The problem posed is a multiobjective optimization problem, and the usual notion of optimality for these types of problems is Pareto optimality.
Scalarization (as proposed in the comments by ChristianClason, TheNobleSunfish, Paul, and DougLipinski) is one way to solve the problem. This approach leverages the large body of theory and algorithms for single objective optimization problems, at which point R packages for single objective optimization could be used. A list of these packages can be found here.
There are other methods for solving multiobjective optimization problems. I haven't had more than a single class on multiobjective optimization methods, so I don't claim to be an expert, but I would look at that literature for details on solution methods. In terms of R packages, you might try looking at mco or emoa. Both methods appear to use evolutionary algorithms, which at first glance look to belong to the same class of algorithms as genetic algorithms.