From cc5ae51f98d82863ff6ae37fc393297bb7f1daa3 Mon Sep 17 00:00:00 2001
From: Gilles Sadowski <gilleseran@gmail.com>
Date: Fri, 27 Aug 2021 17:24:51 +0200
Subject: [PATCH] Favouring the "expanded" simplex over the "reflected" one.

This modification decreases the number of function evaluations in several
test cases. Note however that the original description of the algorithm
uses the strict inequality...
---
 .../noderiv/MultiDirectionalTransform.java    |  2 +-
 ...std_test_func.simplex.multidirectional.csv | 62 +++++++++----------
 2 files changed, 32 insertions(+), 32 deletions(-)

diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/optim/nonlinear/scalar/noderiv/MultiDirectionalTransform.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/optim/nonlinear/scalar/noderiv/MultiDirectionalTransform.java
index bdd53e048..778ff3c13 100644
--- a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/optim/nonlinear/scalar/noderiv/MultiDirectionalTransform.java
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/optim/nonlinear/scalar/noderiv/MultiDirectionalTransform.java
@@ -90,7 +90,7 @@ public class MultiDirectionalTransform
                                                           evaluationFunction);
                 final PointValuePair expandedBest = expandedSimplex.get(0);
 
-                if (comparator.compare(expandedBest, reflectedBest) < 0 ||
+                if (comparator.compare(expandedBest, reflectedBest) <= 0 ||
                     (sa != null &&
                      sa.test(expandedBest.getValue() - reflectedBest.getValue()))) {
                     return expandedSimplex;
diff --git a/commons-math-legacy/src/test/resources/org/apache/commons/math4/legacy/optim/nonlinear/scalar/noderiv/std_test_func.simplex.multidirectional.csv b/commons-math-legacy/src/test/resources/org/apache/commons/math4/legacy/optim/nonlinear/scalar/noderiv/std_test_func.simplex.multidirectional.csv
index acc5e2f59..1e8f88e42 100644
--- a/commons-math-legacy/src/test/resources/org/apache/commons/math4/legacy/optim/nonlinear/scalar/noderiv/std_test_func.simplex.multidirectional.csv
+++ b/commons-math-legacy/src/test/resources/org/apache/commons/math4/legacy/optim/nonlinear/scalar/noderiv/std_test_func.simplex.multidirectional.csv
@@ -31,36 +31,36 @@
 # Caveat: Some tests are commented out (cf. JIRA: MATH-1552).
 #
 PARABOLA, 8, 0 0 0 0 0 0 0 0, 20, 40, 1e-4, 1500, false
-PARABOLA, 8, 0 0 0 0 0 0 0 0, 20, 40, 1e-4, 2500, true
-PARABOLA, 16, 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0, 20, 40, 1e-4, 5800, false
-PARABOLA, 16, 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0, 20, 40, 1e-4, 10260, true
+PARABOLA, 8, 0 0 0 0 0 0 0 0, 20, 40, 1e-4, 2600, true
+PARABOLA, 16, 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0, 20, 40, 1e-4, 5500, false
+PARABOLA, 16, 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0, 20, 40, 1e-4, 10000, true
 ROSENBROCK, 2, 1 1, 0.9, 1.1, 3e-3, 11000, false
-ROSENBROCK, 2, 1 1, 0.9, 1.1, 3e-3, 650, true
-ROSENBROCK, 4, 1 1 1 1, 0.9, 1.1, 3e-3, 45000, false
-ROSENBROCK, 4, 1 1 1 1, 0.9, 1.1, 3e-3, 1850, true
-ROSENBROCK, 8, 1 1 1 1 1 1 1 1, 0.9, 1.1, 4e-3, 130000, false
-ROSENBROCK, 8, 1 1 1 1 1 1 1 1, 0.9, 1.1, 3e-3, 8000, true
-ROSENBROCK, 16, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1, 0.9, 1.1, 2e-1, 430000, false
-ROSENBROCK, 16, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1, 0.9, 1.1, 3e-1, 29000, true
-POWELL, 4, 0 0 0 0, 4, 5, 5e-2, 11800, false
-POWELL, 4, 0 0 0 0, 4, 5, 4e-3, 2200, true
-POWELL, 8, 0 0 0 0 0 0 0 0, 4, 5, 7e-2, 37000, false
-POWELL, 8, 0 0 0 0 0 0 0 0, 4, 5, 4e-2, 8500, true
-CIGAR, 2, 0 0, 2, 3, 5e-5, 240, false
-SPHERE, 2, 0 0, 2, 3, 5e-4, 200, false
-ELLI, 2, 0 0, 3, 4, 1e-4, 350, false
-TWO_AXES, 2, 0 0, 3, 4, 1e-4, 400, false
-CIG_TAB, 2, 0 0, 3, 4, 1e-3, 280, false
-TABLET, 2, 0 0, 3, 4, 2e-4, 340, false
-SUM_POW, 2, 0 0, 3, 4, 1e-2, 190, false
-ACKLEY, 2, 0 0, 2, 4, 1e-6, 310, false
-RASTRIGIN, 2, 0 0, 6, 10, 1e-3, 650, false
-GRIEWANK, 2, 0 0, 2, 3, 1e-1, 500, false
-LEVY, 2, 1 1, 0.9, 1.1, 1e-3, 200, false
-SCHWEFEL, 2, 420.9687 420.9687, 9, 11, 1, 200, false
-ZAKHAROV, 2, 0 0, 3, 4, 1e-4, 1000, false
+ROSENBROCK, 2, 1 1, 0.9, 1.1, 3e-3, 500, true
+ROSENBROCK, 4, 1 1 1 1, 0.9, 1.1, 3e-3, 31000, false
+ROSENBROCK, 4, 1 1 1 1, 0.9, 1.1, 3e-3, 1900, true
+ROSENBROCK, 8, 1 1 1 1 1 1 1 1, 0.9, 1.1, 4e-3, 115000, false
+ROSENBROCK, 8, 1 1 1 1 1 1 1 1, 0.9, 1.1, 3e-3, 8100, true
+ROSENBROCK, 16, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1, 0.9, 1.1, 2e-1, 420000, false
+ROSENBROCK, 16, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1, 0.9, 1.1, 3e-1, 30000, true
+POWELL, 4, 0 0 0 0, 4, 5, 5e-2, 11700, false, target/debug__, 0 1 LAST 0
+POWELL, 4, 0 0 0 0, 4, 5, 4e-3, 1900, true
+POWELL, 8, 0 0 0 0 0 0 0 0, 4, 5, 7e-2, 46000, false
+POWELL, 8, 0 0 0 0 0 0 0 0, 4, 5, 4e-2, 9000, true
+CIGAR, 2, 0 0, 2, 3, 5e-5, 160, false
+SPHERE, 2, 0 0, 2, 3, 5e-4, 120, false
+ELLI, 2, 0 0, 3, 4, 1e-4, 150, false
+TWO_AXES, 2, 0 0, 3, 4, 1e-4, 180, false
+CIG_TAB, 2, 0 0, 3, 4, 1e-3, 170, false
+TABLET, 2, 0 0, 3, 4, 2e-4, 150, false
+SUM_POW, 2, 0 0, 3, 4, 1e-2, 120, false
+ACKLEY, 2, 0 0, 2, 4, 1e-6, 220, false
+RASTRIGIN, 2, 0 0, 6, 10, 1e-3, 160, false
+GRIEWANK, 2, 0 0, 2, 3, 1e-1, 110, false
+LEVY, 2, 1 1, 0.9, 1.1, 1e-3, 120, false
+SCHWEFEL, 2, 420.9687 420.9687, 9, 11, 1, 120, false
+ZAKHAROV, 2, 0 0, 3, 4, 1e-4, 130, false
 PERM, 2, 1 2, 0.9, 1.1, 2e-3, 24000, false
-PERM, 2, 1 2, 0.9, 1.1, 2e-3, 650, true
-STYBLINSKI_TANG, 2, -2.903534 -2.903534, 1, 2, 1e-4, 210, false
-#HAPPY_CAT, 2, -1 -1, 2, 3, 1e-4, 500, false
-#SALOMON, 2, 0 0, 2, 3, 1e-4, 500, false
+PERM, 2, 1 2, 0.9, 1.1, 2e-3, 400, true
+STYBLINSKI_TANG, 2, -2.903534 -2.903534, 1, 2, 1e-4, 120, false
+#HAPPY_CAT, 2, -1 -1, 2, 3, 1e-4, 50, false
+#SALOMON, 2, 0 0, 2, 3, 1e-4, 50, false