From a7666005d7cf3382eb9c48306293c85fa1487198 Mon Sep 17 00:00:00 2001
From: Daniel Weindl <daniel.weindl@helmholtz-munich.de>
Date: Sun, 19 Nov 2023 11:15:17 +0100
Subject: [PATCH] SacessOptimizer: Update worker settings

* Most importantly fix default RefSet sizes (too big before)
* Add default settings for >10 workers
---
 pypesto/optimize/ess/sacess.py | 113 +++++++++++++++++++++++++++------
 1 file changed, 95 insertions(+), 18 deletions(-)

diff --git a/pypesto/optimize/ess/sacess.py b/pypesto/optimize/ess/sacess.py
index 3dfb68cae..f6491f887 100644
--- a/pypesto/optimize/ess/sacess.py
+++ b/pypesto/optimize/ess/sacess.py
@@ -5,6 +5,7 @@
 import multiprocessing
 import os
 import time
+from math import ceil, sqrt
 from multiprocessing import Manager, Process
 from multiprocessing.managers import SyncManager
 from pathlib import Path
@@ -688,90 +689,166 @@ def get_default_ess_options(num_workers: int, dim: int) -> List[Dict]:
     Setting appropriate values for ``n_threads`` and ``local_optimizer`` is
     left to the user. Defaults to single-threaded and no local optimizer.
 
+    Based on https://bitbucket.org/DavidPenas/sacess-library/src/508e7ac15579104731cf1f8c3969960c6e72b872/src/method_module_fortran/eSS/parallelscattersearchfunctions.f90#lines-929
+
     Parameters
     ----------
     num_workers: Number of configurations to return.
     dim: Problem dimension.
     """
-    min_dimrefset = 3
+    min_dimrefset = 5
+
+    def dim_refset(x):
+        return max(min_dimrefset, ceil((1 + sqrt(4 * dim * x)) / 2))
+
     settings = [
         # settings for first worker
         {
-            'dim_refset': 10 * dim,
+            'dim_refset': dim_refset(10),
             'balance': 0.5,
             'local_n2': 10,
         },
         # for the remaining workers, cycle through these settings
         # 1
         {
-            'dim_refset': max(min_dimrefset, dim),
+            'dim_refset': dim_refset(1),
             'balance': 0.0,
             'local_n1': 1,
             'local_n2': 1,
         },
         # 2
         {
-            'dim_refset': 3 * dim,
+            'dim_refset': dim_refset(3),
             'balance': 0.0,
-            'local_n1': 4,
-            'local_n2': 4,
+            'local_n1': 1000,
+            'local_n2': 1000,
         },
         # 3
         {
-            'dim_refset': 5 * dim,
+            'dim_refset': dim_refset(5),
             'balance': 0.25,
             'local_n1': 10,
             'local_n2': 10,
         },
         # 4
         {
-            'dim_refset': 10 * dim,
+            'dim_refset': dim_refset(10),
             'balance': 0.5,
             'local_n1': 20,
             'local_n2': 20,
         },
         # 5
         {
-            'dim_refset': 15 * dim,
+            'dim_refset': dim_refset(15),
             'balance': 0.25,
             'local_n1': 100,
             'local_n2': 100,
         },
         # 6
         {
-            'dim_refset': 12 * dim,
+            'dim_refset': dim_refset(12),
             'balance': 0.25,
-            'local_n1': 50,
-            'local_n2': 50,
+            'local_n1': 1000,
+            'local_n2': 1000,
         },
         # 7
         {
-            'dim_refset': int(7.5 * dim),
+            'dim_refset': dim_refset(7.5),
             'balance': 0.25,
             'local_n1': 15,
             'local_n2': 15,
         },
         # 8
         {
-            'dim_refset': 5 * dim,
+            'dim_refset': dim_refset(5),
             'balance': 0.25,
             'local_n1': 7,
             'local_n2': 7,
         },
         # 9
         {
-            'dim_refset': max(min_dimrefset, 2 * dim),
+            'dim_refset': dim_refset(2),
             'balance': 0.0,
-            'local_n1': 2,
-            'local_n2': 2,
+            'local_n1': 1000,
+            'local_n2': 1000,
         },
         # 10
         {
-            'dim_refset': max(min_dimrefset, int(0.5 * dim)),
+            'dim_refset': dim_refset(0.5),
             'balance': 0.0,
             'local_n1': 1,
             'local_n2': 1,
         },
+        # 11
+        {
+            'dim_refset': dim_refset(1.5),
+            'balance': 1.0,
+            'local_n1': 1,
+            'local_n2': 1,
+        },
+        # 12
+        {
+            'dim_refset': dim_refset(3.5),
+            'balance': 1.0,
+            'local_n1': 4,
+            'local_n2': 4,
+        },
+        # 13
+        {
+            'dim_refset': dim_refset(5.5),
+            'balance': 0.1,
+            'local_n1': 10,
+            'local_n2': 10,
+        },
+        # 14
+        {
+            'dim_refset': dim_refset(10.5),
+            'balance': 0.3,
+            'local_n1': 20,
+            'local_n2': 20,
+        },
+        # 15
+        {
+            'dim_refset': dim_refset(15.5),
+            'balance': 0.2,
+            'local_n1': 1000,
+            'local_n2': 1000,
+        },
+        # 16
+        {
+            'dim_refset': dim_refset(12.5),
+            'balance': 0.2,
+            'local_n1': 10,
+            'local_n2': 10,
+        },
+        # 17
+        {
+            'dim_refset': dim_refset(8),
+            'balance': 0.75,
+            'local_n1': 15,
+            'local_n2': 15,
+        },
+        # 18
+        {
+            'dim_refset': dim_refset(5.5),
+            'balance': 0.75,
+            'local_n1': 1000,
+            'local_n2': 1000,
+        },
+        # 19
+        {
+            'dim_refset': dim_refset(2.2),
+            'balance': 1.0,
+            'local_n1': 2,
+            'local_n2': 2,
+        },
+        # 20
+        {
+            'dim_refset': dim_refset(1),
+            'balance': 1.0,
+            'local_n1': 1,
+            'local_n2': 1,
+        },
     ]
     return [
         settings[0],