4 research outputs found
ΠΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ Π³Π΅Π½Π΅ΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ Π°Π»Π³ΠΎΡΠΈΡΠΌΠ° Π΄Π»Ρ Π½Π°Ρ ΠΎΠΆΠ΄Π΅Π½ΠΈΡ ΡΠ΅Π΄Π°ΠΊΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΡΠ°ΡΡΡΠΎΡΠ½ΠΈΡ ΠΌΠ΅ΠΆΠ΄Ρ ΠΌΠΎΠ΄Π΅Π»ΡΠΌΠΈ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ²
Finding graph-edit distance (graph similarity) is an important task in many computer science areas, such as image analysis, machine learning, chemicalinformatics. Recently, with the development of process mining techniques, it became important to adapt and apply existing graph analysis methods to examine process models (annotated graphs) discovered from event data. In particular, finding graph-edit distance techniques can be used to reveal patterns (subprocesses), compare discovered process models. As it was shown experimentally and theoretically justified, exact methods for finding graph-edit distances between discovered process models (and graphs in general) are computationally expensive and can be applied to small models only. In this paper, we present and assess accuracy and performance characteristics of an inexact genetic algorithm applied to find distances between process models discovered from event logs. In particular, we find distances between BPMN (Business Process Model and Notation) models discovered from event logs by using different process discovery algorithms. We show that the genetic algorithm allows us to dramatically reduce the time of comparison and produces results which are close to the optimal solutions (minimal graph edit distances calculated by the exact search algorithm).ΠΠΎΠΈΡΠΊ ΡΠ΅Π΄Π°ΠΊΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΡΠ°ΡΡΡΠΎΡΠ½ΠΈΡ ΠΌΠ΅ΠΆΠ΄Ρ Π³ΡΠ°ΡΠΎΠ²ΡΠΌΠΈ ΠΌΠΎΠ΄Π΅Π»ΡΠΌΠΈ (ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΡΡ
ΠΎΠΆΠ΅ΡΡΠΈ Π³ΡΠ°ΡΠΎΠ²ΡΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ) ΡΠ²Π»ΡΠ΅ΡΡΡ Π²Π°ΠΆΠ½ΠΎΠΉ Π·Π°Π΄Π°ΡΠ΅ΠΉ Π² ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
ΠΎΠ±Π»Π°ΡΡΡΡ
ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΡΡ
Π½Π°ΡΠΊ, ΡΠ°ΠΊΠΈΡ
ΠΊΠ°ΠΊ Π°Π½Π°Π»ΠΈΠ· ΠΈΠ·ΠΎΠ±ΡΠ°ΠΆΠ΅Π½ΠΈΠΉ, ΠΌΠ°ΡΠΈΠ½Π½ΠΎΠ΅ ΠΎΠ±ΡΡΠ΅Π½ΠΈΠ΅, Ρ
ΠΈΠΌΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΊΠ°. Π ΠΏΠΎΡΠ»Π΅Π΄Π½Π΅Π΅ Π²ΡΠ΅ΠΌΡ, Π² ΡΠ²ΡΠ·ΠΈ Ρ ΡΠ°Π·Π²ΠΈΡΠΈΠ΅ΠΌ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΠΈΠ·Π²Π»Π΅ΡΠ΅Π½ΠΈΡ ΠΈ Π°Π½Π°Π»ΠΈΠ·Π° ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ², ΠΏΠΎΡΠ²ΠΈΠ»Π°ΡΡ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΡ Π² Π°Π΄Π°ΠΏΡΠ°ΡΠΈΠΈ ΡΡΡΠ΅ΡΡΠ²ΡΡΡΠΈΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ Π³ΡΠ°ΡΠΎΠ²ΡΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ Π΄Π»Ρ Π°Π½Π°Π»ΠΈΠ·Π° ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² (Π°Π½Π½ΠΎΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
Π³ΡΠ°ΡΠΎΠ²), ΠΈΠ·Π²Π»Π΅ΠΊΠ°Π΅ΠΌΡΡ
ΠΈΠ· Π»ΠΎΠ³ΠΎΠ² ΡΠΎΠ±ΡΡΠΈΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΡΡ
ΡΠΈΡΡΠ΅ΠΌ. ΠΠ΅ΡΠΎΠ΄Ρ Π½Π°Ρ
ΠΎΠΆΠ΄Π΅Π½ΠΈΡ ΠΌΠΈΠ½ΠΈΠΌΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠ΅Π΄Π°ΠΊΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΡΠ°ΡΡΡΠΎΡΠ½ΠΈΡ ΠΌΠ΅ΠΆΠ΄Ρ Π³ΡΠ°ΡΠ°ΠΌΠΈ ΠΌΠΎΠ³ΡΡ Π±ΡΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½Ρ Π΄Π»Ρ ΠΎΠ±Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ ΡΠ°Π±Π»ΠΎΠ½ΠΎΠ² (ΠΏΠΎΠ΄ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ²), Π° ΡΠ°ΠΊΠΆΠ΅ Π΄Π»Ρ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΠΈΠ·Π²Π»Π΅ΠΊΠ°Π΅ΠΌΡΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ². ΠΠ°ΠΊ Π±ΡΠ»ΠΎ ΠΏΠΎΠΊΠ°Π·Π°Π½ΠΎ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΎ ΠΈ ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΈ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΎ, ΡΠΎΡΠ½ΡΠ΅ ΠΌΠ΅ΡΠΎΠ΄Ρ Π½Π°Ρ
ΠΎΠΆΠ΄Π΅Π½ΠΈΡ ΠΌΠΈΠ½ΠΈΠΌΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠ΅Π΄Π°ΠΊΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΡΠ°ΡΡΡΠΎΡΠ½ΠΈΡ ΠΌΠ΅ΠΆΠ΄Ρ ΠΈΠ·Π²Π»Π΅ΠΊΠ°Π΅ΠΌΡΠΌΠΈ ΠΌΠΎΠ΄Π΅Π»ΡΠΌΠΈ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² (ΠΈ Π³ΡΠ°ΡΠ°ΠΌΠΈ Π² ΠΎΠ±ΡΠ΅ΠΌ ΡΠ»ΡΡΠ°Π΅) ΠΈΠΌΠ΅ΡΡ Π±ΠΎΠ»ΡΡΡΡ Π²ΡΠ΅ΠΌΠ΅Π½Π½ΡΡ ΡΠ»ΠΎΠΆΠ½ΠΎΡΡΡ ΠΈ ΠΌΠΎΠ³ΡΡ Π±ΡΡΡ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½Ρ Π»ΠΈΡΡ ΠΊ Π½Π΅Π±ΠΎΠ»ΡΡΠΈΠΌ ΠΌΠΎΠ΄Π΅Π»ΡΠΌ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ². Π ΡΡΠΎΠΉ ΡΡΠ°ΡΡΠ΅ ΠΌΡ ΠΎΡΠ΅Π½ΠΈΠ²Π°Π΅ΠΌ ΡΠΎΡΠ½ΠΎΡΡΡ ΠΈ Π²ΡΠ΅ΠΌΠ΅Π½Π½ΡΠ΅ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΈ Π³Π΅Π½Π΅ΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ Π°Π»Π³ΠΎΡΠΈΡΠΌΠ°, ΠΏΡΠΈΠΌΠ΅Π½ΡΠ΅ΠΌΠΎΠ³ΠΎ Π΄Π»Ρ Π½Π°Ρ
ΠΎΠΆΠ΄Π΅Π½ΠΈΡ ΡΠ°ΡΡΡΠΎΡΠ½ΠΈΠΉ ΠΌΠ΅ΠΆΠ΄Ρ ΠΌΠΎΠ΄Π΅Π»ΡΠΌΠΈ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ², ΠΈΠ·Π²Π»Π΅ΠΊΠ°Π΅ΠΌΡΡ
ΠΈΠ· Π»ΠΎΠ³ΠΎΠ² ΡΠΎΠ±ΡΡΠΈΠΉ. Π ΡΠ°ΡΡΠ½ΠΎΡΡΠΈ ΠΌΡ Π½Π°Ρ
ΠΎΠ΄ΠΈΠΌ ΡΠ°ΡΡΡΠΎΡΠ½ΠΈΡ ΠΌΠ΅ΠΆΠ΄Ρ BPMN (Business Process Model and Notation) ΠΌΠΎΠ΄Π΅Π»ΡΠΌΠΈ, ΠΈΠ·Π²Π»Π΅ΠΊΠ°Π΅ΠΌΡΠΌΠΈ ΠΈΠ· Π»ΠΎΠ³ΠΎΠ² ΡΠΎΠ±ΡΡΠΈΠΉ Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΡΠΈΠ½ΡΠ΅Π·Π°. Π ΡΡΠΎΠΉ ΡΠ°Π±ΠΎΡΠ΅ ΠΏΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Π½ΡΠΉ Π³Π΅Π½Π΅ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ Π°Π»Π³ΠΎΡΠΈΡΠΌ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ Π² Π·Π½Π°ΡΠΈΡΠ΅Π»ΡΠ½ΠΎΠΉ ΡΡΠ΅ΠΏΠ΅Π½ΠΈ ΡΠΌΠ΅Π½ΡΡΠΈΡΡ Π²ΡΠ΅ΠΌΡ Π²ΡΡΠΈΡΠ»Π΅Π½ΠΈΠΉ, ΠΏΡΠΈ ΡΡΠΎΠΌ ΠΏΠΎΠΊΠ°Π·ΡΠ²Π°Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ, Π±Π»ΠΈΠ·ΠΊΠΈΠ΅ ΠΊ ΠΎΠΏΡΠΈΠΌΠ°Π»ΡΠ½ΡΠΌ (ΠΌΠΈΠ½ΠΈΠΌΠ°Π»ΡΠ½ΡΠΌ ΡΠ΅Π΄Π°ΠΊΡΠΈΠΎΠ½Π½ΡΠΌ ΡΠ°ΡΡΡΠΎΡΠ½ΠΈΡΠΌ)
Study of the Kinetics of Cadmium Cementation in the Presence of a Flocculant
ΠΠΎΡΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΈΠ΅ ΠΈΠΎΠ½ΠΎΠ² ΠΊΠ°Π΄ΠΌΠΈΡ ΠΈΠ· Π²ΠΎΠ΄Π½ΡΡ
ΡΠ°ΡΡΠ²ΠΎΡΠΎΠ² ΠΏΡΠΎΠ²ΠΎΠ΄ΠΈΠ»ΠΈ ΠΏΠΎΡΠΎΡΠΊΠΎΠΌ ΡΠΈΠ½ΠΊΠ°,
ΠΊΡΡΠΏΠ½ΠΎΡΡΡΡ ΠΎΡ 63 Π΄ΠΎ 200 ΠΌΠΊΠΌ. Π ΡΡΠ΄Π΅ ΠΎΠΏΡΡΠΎΠ² ΠΏΡΠΎΠ²Π΅ΡΡΠ»ΠΈ Π²Π»ΠΈΡΠ½ΠΈΠ΅ Π½Π° ΠΏΡΠΎΡΠ΅ΡΡ ΡΠ΅ΠΌΠ΅Π½ΡΠ°ΡΠΈΠΈ ΠΊΠ°Π΄ΠΌΠΈΡ
ΠΊΠ°ΡΠΈΠΎΠ½ΠΎΠ°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠ»ΠΎΠΊΡΠ»ΡΠ½ΡΠ° Besfloc K6645. ΠΡΠΎΡΠ΅ΡΡ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΈΠ»ΠΈ Π² ΠΎΠ±Π»Π°ΡΡΠΈ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡ ΠΎΡ 30
Π΄ΠΎ 50 ΠΎΠ‘ ΠΏΡΠΈ Π½Π΅ΠΏΡΠ΅ΡΡΠ²Π½ΠΎΠΌ ΠΏΠ΅ΡΠ΅ΠΌΠ΅ΡΠΈΠ²Π°Π½ΠΈΠΈ ΡΠΎ ΡΠΊΠΎΡΠΎΡΡΡΡ 200 ΠΎΠ±/ΠΌΠΈΠ½ Π²Π΅ΡΡ
Π½Π΅ΠΏΡΠΈΠ²ΠΎΠ΄Π½ΠΎΠΉ ΠΌΠ΅ΡΠ°Π»ΠΊΠΎΠΉ.
ΠΠΈΠ½Π΅ΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΊΡΠΈΠ²ΡΠ΅ ΠΏΠΎΡΡΡΠΎΠΈΠ»ΠΈ Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΠΊΠ°Π΄ΠΌΠΈΠΉ-ΡΠ΅Π»Π΅ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ
ΡΠ»Π΅ΠΊΡΡΠΎΠ΄Π°. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ,
ΡΡΠΎ ΠΏΠΎΠ²ΡΡΠ΅Π½ΠΈΠ΅ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΡ ΠΏΡΠΎΡΠ΅ΠΊΠ°Π½ΠΈΡ ΡΠ΅Π°ΠΊΡΠΈΠΈ ΠΏΠΎΠ»ΠΎΠΆΠΈΡΠ΅Π»ΡΠ½ΠΎ Π²Π»ΠΈΡΠ΅Ρ Π½Π° ΡΠ΅ΠΌΠ΅Π½ΡΠ°ΡΠΈΡ. ΠΠ²Π΅Π΄Π΅Π½ΠΈΠ΅
Π² ΡΠ»Π΅ΠΊΡΡΠΎΠ»ΠΈΡ ΡΠ»ΠΎΠΊΡΠ»ΡΠ½ΡΠ° Π² ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π΅ 70 ΠΌΠ³/Π» ΡΠ½ΠΈΠΆΠ°Π»ΠΎ ΡΡΠ΅ΠΏΠ΅Π½Ρ ΡΠ΅ΠΌΠ΅Π½ΡΠ°ΡΠΈΠΈ ΠΊΠ°Π΄ΠΌΠΈΡ. ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅
Π΄Π°Π½Π½ΡΠ΅ ΠΏΠΎΠ·Π²ΠΎΠ»ΠΈΠ»ΠΈ ΡΠ°ΡΡΡΠΈΡΠ°ΡΡ ΠΊΠ°ΠΆΡΡΠΈΠ΅ΡΡ ΡΠ½Π΅ΡΠ³ΠΈΠΈ Π°ΠΊΡΠΈΠ²Π°ΡΠΈΠΈ, ΠΊΠΎΡΠΎΡΡΠ΅ ΡΠΎΡΡΠ°Π²ΠΈΠ»ΠΈ ΠΏΡΠΈ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ΠΈΠΈ
ΠΏΡΠΎΡΠ΅ΡΡΠ° Π±Π΅Π· Π΄ΠΎΠ±Π°Π²ΠΊΠΈ ΡΠ»ΠΎΠΊΡΠ»ΡΠ½ΡΠ° ΠΎΡΠΈΠ΅Π½ΡΠΈΡΠΎΠ²ΠΎΡΠ½ΠΎ 46, 33 ΠΈ 11 ΠΊΠΠΆ/ΠΌΠΎΠ»Ρ Π½Π° ΠΏΠ΅ΡΠ²ΠΎΠΌ, Π²ΡΠΎΡΠΎΠΌ
ΠΈ ΡΡΠ΅ΡΡΠ΅ΠΌ ΡΡΠ°ΡΡΠΊΠ°Ρ
ΠΊΠΈΠ½Π΅ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΡΠΈΠ²ΡΡ
, ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²Π΅Π½Π½ΠΎ, ΠΏΡΠΈ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ΠΈΠΈ Π²ΠΎΡΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΈΡ Π±Π΅Π·
Π΄ΠΎΠ±Π°Π²ΠΊΠΈ ΡΠ»ΠΎΠΊΡΠ»ΡΠ½ΡΠ° ΠΈ 117β130 ΠΈ 82β85 ΠΊΠΠΆ/ΠΌΠΎΠ»Ρ Π² ΠΏΡΠΈΡΡΡΡΡΠ²ΠΈΠΈ ΡΠ»ΠΎΠΊΡΠ»ΡΠ½ΡΠ° Besfloc K6645. ΠΡΠΈ
Π²ΠΎΡΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΈΠΈ ΠΊΠ°Π΄ΠΌΠΈΡ Π² ΠΏΡΠΈΡΡΡΡΡΠ²ΠΈΠΈ ΡΠ»ΠΎΠΊΡΠ»ΡΠ½ΡΠ° ΠΊΠ°ΠΆΡΡΠ°ΡΡΡ ΡΠ½Π΅ΡΠ³ΠΈΡ Π°ΠΊΡΠΈΠ²Π°ΡΠΈΠΈ Π²ΠΎΠ·ΡΠ°ΡΡΠ°Π»Π°
Π±ΠΎΠ»Π΅Π΅ ΡΠ΅ΠΌ Π² Π΄Π²Π° ΡΠ°Π·Π°The reduction of cadmium ions from aqueous solutions was carried out with zinc powder, particle size from 63 to 200 ΞΌm. In a number of experiments, the influence of the cationic flocculant Besfloc K6645 on the cadmium cementation process was tested. The process was carried out in the temperature range from 30 to 50 Β°C with continuous stirring at a speed of 200 rpm with an overhead stirrer. Kinetic curves were built using a cadmium selective electrode. It is shown that an increase in the reaction temperature has a positive effect on cementation. The introduction of a flocculant in the amount of 70 mg/l into the electrolyte reduced the degree of cadmium cementation. respectively, when carrying out the reduction without the addition of a flocculant, and 117β130 and 82β85 kJ/mol in the presence of the Besfloc K6645 flocculant. When cadmium was reduced in the presence of a flocculant, the apparent activation energy more than double
Application of Genetic Algorithms for Finding Edit Distance between Process Models
Finding graph-edit distance (graph similarity) is an important task in many computer science areas, such as image analysis, machine learning, chemicalinformatics. Recently, with the development of process mining techniques, it became important to adapt and apply existing graph analysis methods to examine process models (annotated graphs) discovered from event data. In particular, finding graph-edit distance techniques can be used to reveal patterns (subprocesses), compare discovered process models. As it was shown experimentally and theoretically justified, exact methods for finding graph-edit distances between discovered process models (and graphs in general) are computationally expensive and can be applied to small models only. In this paper, we present and assess accuracy and performance characteristics of an inexact genetic algorithm applied to find distances between process models discovered from event logs. In particular, we find distances between BPMN (Business Process Model and Notation) models discovered from event logs by using different process discovery algorithms. We show that the genetic algorithm allows us to dramatically reduce the time of comparison and produces results which are close to the optimal solutions (minimal graph edit distances calculated by the exact search algorithm)