The real Pareto is the lawyer who was the victim of the Telerj prank call in the 80s. Don't be fooled!
Pareto Front
101–110 of 116 posts
Re: Pareto Front
#102> and every solution not in the set is outperformed by at least one solution in the Pareto front in every objective
Is that trying to say:
"for every solution not in the set, there exists at least one objective such that at least one solution in the Pareto set beats that solution in that objective" i.e. every non-Pareto-front solution is beaten in some objective(s) by a Pareto-front solution, however it may be unbeaten in other objectives.
Or is it:
"for every objective in the system, every solution that is not in the set is beaten in that objective by one or more Pareto-set solutions."
Or is it:
"For every solution not in the set, there exists at least one Pareto solution which beats it in every objective."
Re: Pareto Front
#103I am training for a marathon, and, as I increase both by distance and pace, I am always excited when I have a "Pareto run": a run along the Pareto frontier of me trying to maximize distance and speed. When explaining it to some coworkers, I stumbled on a fairly intuitive explanation: "I've run farther before, and I've run faster before, but I've never run _this_ far, _this fast." There was some pushback about why not…
So, while it's true that your runs with high speed and distance when both are considered are Pareto points, your max speed run and max distance run overall are also Pareto points. So calling these high distance+speed runs "Pareto" doesn't actually distinguish them completely from other runs. A point is Pareto so long as it is non-dominated —that is, you're not looking for dominating points, you're looking for points…
They never said it was the only Pareto run? Just a new one, improving the overall Pareto front
Re: Pareto Front
#104> and every solution not in the set is outperformed by at least one solution in the Pareto front in every objective Is that trying to say: "for every solution not in the set, there exists at least one objective such that at least one solution in the Pareto set beats that solution in that objective" i.e. every non-Pareto-front solution is beaten in some objective(s) by a Pareto-front solution, however it may be unbeat…
The latter. Every solution not in the set is 'dominated' (outperformed in every objective) by some specific point in the set.
Re: Pareto Front
#105Earlier quoted context omitted.
So, while it's true that your runs with high speed and distance when both are considered are Pareto points, your max speed run and max distance run overall are also Pareto points. So calling these high distance+speed runs "Pareto" doesn't actually distinguish them completely from other runs. A point is Pareto so long as it is non-dominated —that is, you're not looking for dominating points, you're looking for points…
They never said it was the only Pareto run? Just a new one, improving the overall Pareto front
Ugh, you're right! I read too quickly. Please disregard me OP. I'll leave the comment here just in case it clarifies things for poor readers such as myself lol.
Re: Pareto Front
#106I’m sadly twitchy when I hear “Pareto” - having endured numerous middle managers suggesting they can deliver 80% of the scope in 20% of the time (unrelated to the frontier topic here). Do that at each level of an org and the nonsense multiples rapidly. The 80/20 “rule,” as far as I know, is meant to be descriptive after the fact. It can’t be used as a planning assumption. To be fair to those managers, they don’t real…
Managers trying to justify _cutting_ scope... Is your planet accepting immigrants? I think I'd like it there
They don’t cut the visible scope. They cut the monitoring, failover, automated patching, test coverage, deployment improvements, documentation, etc.
Re: Pareto Front
#107A kind of Pareto domination criterion is used in C++ for determining overload resolution: which function overload gets the call.
The objectives are matching arguments to parameters.
A set of functions is identified among the candidates: those that are possible for the call at all, like having a compatible number of parameters.
Essentially, the overload rule says that the Pareto front set of candidates must contain one member, otherwise the call is considered ambiguous, and diagnosable rule violation.
The objectives being optimized are individual parameter positions, each in the dimension of suitability: being a better match.
One candidate is better than another if it is no worse a type match in every parameter, and strictly better in at least one parameter.
Re: Pareto Front
#108> and every solution not in the set is outperformed by at least one solution in the Pareto front in every objective Is that trying to say: "for every solution not in the set, there exists at least one objective such that at least one solution in the Pareto set beats that solution in that objective" i.e. every non-Pareto-front solution is beaten in some objective(s) by a Pareto-front solution, however it may be unbeat…
The latter. Every solution not in the set is 'dominated' (outperformed in every objective) by some specific point in the set.
The way it's written is misleading. The Pareto front solutions are all dominators of the non-solutions, but not dominators of each other.
For A to dominate B, A has to be at least as good (i.e. no worse) than B in every objective under consideration and A has to be strictly better than B in at least one objective.
Every solution in the Pareto front set dominates every solution not in that set: is at least as good in all optimization parameters and strictly better in at least one.
Among the front set, there is no mutual dominance: if we pick any pair out of the set, one may be better than the other in one or more parameters, but worse in one or more. If it were not worse in one or more than the other, that other would not belong in the front set due to being dominated.
Consider a space where we have two solutions. One is no worse than the other in every objective, and strictly better in one objective. Here, our Pareto front set contains that one solution and the other one is not in the set. Yet, the one not in the set is not beaten in every objective, just in that objective where the dominator is strictly better.
Re: Pareto Front
#109Earlier quoted context omitted.
The latter. Every solution not in the set is 'dominated' (outperformed in every objective) by some specific point in the set.
The way it's written is misleading. The Pareto front solutions are all dominators of the non-solutions, but not dominators of each other. For A to dominate B, A has to be at least as good (i.e. no worse) than B in every objective under consideration and A has to be strictly better than B in at least one objective. Every solution in the Pareto front set dominates every solution not in that set: is at least as good in…
Yes sorry, dominant means strictly better in some sense, but may be equal in many objectives.
> Every solution in the Pareto front set dominates every solution not in that set
Not quite – for each solution not in the set, there exists a solution in the set that dominates it. For instance a front with (0,2) (1,1) (2,0) would not have (1,0). While (0,2) doesn't dominate (1,0), something else does.
Re: Pareto Front
#110Earlier quoted context omitted.
The way it's written is misleading. The Pareto front solutions are all dominators of the non-solutions, but not dominators of each other. For A to dominate B, A has to be at least as good (i.e. no worse) than B in every objective under consideration and A has to be strictly better than B in at least one objective. Every solution in the Pareto front set dominates every solution not in that set: is at least as good in…
Yes sorry, dominant means strictly better in some sense, but may be equal in many objectives. > Every solution in the Pareto front set dominates every solution not in that set Not quite – for each solution not in the set, there exists a solution in the set that dominates it. For instance a front with (0,2) (1,1) (2,0) would not have (1,0). While (0,2) doesn't dominate (1,0), something else does.
Yes; it is not relevant whether the dominating solution is in the set or not.
It is a fact that the solutions in the front dominate all those not in the front, but the weakest statement we can make is that if a for a given solution B, we find another one A which is a dominant of B, then B is not in the front (regardless of whether or not A is).
Anyway, a couple of hours ago, I fixed up the informal wording in the article, which had misleading interpretations.