I have said the following in other threads.
There are several types of optimization and not all forms include power gaming or mini-maxing, I distinguish between the three and none of which need include cheating which is a separate issue.
Player motivations can play a role in the type of optimization, Robin Law identified several player motivations as did D&D 4e. I don't have my 5e DMG with me so I don't recall what it had to say. The categories Butt-Kicker (4e Slayer), Power Gamer, Method Actor (4e Actor), Specialist (no 4e equivalent), Storyteller, Tactitcan (4e Thinker), Casual (4e Watcher) while D&D 4e added the Explorer and Instigator These motivations can lead to different optimization goals, different beliefs about what type of optimization and/or degree of optimization is appropriate or inappropriate, and the purpose of playing the game. When one or more of these views are in opposition to those of others at table, conflict can arise. It is also important to realize that individual players tend to be a mix of the different motivations
These are my thoughts on optimization which I have shared in other threads
1. Optimization is a tool to meet a goal or goals related to one's character concept. The goal can be directed to combat, power, a focus on a particular skill, or to best mechanically reflects an overall character concept. Any time that a player assigns/allocates resources to meet a particular goal or concept they are engaging in optimization. The only way to avoid optimization would be to randomly generate the character or assign things haphazardly without thought of the character and how to represent it .
2. Optimization is not binary. There are degrees of optimization. It is a continuum on an axis. Someone randomly rolling the mechanical aspects without any choice in assignment or haphazardly assigning without thought would be 0 (or not engaging) on the axis. However, as soon as one begins prioritizing resources to a concept, they are participating in some degree of optimization. For instance, placing one's highest ability score in Dex, because it gives your rogue bonuses on their rogue related proficiencies is optimizing. Taking a skill or proficiency to mechanically reflect a character's training and gain the mechanical benefit is also engaging in a degree of optimization. Someone scouring every tome for every last point is going to be at the far end of the spectrum.
3. Optimization need not have the goal of focusing on a single area and getting the most efficiency or output possible in that area. First, as stated in #2 above, optimization is on a continuum. Second, it is possible to have multiple goals that need to be met. When this occurs, it is often necessary to trade off maximum possible efficency/output in one or more areas to meet established goals for other areas This is called Systems Optimization.
4. If the mechanical representation of a character is a goal involving at least some forethought in the allocation of resources to achieve that representation, I submit that what many people consider just "building a character" does involve a degree of optimization. One has a vision of their character and assigns resources (ability scores (and points if doing point buy), proficiencies (or skill points in some editions). Furthermore, since optimization is not binary, the degree of optimization is how much effort is spent by the player fine tuning the mechanical aspects and bonuses to best get close to the ideal vision he or she character at the point of beginning play.
The two primary players motivations that I see complaints about are the Butt-Kicker and Power Gamer. However, at their base, both are motivations and neither requires optimization. The Butt-Kicker's is focused on combat. The Power Gamer desires to play a powerful character (whatever that means in terms of the game).
Butt-Kickers tend to focus on combat. When they optimize, they tend to focus upon larger numbers related to hitting opponents and damage output, because combat is their emphasis for playing and around which they build their character .
The Power Gamer is often confused with the butt-kicker. However, If the campaign or system is not heavy in combat, an optimizing Power Gamer will optimize toward whatever is considered powerful for that campaign/system. More importantly, both Laws (in his book on good gaming) and D&D 4e defined the Power Gamer as being motivated by playing a powerful character and/or the accumulation of power. Thus, there are different types of Power Gamers. 1) A Power Gamer can simply be someone playing with an emphasis upon the cycle of leveling, gaining cool powers/equipment, and the accumulation of power (the standard play cycle of D&D) which needs no engagement in optimization; 2) Playing a powerful character can mean the player requires that a PC have a level minimum competence level (e.g. SWAT officer, Special Forces, or Olympic Athlete) or some other minimum above an average person for a character to be playable (this can be met by choice of game or in a game like D&D starting at a higher level; or 3) the player wants their character to outshine other PCs as wells as NPCs (which is an issue in and of itself for a cooperative game) Therefore, as with Butt-kickers, Power Gamers need not optimize, but it is a useful tool toward their goal
For both the Butt-Kicker and Power Gamer optimization is a useful tool, However, optimization by either type of player need not be a problem in and of itself, because optimization is a continuum on an axis. It is only when the player's degree of optimization crosses a certain threshold (dependent on the preference of the GM and/or other group members) that it becomes becomes a problem. This is a play style preference issue and can happen when a particular player's preference(s) (regardless of style/motivation) does not mesh with that of the GM and/or group of as a whole (e.g. a storyteller in a group of Butt-Kickers that rate low on the storytelling axis). The solution is talking out expectations before character generation and, if necessary, when expectations come into conflict to address the issue whether that means a compromise can be reached or it is decided that individual expectations are not a match and the player in question would be better off with a more compatible group.