Answer: {Fighter 1 / Warlock 19} is the Optimal Build (Hat Tip to Strill!)

By exploiting Devil's Sight + Darkness cheese available as early as level 4, you can reliably increase your accuracy enough against most foes throughout the game that the Greatsword combined with Great Weapon Master provides the best average damage numbers. Dragonborn Warlocks (and Human Variant Warlocks, see below) specifically are perfect for exploiting Devil's Sight because they don't get Darkvision as a racial trait and so for maximum effectiveness you really have to take Devil's Sight anyway! You might as well get a return on your investment by being able to pull a Riddick on groups of unsuspecting foes who may feel perfectly at home in non-magical darkness, like Half-Elf or Drow Warlocks who opted not to take Devil's Sight because they could already see in the dark. Keep in mind you can cast Darkness at targets as far away as 60 feet, and affect enemies within a 15 foot sphere of the target so this tactic isn't restricted to just melee combat. It's also an effective way to reliably get advantage on ranged attack rolls. The only downside is your team-mates are unlikely to be able to effectively engage enemies caught within the sphere. On the other hand, for maximum damage you really want to be hitting targets with Eldritch Blast that have been affected by Hex first. Unfortunately, Hex and Darkness cannot be active simultaneously because they both require concentration.

When not casting Hex or Darkness, make sure you respond to enemy attacks with Hellish Rebuke. One of the big advantages to this build is it doesn't take up your reaction with the off-hand attack from Polearm Master but still offers comparable damage, and that reaction can be used to great effect with Hellish Rebuke. Further DPR optimization can be obtained from Fire Shield which is available as a 4th-level spell gained from the Fiend patron. Another reason to take Fire Shield is for resistance purposes. Combining Dragonborn resistance, Fire Shield, and Fiendish Resilience (level 10 Fiend Patron benefit) allows you to gain three different elemental resistances. Later on you can take Foresight as your 9th-level Mystic Arcanum at level 18 and you will basically be an unstoppable killing machine with or without Darkness. Fun fact: Foresight grants advantage on initiative rolls since initiative is a Dexterity ability check! Magical weapons will further increase your destructive potential.

Using point-buy as opposed to the standard ability score array allows the build to remain Adventurer's League legal while also minimizing the need for Ability Score Improvements to get STR and CHA to 20. This allows us to fit the Heavy Armor Master feat in for improved survivability at level 9. If you prefer or are required to use the standard array for whatever reason, take the STR+2 Ability Score Improvement instead.

As an aside concerning Human Bladelocks, if you choose the Human Variant race and take +1 to STR and +1 to CHA as your stat bonuses, you can take the Athlete feat and increase STR by another +1 to make your starting ability scores identical to the Dragonborn version of the build. In effect, you are trading the Dragonborn benefits (Draconic language proficiency, Breath weapon, Resistance, advantage on social interactions with dragons) for the benefits of the Athlete feat (better mobility). Any feat that provides +1 to STR could fill this role, but at the time of writing this answer Athlete is in my humble opinion the best option for this build.

Minor Hoard of the Dragon Queen Spoiler Below (Hover over it for text)

Hoard of the Dragon Queen contains a magical Greatsword called Hazirawn which is wielded by the half-dragon Rezmir. Whether you are playing this build in Adventurer's League or just playing the published adventure at home, Hazirawn will provide big boosts to damage numbers and provides great flavor for an Evil Bladelock. Make efforts to retrieve the sword for maximum DPR. I should point out that technically by RAW because Hazirawn is sentient according to its stat writeup it is disqualified from being your Pact Weapon however the argument could be made that Hazirawn was defined before the wording of the PHB was finalized. It also lacks qualities that a sentient weapon should possess according to the DMG. For example, in the HotDQ writeup, Hazirawn has no defined mental ability scores. Also, nothing is given about its personality.

Build Requirements

• Initial attributes are 17/16/13/12/8/8 (STR/CHA/CON/WIS/INT/DEX)
  • 15/15/13/12/8/8 without racial modifiers, obtained from point-buy.
  • 16/16/13/12/10/8 if using the standard ability score array (14/15/13/12/10/8 without racial modifiers)
• Take the Fighter class at character generation.
• Choose the Great Weapon Fighting style.
• Purchase your initial equipment: Greatsword, Chain Mail, Arcane Focus
• Get Plate Mail armor as soon as possible for 18 AC. Magic armor and a Ring of Protection can increase this further later on. See the final recommendations at the bottom of this answer for a list of magic items from the DMG which would be useful to craft or otherwise obtain.
• Take the Warlock class with a Fiend patron, choose Eldritch Blast as one of your initial two cantrips, and choose the Hellish Rebuke and Hex spells as your initial two 1st-level spells at level 2.
• Choose the Devil's Sight and Agonizing Blast invocations at level 3.
• Choose the Darkness spell as your initial 2nd-level spell and the Pact of the Blade expansion feature at level 4.
• Choose the Great Weapon Master feat instead of an Ability Score Improvement at level 5.
• Choose the Thirsting Blade invocation at level 6.
• Choose the Fire Shield spell as your initial 4th-level spell at level 8.
• Choose the Heavy Armor Master feat instead of an Ability Score Improvement at level 9.
• Choose the Lifedrinker invocation and the Ability Score Improvement (STR+2) option at level 13.
• Choose the Ability Score Improvement (CHA+2) option at level 17.
• Choose the Foresight spell as your 9th-level Mystic Arcanum at level 18.
• Choose the Ability Score Improvement (CHA+2) option at level 20.

Average Pact Weapon Attack Rolls By Level /w Advantage (AnyDice Link)

• Level 4: [highest 1 of 2d20]+(2+3) [average ~19]
• Level 5: [highest 1 of 2d20]+(3+3) [average ~20]
• Level 9: [highest 1 of 2d20]+(4+4) [average ~22]
• Level 13: [highest 1 of 2d20]+(5+5) [average ~24]
• Level 17: [highest 1 of 2d20]+(6+5) [average ~25]

As long as you have advantage on the roll, you have a 9.75% chance to land a critical hit and activate the bonus attack from Great Weapon Master. That chance drops to 5% without advantage, but hopefully those instances will be few and far between. The real beauty here though is that the lowest average attack roll with advantage is a 19! That means on average you can take the -5 penalty in exchange for +10 damage from Great Weapon Master and still end up with a 14 or better! That is good enough to hit most creatures in the early game, and by the time you reach top tier play (levels 17-20) your average attack roll after the penalty will still be 20 or higher. To put that another way, that's almost high enough to hit a Challenge 21 Ancient Blue Dragon!

Average Eldritch Blast Attack Rolls By Level /w Advantage (AnyDice Link)

• Level 4: [highest 1 of 2d20]+(2+3) [average ~19]
• Level 5: [highest 1 of 2d20]+(3+3) [average ~20]
• Level 9: [highest 1 of 2d20]+(4+3) [average ~21]
• Level 13: [highest 1 of 2d20]+(5+3) [average ~22]
• Level 17: [highest 1 of 2d20]+(6+4) [average ~24]
• Level 20: [highest 1 of 2d20]+(6+5) [average ~25]

As long as you have advantage on the roll, you have a 9.75% chance to land a critical hit. That chance drops to 5% without advantage, but hopefully those instances will be few and far between. We also see the same lowest average attack roll with advantage from our Pact Weapon. The big difference between these numbers and the Pact Weapon numbers is these will scale up more slowly because we are bumping CHA last to maximize melee damage first. The good news is we don't have to worry about the -5 penalty from Great Weapon Master with Eldritch Blast attack rolls, so scaling up more slowly won't be too big of a deal. It will also not be as rough on your Eldritch Blast attack rolls if for some reason you can't get advantage, or if you want to use Hex instead of Darkness.

Average Pact Weapon Damage Rolls By Level (AnyDice Link)

• Level 1: [gwf 2d6 as 6]+3 [average 11.33]
• Level 5: ([gwf 2d6 as 6]+3+10) [average 21.33]
• Level 6: ([gwf 2d6 as 6]+3+10)*2 [average 42.67]
• Level 9: ([gwf 2d6 as 6]+4+10)*2 [average 44.67]
• Level 13: ([gwf 2d6 as 6]+5+3+10)*2 [average 52.67]
• Level 17: ([gwf 2d6 as 6]+5+4+10)*2 [average 54.67]
• Level 18: ([gwf 2d6 as 6]+1d6+5+4+10)*2 [average 61.67]
• Level 20: ([gwf 2d6 as 6]+1d6+5+5+10)*2 [average 63.67]

As you can see, assuming you hit with every attack, with this build you can be dealing ~43 on average per turn with just your Pact Weapon as early as level 6. Add in damage from Hellish Rebuke and Fire Shield for devastating results (see below). Once you get Foresight at level 18, you can drop Darkness from your strategy and add Hex damage on top of your already brutal attacks. Just because I'm so nice, here is another AnyDice link which provides numbers for an additional attack in case you trigger the bonus attack from Great Weapon Master or have the Haste buff thanks to a Wizard party member.

Average Eldritch Blast Damage Rolls By Level (AnyDice Link)

• Level 2: (1d10+1d6) [average 9]
• Level 3: (1d10+1d6+3) [average 12]
• Level 5: (1d10+1d6+3)*2 [average 24]
• Level 11: (1d10+1d6+3)*3 [average 36]
• Level 17: (1d10+1d6+4)*4 [average 52]
• Level 20: (1d10+1d6+5)*4 [average 56]

The numbers above include Hex damage. They are almost identical to Strill's answer, though there is a slight deviation resulting from me choosing my ability score improvements differently. Here is another AnyDice link to numbers that don't take Hex into account in case you're attacking difficult-to-hit foes with Darkness for advantage on your attack rolls.

Average Hellish Rebuke Damage Rolls By Level (AnyDice Link)

• Level 2: 2d10 [average 11]
• Level 4: 3d10 [average 16.5]
• Level 6: 4d10 [average 22]
• Level 8: 5d10 [average 27.5]
• Level 10+: 6d10 [average 33]

This is important because if you had chosen Polearm Master and a Glaive you would not be able to cast Hellish Rebuke using your reaction. There are at least two ways to approach average Hellish Rebuke damage: assume the target fails its save or assume the target succeeds its save. The numbers shown above opt for the former option. However, here is another AnyDice link which shows the numbers for successful saves.

Bottom Line: Total Average Melee DPR By Tier

• Level 6: Pact Weapon + Hellish Rebuke = 42.67 + 16.12 [average 58.79] [critical average 88.45]
• Level 9: Pact Weapon + Hellish Rebuke + Fire Shield = 44.67 + 20.25 + 2d8 [average 73.92] [critical average 104.58]
• Level 13: Pact Weapon + Hellish Rebuke + Fire Shield = 52.67 + 24.38 + 2d8 [average 86.05] [critical average 120.71]
• Level 17: Pact Weapon + Hellish Rebuke + Fire Shield = 54.67 + 24.38 + 2d8 [average 88.05] [critical average 123.71]
• Level 20: Pact Weapon (/w Hex) + Hellish Rebuke + Fire Shield = 63.67 + 24.38 + 2d8 [average 97.05] [critical average 137.21]

The above numbers are single target damage. They assume you hit your target with all applicable melee attacks. Averages for critical strikes are also given assuming only one crit for each distinct multiple attack sequence. For each additional crit add 8.33, which is the average damage for a Greatsword with Great Weapon Fighting and no bonuses to represent doubling the damage dice from 2d6 to 4d6. It is further assumed that the target you are attacking is attacking you back. These numbers do not assume targets of Hellish Rebuke fail their saves. Instead, for total average DPR I used the average damage for a successful save and the average damage for a failed save at that level to find an average damage independent of the saving throw. You can check out my formulas for this at this AnyDice link.

Final Recommendations

These last few pieces of advice are not absolutely vital to the build, but I felt I would share my feelings on final spell and invocation choices at level 20. I've also included some suggestions for what magic items from the DMG are best to craft in the event your DM allows you to craft magic items using your money and downtime. They are organized by item rarity.

Invocations by Level

If you can't convince your DM to let you bind Hazirawn as your Pact Weapon or you're not going to be playing Hoard of the Dragon Queen, then you may want to swap out either Mask of Many Faces or Visions of Distant Realms for Eldritch Sight.

• Devil's Sight - Level 3
• Agonizing Blast - Level 3
• Thirsting Blade - Level 6
• Beguiling Influence - Level 8
• Mask of Many Faces - Level 10
• Lifedrinker - Level 13
• Witch Sight - Level 16
• Visions of Distant Realms - Level 19

Final Spell Choices

Some of these are admittedly purely for flavor reasons (hi Plane Shift!). At level 18 I gained Foresight and swapped out Darkness for Invisibility. Disguise Self and Arcane Eye are the result of at-will invocations from the list above. As previously mentioned, you may or may not want to swap one of those at-will utility spells for Detect Magic.

• Cantrips: Eldritch Blast, Mage Hand, Minor Illusion, Prestidigitation
• 1st-level: Armor of Agathys, Command, Disguise Self, Hellish Rebuke, Hex
• 2nd-level: Invisibility, Mirror Image, Scorching Ray
• 3rd-level: Dispel Magic, Fireball, Fly, Hypnotic Pattern
• 4th-level: Arcane Eye, Banishment, Fire Shield, Dimension Door
• 5th-level: Scrying
• 6th-level: Mass Suggestion
• 7th-level: Plane Shift
• 8th-level: Glibness or Feeblemind (I haven't quite decided which one I feel is the best option yet)
• 9th-level: Foresight

DMG's Magic Item Crafting Considerations

For the Rod of the Pact Keeper, ask your DM if you can make it a ring instead that you can wear.

Uncommon:

• Adamantine Plate Mail Armor, DMG page 150
• Cloak of Protection, DMG page 159
• Mithral Plate Mail Armor, DMG page 182
• Ring of Mind Shielding, DMG page 191
• Rod of the Pact Keeper +1, DMG page 197

Rare:

• Dragon Slayer, DMG page 166
• Plate Mail Armor +1, DMG page 152
• Ring of Protection, DMG page 191
• Rod of the Pact Keeper +2, DMG page 197

Very Rare:

• Dwarven Plate Mail Armor, DMG page 167
• Plate Mail Armor +2, DMG page 152
• Ring of Regeneration, DMG page 191
• Rod of the Pact Keeper +3, DMG page 197

Legendary:

• Defender, DMG page 164
• Plate Mail Armor +3, DMG page 152
• Plate Mail Armor of Etherealness, DMG page 185
• Plate Mail Armor of Invulnerability, DMG page 152

What level find familiar is cast at depends on how the warlock casts it.

When she gains the Pact of the Chain class feature, the warlock learns find familiar. It doesn't count against her spells known, but nothing in the ability text prevents her from casting it with her spell slots. If she casts it with her spell slots, it works exactly like any other spell she knows how to cast. If she is 5th level when she casts it, she casts it as a third-level spell.

In addition, the warlock gains the ability to cast find familiar -- and only find familiar -- as a ritual. When a spell is cast as a ritual, it always uses the normal spell level of a spell. When the warlock casts find familiar as a ritual, she casts it as a first-level spell no matter what her warlock level may be.