 %      - single-objective genetic algoritm (mixed integer)
 %      - multi-objective genetic algoritm (continuous variables)
 %
-%   See also RUN_OPTIM, GET_OPTIM, GET_PRE_PROC, GET_SOLUTION.
+%   The problem solved in this example is trivial and not very interesting.
+%
+%   See also RUN_OPTIM, GET_MULTI_OBJ_OPT, GET_PRE_PROC, GET_SOLUTION.
 
 %   Thomas Guillod.
 %   2020 - BSD License.
@@ -183,7 +186,7 @@
 x_4 = input.x_4;
 
 % compute
-y_1 = x_1.^2+x_2.^2+x_3;
+y_1 = x_1.^2+(x_2-2).^2+x_3;
 y_2 = 0.5*((x_1-2).^2+(x_2+1).^2)+2+x_4;
 
 end

readme_img/input.png

@@ -3,7 +3,7 @@ function run_example()
 %
 %   The description of the problem can be found in 'get_data'.
 %
-%   See also GET_OPTIM, GET_DATA.
+%   See also GET_MULTI_OBJ_OPT, GET_DATA.
 
 %   Thomas Guillod.
 %   2020 - BSD License.
@@ -13,17 +13,29 @@ function run_example()
 
 %% solve brute force optimization
 [var_param, solver_param] = get_data('bruteforce');
-data_bruteforce = get_optim('bruteforce', var_param, solver_param);
+data_bruteforce = get_multi_obj_opt('bruteforce', var_param, solver_param);
 
 %% solve single-objective optimization with genetic algorithm
 [var_param, solver_param] = get_data('ga');
-data_ga = get_optim('ga', var_param, solver_param);
+data_ga = get_multi_obj_opt('ga', var_param, solver_param);
 
 %% solve multi-objective optimization with genetic algorithm
 [var_param, solver_param] = get_data('gamultiobj');
-data_gamultiobj = get_optim('gamultiobj', var_param, solver_param);
+data_gamultiobj = get_multi_obj_opt('gamultiobj', var_param, solver_param);
 
 %% plot the results
+figure()
+plot3(data_bruteforce.sol.input.x_1, data_bruteforce.sol.input.x_2, data_bruteforce.sol.input.x_3, 'xb')
+hold('on')
+plot3(data_gamultiobj.sol.input.x_1, data_gamultiobj.sol.input.x_2, data_gamultiobj.sol.input.x_3, 'dr')
+plot3(data_ga.sol.input.x_1, data_ga.sol.input.x_2, data_ga.sol.input.x_3, 'og', 'markerfacecolor', 'g')
+grid('on')
+xlabel('x_{1}')
+ylabel('x_{2}')
+zlabel('x_{3}')
+legend({'bruteforce', 'gamultiobj', 'ga'}, 'Location', 'northeast')
+title('Multi-Objective Optimization / Input')
+
 figure()
 plot(data_bruteforce.sol.output.y_1, data_bruteforce.sol.output.y_2, 'xb')
 hold('on')
@@ -32,8 +44,8 @@ function run_example()
 grid('on')
 xlabel('y_{1}')
 ylabel('y_{2}')
-legend('bruteforce', 'gamultiobj', 'ga')
-title('Multi-Objective Optimization')
+legend({'bruteforce', 'gamultiobj', 'ga'}, 'Location', 'northeast')
+title('Multi-Objective Optimization / Output')
 
 end
 

readme_img/output.png

@@ -1,6 +1,6 @@
-function data = get_optim(name, var_param, solver_param)
-%GET_OPTIM Solve a multi-objective optimization problem with different solvers.
-%   data = GET_OPTIM(name, var_param, solver_param)
+function data = get_multi_obj_opt(name, var_param, solver_param)
+%GET_MULTI_OBJ_OPT Solve a multi-objective optimization problem with different solvers.
+%   data = GET_MULTI_OBJ_OPT(name, var_param, solver_param)
 %   name - name of the problem (string)
 %   var_param - struct with the variable description (struct)
 %   solver_param - struct with the solver data (struct)

run_example.m

@@ -50,7 +50,7 @@
 %         - Scale the 'float' variables with 'lin', 'log', 'exp', 'square', or 'sqrt'
 %         - Mapping integer variables from [x1, x1, ..., xn] to [1, 2, ..., n]
 %
-%   See also GET_OPTIM, GET_SOLUTION.
+%   See also GET_MULTI_OBJ_OPT, GET_SOLUTION.
 
 %   Thomas Guillod.
 %   2020 - BSD License.

src/get_optim.m renamed to src/get_multi_obj_opt.m

@@ -52,7 +52,7 @@
 %   This function performs optimization with different solvers.
 %   Please note that the 'gamultiobj' cannot deal with integer variables.
 %
-%   See also GET_OPTIM, GET_PRE_PROC, GET_VECTORIZED, BRUTEFORCE, GA GAMULTIOBJ.
+%   See also GET_MULTI_OBJ_OPT, GET_PRE_PROC, GET_VECTORIZED, BRUTEFORCE, GA GAMULTIOBJ.
 
 %   Thomas Guillod.
 %   2020 - BSD License.