It depends of the problem. If you have NP-Hard combinatorial problem the precision does not matters. If you have real-time military system, for example, the CPU is everything.

Most operational optimization problems such as the ones related to routing and/or scheduling of vehicles and crews, fleet assignment and network recovery, to mention some examples, need rapid answers, but are NP-hard problems. In these cases, it is more important to get near-optimal solutions in short times than a very precise answer. This is the reason for the development of heuristics and meta-heuristics models to solve them.

Just adding something to the replies above. I've been working on a method to dynamically find an equilibrium between time and solution quality by adjusting the population size of population-based metaheuristics on-the-run.

This is my first paper on this subject: Conference Paper Population Size Control for Efficiency and Efficacy Optimiza...

Obviously these are preliminary results and a much more interesting paper is being prepared.

Dear colleagues

Any optimization methodology has to be Performant and Convergent.

So, in optimization process both Precision and CPU time are required:

Precision refer to the Performance of the tool (the algorithm or the methodology) and CPU time refer to the algorithm's time complexity which refer in turn to its Convergence.

Sincerely, Djamel

With respect to the two criteria "Time" and "Precision", optimization problems can be classified into two main categories: "Unimodal" and "Multimodal". In a unimodal optimization problem (e.g. sphere modal), only a single optimum (maximum or minimum) solution exists around many other non-optima solutions. For such problems, it is reasonable to check the "velocity" (i.e. "line-oriented search" or "path-oriented search") ability of the algorithm to find such single optimum solution as quickly as possible. Thus, here, "Time" is critical. For a multimodal optimization problem, however, many "local optima" exist, trapping the "global optimum single solution". For such problems, it is more reasonable to check the "volume-oriented search" ability of the algorithm to "precisely" escape form those local traps and to locate "reliably" the near optimal solutions or, in the best case, to find the global optimum solution. It is worth to note that, almost all real-world optimization problems fall into the category of multimodal problems.

Precision

Both of them are important because you should concern the trade-off. However, generally, Precision more important than time.

I liked what it has been said above. I just want to add my thought. Basically, when using approximation approaches to solve optimization problems, precision and time are two conflicting factors. This means one of them should be sacrificed to improve the other, but, the level of sacrifice is problem-dependent, though I am keen to the idea that in most optimization problems the precision is more crucial.

Dear Anwar,

I agree with you. I have pointed out in my answer that there are kinds of problems that are of the NP-Hard class and, so, they cannot be solved in desired times by exact methods, requiring the use of heuristics or metaheuristics to be solved, with sacrifice of precision.

Precision is more important than the CPU Time in Most of the optimization problems