Let’s say in a problem solving situation or an exertion of the will of a being with a purpose, when all of the downsides, negatives, and evils have been reduced as much as they can given the parameters of the problem and the tools available for solving it, then the evils associated with the solution or act have been optimized. It is not enough that some good come from an evil, nor is it enough that more good come from the evils. It might not be worth it, or there might be some better solution available with less evil. Suppose that you have a tooth that has a cavity that needs to be treated. You could continue to ignore it. Or a neighbor has offered to pull it out with some pliers with no anaesthetic for free. Or you can go to the dentist on 25th street who will fill the cavity for $500. Or there is another dentist on B street who will fill the cavity for $250, and you have every reason to think that the 25th street dentist and the B street dentist will do equivalent work. You can afford $250, but not $500 for the problem. There are 4 solutions available in the situation, but one of them is better overall than the others. The evil that you will have to endure with the B street dentist, the discomfort of getting the tooth worked on, the lost time from work, and the $250, is optimized with regard to the solution which is addressing the cavity.
Theistic solutions to the problem of evil should be understood from the other side of the equation. We find ourselves in the midst of what might possibly be the equivalent of a complicated, painful, and very large procedure that is lasting for eons. If there is an omni God, then the evils of the procedure would have been optimized. Every pain, every death, every bit of suffering, and every parking ticket or ingrown toenail would have been minimized as much as is logically possible. But we don’t and can’t know from seeing the planning and decision making process that things have in fact been optimized. We don’t even know that there was planning or decision making process at all or that any of it has a point. And the analogy is strained by the fact that God is alleged to be an omni-being. The dentist (and your neighbor) is limited by her knowledge, her tools, her education, her ability to deaden pain, and her materials. She will readily admit that her methods are not perfect, but they are the best she can do. But an omni-being would suffer none of those physical limitations of knowledge and power. An omni-being would be able to produce the best solution that is logically, not just physically, possible.
From where we are in all of this, all we can do is observe features of the events surrounding us and try to figure out first, if there was a planning and decision making process to it at all, and second if there are any reasons to think from the events around us that every single evil that has ever transpired is an optimized evil. Is someone going to work on us with a pair of rusty pliers? Is there any point to it all? Or is it evident that this is the most highly tuned, sensitive and pain-efficient procedure that an infinitely wise, good, and powerful being could have produced?
In every case in your life where you perform some action from the most trivial to the most important, you do so on the presumption that the world could be better in some fashion than it actually is. Things would be better if I had a cup of coffee. Things would be better if we could achieve peace in the middle east. Things would be better if a Democrat was elected president. Things would be better if I stepped out of the path of that oncoming bus. Right now, without even thinking about it very hard, you can come up with a thousand ways in which the world could be improved. And you can come up with a list that isn’t just about improving it selfishly for you, but ways in which it could really be improved for everybody.
First, it’s hard to see how we could possibly rectify believing that evil has been cosmically optimized with any sort of action on our parts. Second, it’s also obvious that every decision that you make, opinion that you express, and action you perform presumes that evil has not been optimized in the world. If we didn’t presume that things are not optimal, we’d have no grounds for acting. Third, of the face of it, every one of us encounters a multitude of situations every day where it sure looks like things could be better than they are, if only by a little bit.
So the burden of proof for theism in the face of the problem of evil is to overcome all of the evidence in all of our lives for a suboptimal world and show that evil has been optimized in every regard for every moment of all of history. The indirect route of doing that is to give an argument for an OG’s existence that is more compelling than the extent to which evil does not appear to be optimized. Can the burden of proof that all evil in the history of sentience is optimized evil be met? Do we have reasons for believing in God that are more compelling than all of the suffering in history. I don’t think that we have such reasons. The vast majority of people, even the believers, seem to agree that the existence of God is not the sort of thing that can be proven or shown through argument.