Skip to content

Archive Container

The pareto::archive container is also both an adapter and an extension of spatial containers to cache objects representing conflicting alternatives:

1
2
// Three-dimensional Pareto archive
pareto::archive<double, 3, unsigned> m;

1
2
# Python Three-dimensional Pareto archive
m = pareto.archive()

They are useful in dynamic applications where the best objects might not be available in the future and we might need a second best. Archives are especially useful in all dynamic applications that use fronts, such as:

  • P2P networks
  • multi-criteria decision making
  • generate-and-test optimization algorithms
  • robust optimization

Tip

You can think of archives as a multidimensional stack.

Example

This is what a two-dimensional archive would look like:

2-dimensional front

Plotting Archives

The header pareto/matplot/archive.h includes some snippets to plot these archives with Matplot++.

Archive Capacity

All archive constructors include an optional parameter to define the maximum number of elements in the archive. If no maximum capacity for the archive is explicitly set, the capacity is set to \(\min(50 \times 2^m, 100000)\). The exponential factor \(2^m\) in this heuristic is meant to take the curse of dimensionality in consideration.

Data scientists often use linear lists to represent these fronts, with a cost of \(O(mn^3)\) p1 for several operations. With spatial indexes, this cost reduces to just \(O(m \log^2 n)\).

You have probably noticed by now that containers for fronts and archives have lots of use cases:

Use case Common keys
Machine Learning Accuracy vs. Complexity vs. Time
Approximation algorithms Error vs. Time
Product design Investment vs. Profit vs. Safety vs. Performance vs. Scope
P2P networks Latency vs. Trust vs. Availability
Robust optimization Average quality vs. Robustness
Design Average quality vs. Standard deviation
Systems control Performance vs. Price vs. Quality
Portfolio optimization Expected return vs. Risk
More... ...