Enhance equipment with multi-objective linear programming

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Enhance equipment with multi-objective linear programming This document describes the optimization of equipment enhancement using multipurpose linear programming. The elements of optimization are enhance, refine, evolution, gem, trinket, pet, skill, and guild’s skill with primary, secondary, glove, shoulder, armor, pants, belt, and boot of the equipment part. And the element which becomes the objective function becomes the basic attribute of hp, siphon, hp boost, atk, hit, crit, crit damage, damage boost, fire damage, water damage, earth damage, def, mres, mres boost, dodge, damage reduction, crit res, fire res, water res, earth res, and run speed.

1 Target element This is the definition of premise. Define the object of enhancement as follows. These enhancements enhance the basic attributes and attributes of the character and increase its value. { x = Enhance′ P rimary, Enhance′ Secondary, Enhance′ Glove, Enhance′ Shoulder, Enhance′ Armor, Enhance′ P ants, Enhance′ Belt, Enhance′ Boot, Ref ine′ P rimary, Ref ine′ Secondary, Ref ine′ Glove, Ref ine′ Shoulder, Ref ine′ Armor, Ref ine′ P ants, Ref ine′ Belt, Ref ine′ Boot, Evolution′ P rimary, Evolution′ Secondary, Evolution′ Glove, Evolution′ Shoulder, Evolution′ Armor, Evolution′ P ants, Evolution′ Belt, Evolution′ Boot, Gem′ P rimary, Gem′ Secondary, Gem′ Glove, Gem′ Shoulder, Gem′ Armor, Gem′ P ants, Gem′ Belt, Gem′ Boot, T rinket′ Ring, T rinket′ Earring, T rinket′ T alisman, T rinket′ Statue, T rinket′ N ecklace, T rinket′ Bracelet,

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T rinket′ Brooch, T rinket′ Badge, P et′ P etEgg, P et′ RedBeast, P et′ T anemon, P et′ Chibimon, P et′ Biodoof, P et′ BunnyRabbit, P et′ T winsf oxtail, P et′ GiantBear, P et′ DollyDragon, P et′ W hiteEyebrow, Skill′ Slash, Skill′ CycloneBlade, Skill′ F rostBreak, Skill′ DivineBlade, Skill′ N etherwindString, Skill′ F oliageSlash, Skill′ ShockwaveStrike, Skill′ ShadowCyclone, GuildSkill′ HP, GuildSkill′ AT K, GuildSkill′ DEF, GuildSkill′ M RES, GuildSkill′ Hit, GuildSkill′ Dodge, GuildSkill′ Crit, GuildSkill′ CritRES, GuildSkill′ CritDM G, GuildSkill′ F ireRES, GuildSkill′ W aterRES, GuildSkill′ EarthRES, GuildSkill′ F ireDM G, GuildSkill′ W aterDM G, GuildSkill′ EarthDM G

}

2 Objective function(hp) In this section we define hp’s optimization with the objective function. Here, the ”Enhance′ Shoulder” of x4 shows a value increase of 0.191 by one enhancement. x with a coefficient of 0 is not enhanced.

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max.f1 (x) = 0.191x4 + 0.287x5 + 0.287x6 + 0.191x8 + 2.302x12 + 3.452x13 + 3.196x14 +2.132x16 + 2.302x20 + 3.452x21 + 3.196x22 + 2.132x24 + 0.174x33 + 0.266x41

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+0.471x42 + 0.471x43 + 0.471x44 + 0.941x45 + 0.941x46 + 0.941x47 + 1.207x48 +1.207x49 + 1.207x50 + 0.085x51 + 0.085x54 + 0.085x59

3 Objective function(siphon) In this section we define siphon’s optimization with the objective function. Here, the ”Skill′ DivineBlade” of x54 shows a value increase of 8.485 by one enhancement. x with a coefficient of 0 is not enhanced.

max.f2 (x) = 8.485x54

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4 Objective function(hp boost) In this section we define hp boost’s optimization with the objective function.

Here, the

′

”Ref ine Armor” of x13 shows a value increase of 5.774 by one enhancement. x with a coefficient of 0 is not enhanced.

max.f3 (x) = 5.774x13 + 5.774x21 + 2.309x29

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5 Objective function(atk) In this section we define atk’s optimization with the objective function. Here, the ”Enhance′ P rimary” of x1 shows a value increase of 0.439 by one enhancement. x with a coefficient of 0 is not enhanced.

max.f4 (x) = 0.439x1 + 0.293x2 + 4.990x9 + 3.180x10 + 4.990x17 + 3.180x18 + 0.133x37 +0.133x40 + 0.412x44 + 0.931x48 + 0.785x50 + 0.067x55 + 0.067x58 + 0.067x60

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6 Objective function(hit) In this section we define hit’s optimization with the objective function. Here, the ”Gem′ P rimary” of x25 shows a value increase of 2.072 by one enhancement. x with a coefficient of 0 is not enhanced.

max.f5 (x) = 2.072x25 + 2.072x27 + 2.072x29 + 2.072x32 + 5.180x45 + 5.180x48 + 0.207x55 +0.207x56 + 1.036x63

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7 Objective function(crit) In this section we define crit’s optimization with the objective function. Here, the ”Gem′ Secondary” of x26 shows a value increase of 2.072 by one enhancement. x with a coefficient of 0 is not enhanced.

max.f6 (x) = 2.072x26 + 2.072x27 + 2.072x28 + 2.072x29 + 5.180x48 + 5.180x50 + 0.207x57 +0.207x58 + 1.036x65

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8 Objective function(crit dmg) In this section we define crit dmg’s optimization with the objective function. Here, the ”Gem′ P rimary” of x25 shows a value increase of 4.243 by one enhancement. x with a coefficient of 0 is not enhanced.

max.f7 (x) = 4.243x25 + 4.243x26 + 4.243x27 + 4.243x67

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9 Objective function(damage boost) In this section we define damage boost’s optimization with the objective function.

Here, the

′

”Gem P rimary” of x13 shows a value increase of 4.243 by one enhancement. x with a coefficient of 0 is not enhanced.

max.f8 (x) = 5.774x13 + 5.774x21 + 2.309x28

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10 Objective function(fire dmg) In this section we define fire dmg’s optimization with the objective function. ′

”Ref ine P rimary” of x9 shows a value increase of 3.273 by one enhancement.

Here, the

x with a coeffi-

cient of 0 is not enhanced.

max.f9 (x) = 3.273x9 + 3.273x10 + 3.273x17 + 3.273x18 + 2.619x25 + 2.619x26 + 2.619x27 +2.619x32 + 1.309x71

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11 Objective function(water dmg) In this section we define water dmg’s optimization with the objective function. ′

Here, the

”Ref ine P rimary” of x9 shows a value increase of 3.273 by one enhancement. x with a coefficient of 0 is not enhanced. 3

max.f10 (x) = 3.273x9 + 3.273x10 + 3.273x17 + 3.273x18 + 2.619x25 + 2.619x26 + 2.619x27 +2.619x32 + 1.309x72

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12 Objective function(earth dmg) In this section we define earth dmg’s optimization with the objective function. ”Ref ine′ P rimary” of x9 shows a value increase of 3.273 by one enhancement.

Here, the

x with a coeffi-

cient of 0 is not enhanced.

max.f11 (x) = 3.273x9 + 3.273x10 + 3.273x17 + 3.273x18 + 2.619x25 + 2.619x26 + 2.619x27 +2.619x32 + 1.309x73

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13 Objective function(def) In this section we define def’s optimization with the objective function. Here, the ”Enhance′ Glove” of x3 shows a value increase of 0.408 by one enhancement. x with a coefficient of 0 is not enhanced.

max.f12 (x) = 0.408x3 + 0.241x4 + 0.167x5 + 4.637x11 + 3.004x12 + 2.003x13 + 4.637x19 +3.004x20 + 2.003x21 + 0.148x34 + 0.148x35 + 0.927x36 + 0.389x43 + 0.797x46

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+0.983x49 + 0.074x52 + 0.074x53 + 0.074x61

14 Objective function(mres) In this section we define mres’s optimization with the objective function. Here, the ”Enhance′ P ants” of x6 shows a value increase of 0.173 by one enhancement. x with a coefficient of 0 is not enhanced.

max.f13 (x) = 0.173x6 + 0.422x7 + 0.250x8 + 1.920x14 + 4.800x15 + 2.880x16 + 1.920x22 +4.800x23 + 2.880x24 + 0.154x38 + 0.154x39 + 0.403x42 + 0.826x45 + 0.883x47

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+0.077x56 + 0.077x57 + 0.077x62

15 Objective function(mres boost) In this section we define mres boost’s optimization with the objective function.

Here, the

′

”Ref ine Belf ” of x15 shows a value increase of 5.774 by one enhancement. x with a coefficient of 0 is not enhanced.

max.f14 (x) = 5.774x15 + 5.774x23 + 2.309x31

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16 Objective function(dodge) In this section we define dodge’s optimization with the objective function. Here, the ”Gem′ P rimary” of x25 shows a value increase of 2.073 by one enhancement. x with a coefficient of 0 is not enhanced. max.f15 (x) = 2.073x25 + 2.073x30 + 2.073x31 + 2.073x32 + 5.182x47 + 5.182x49 + 0.207x53 +1.036x64

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17 Objective function(dmg reduction) In this section we define dmg reduction’s optimization with the objective function.

Here, the

′

”Ref ine P ants” of x14 shows a value increase of 5.774 by one enhancement. x with a coefficient of 0 is not enhanced.

max.f16 (x) = 5.774x14 + 5.774x22 + 2.309x30

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18 Objective function(crit res) In this section we define crit res’s optimization with the objective function. Here, the ”Gem′ Secondary” of x26 shows a value increase of 2.072 by one enhancement. x with a coefficient of 0 is not enhanced. max.f17 (x) = 2.072x26 + 2.072x28 + 2.072x30 + 2.072x31 + 5.180x46 + 5.180x49 + 0.207x51 +0.207x52 + 1.036x66

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19 Objective function(fire res) In this section we define fire res’s optimization with the objective function. Here, the ”Ref ine′ Glove” of x11 shows a value increase of 3.273 by one enhancement. x with a coefficient of 0 is not enhanced. max.f18 (x) = 3.273x11 + 3.273x13 + 3.273x19 + 3.273x21 + 2.619x28 + 2.619x29 + 2.619x30 +2.619x31 + 1.309x68

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20 Objective function(water res) In this section we define water res’s optimization with the objective function. Here, the ”Ref ine′ Glove” of x11 shows a value increase of 3.273 by one enhancement. x with a coefficient of 0 is not enhanced. max.f19 (x) = 3.273x11 + 3.273x16 + 3.273x19 + 3.273x24 + 2.619x28 + 2.619x29 + 2.619x30 +2.619x31 + 1.309x69 5

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21 Objective function(earth res) In this section we define earth res’s optimization with the objective function. Here, the ”Ref ine′ P ants” of x14 shows a value increase of 3.273 by one enhancement. x with a coefficient of 0 is not enhanced.

max.f20 (x) = 3.273x14 + 3.273x15 + 3.273x22 + 3.273x23 + 2.619x28 + 2.619x29 + 2.619x30 +2.619x31 + 1.309x70

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22 Objective function(run speed) In this section we define run speed’s optimization with the objective function. Here, the ”Gem′ Boot” of x32 shows a value increase of 1.664 by one enhancement. x with a coefficient of 0 is not enhanced.

max.f21 (x) = 1.664x32 + 8.321x53

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23 Objective function(diamonds) This is the cost per material required for enhancement. This cost is multiplied by an incremental material rising by level in addition to one material. For example, in enhancement the price of enhance stone is 5 diamonds. Fifteen necessary materials will increase for each level. It is 75 from these cost.

min.f22 (x) = 75.000x1 + 75.000x2 + 75.000x3 + 75.000x4 + 75.000x5 +75.000x6 + 75.000x7 + 75.000x8 + 2500.000x9 + 2500.000x10 +2500.000x11 + 2500.000x12 + 2500.000x13 + 2500.000x14 + 2500.000x15 +2500.000x16 + 140.000x17 + 140.000x18 + 140.000x19 + 140.000x20 +140.000x21 + 140.000x22 + 140.000x23 + 140.000x24 + 1500.000x25 +1500.000x26 + 1500.000x27 + 1500.000x28 + 1500.000x29 + 1500.000x30 +1500.000x31 + 1500.000x32 + 4250.000x33 + 4250.000x34 + 4250.000x35 +4250.000x36 + 4250.000x37 + 4250.000x38 + 4250.000x39 + 4250.000x40 +80000.000x41 + 80000.000x42 + 80000.000x43 + 80000.000x44 + 80000.000x45 +80000.000x46 + 80000.000x47 + 80000.000x48 + 80000.000x49 + 80000.000x50 +0.500x51 + 0.500x52 + 0.500x53 + 0.500x54 + 0.500x55 +0.500x56 + 0.500x57 + 0.500x58 + 200.000x59 + 200.000x60 +200.000x61 + 200.000x62 + 200.000x63 + 200.000x64 + 200.000x65 +200.000x66 + 200.000x67 + 200.000x68 + 200.000x69 + 200.000x70 +200.000x71 + 200.000x72 + 200.000x73

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