From 7cc0f793f71dd7b61c5c8ba6880ef939a449fa0d Mon Sep 17 00:00:00 2001 From: Michael Baumgartner Date: Fri, 6 Dec 2024 16:43:14 +0100 Subject: [PATCH] Fix Typo in Hypervolume formula See also Hypervolume-slide for the correct formula --- Multi-Objective Optimisation - Part 1.ipynb | 2 +- rendered/Multi-Objective Optimisation - Part 1.md | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/Multi-Objective Optimisation - Part 1.ipynb b/Multi-Objective Optimisation - Part 1.ipynb index a1de7a7..92a142e 100644 --- a/Multi-Objective Optimisation - Part 1.ipynb +++ b/Multi-Objective Optimisation - Part 1.ipynb @@ -2559,7 +2559,7 @@ } }, "source": [ - "That is, the hypervolume of a front $V = \\{v^{(1)}, v^{(2)},\\ldots, v^{(m)} \\}$ with respect to reference point $r$ in this case reduces to calculating: $H(V, r) = (r_1 - v_1^{(1)})(r_2 - v_2^{(1)}) + \\displaystyle\\sum_{i=2}^m (r_1 - v_1^{(i)})(r_2^{(i-1)} - v_2^{(i)})$\n", + "That is, the hypervolume of a front $V = \\{v^{(1)}, v^{(2)},\\ldots, v^{(m)} \\}$ with respect to reference point $r$ in this case reduces to calculating: $H(V, r) = (r_1 - v_1^{(1)})(r_2 - v_2^{(1)}) + \\displaystyle\\sum_{i=2}^m (r_1 - v_1^{(i)})(v_2^{(i-1)} - v_2^{(i)})$\n", "\n", "In code, for our two objective values, this looks as follows:" ] diff --git a/rendered/Multi-Objective Optimisation - Part 1.md b/rendered/Multi-Objective Optimisation - Part 1.md index 4aa74d4..dc4b521 100644 --- a/rendered/Multi-Objective Optimisation - Part 1.md +++ b/rendered/Multi-Objective Optimisation - Part 1.md @@ -106563,7 +106563,7 @@ ax.add_patch(rect) -That is, the hypervolume of a front $V = \{v^{(1)}, v^{(2)},\ldots, v^{(m)} \}$ with respect to reference point $r$ in this case reduces to calculating: $H(V, r) = (r_1 - v_1^{(1)})(r_2 - v_2^{(1)}) + \displaystyle\sum_{i=2}^m (r_1 - v_1^{(i)})(r_2^{(i-1)} - v_2^{(i)})$ +That is, the hypervolume of a front $V = \{v^{(1)}, v^{(2)},\ldots, v^{(m)} \}$ with respect to reference point $r$ in this case reduces to calculating: $H(V, r) = (r_1 - v_1^{(1)})(r_2 - v_2^{(1)}) + \displaystyle\sum_{i=2}^m (r_1 - v_1^{(i)})(v_2^{(i-1)} - v_2^{(i)})$ In code, for our two objective values, this looks as follows: