nondLib: A C++ library for archiving operations on nondominated point sets

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Maintainer: Duarte M. Dias

Contributors: Duarte M. Dias, Alexandre D. Jesus, Luís Paquete.

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This library implements several operations to filter and maintain a set of nondominated points. In particular, the current version supports the following operations:

• filter - filters a set of nondominated points from a larger set of points
• update - updates the nondominated point set with a new point

Both in-place and not-in-place versions exist for all currently implemented functions, such that the former implies modifying the container that is passed to the function, and the latter simply returns a new container.

The details for some of the functions are explained in the following article:

Duarte M. Dias, Alexandre D. Jesus, Luís Paquete, A software library for archiving nondominated points, GECCO 2021 (to appear).

Note: this is an early version of the library, and as such there may be breaking changes.

Usage

The library is provided as a single header for ease of portability. As such, all there is to do is copy the nondlib.hpp file into your project and include it in your .cpp files. Note that the use of this library currently requires at least C++ 14.

For a usage example, see the examples folder.

Library Functions Details

Currently, most functions require an archive to be passed as a reference to an std::vector<C>, such that type C denotes a point in the objective space implemented as a container. Exactly which containers are supported for C depends on the particular library function but random access containers are always valid, e.g std::vector, std::array, and std::deque.

Moreover, most functions also require a random access container parameter named maxima, which denotes whether minimization (maxima[i] = -1) or maximization (maxima[i] = 1) should be considered for a given objective i.

In-place functions

The following in-place functions are implemented

Quadratic-time algorithm for filter operation and any number of dimensions

// Parameters:
//   v - Point set to be filtered
//   maxima - A random access container denoting whether minimization or
//            maximization should be considered for each objective
//
// Undefined behavior if:
//   - v[i].size() != maxima.size() for any i
//   - abs(maxima[i]) != 1
template <typename C, typename M>
void nondlib::inplace::filterQuadD(std::vector<C> &v, M const& maxima);

Dimension-sweep algorithm for filter operation in 2D

// Parameters:
//   v - Point set to be filtered
//   maxima - A random access container denoting whether minimization or
//            maximization should be considered for each objective
//
// Undefined behavior if:
//   - v[i].size() != maxima.size() for any i
//   - abs(maxima[i]) != 1
template <typename C, typename M>
void nondlib::inplace::filterDimSweep2D(std::vector<C> &v, M const& maxima);

Dimension-sweep algorithm for filter operation in 3D

// Parameters:
//   v -Point set to be filtered
//   maxima - A random access container denoting whether minimization or
//            maximization should be considered for each objective
//   obj - Specifies the primary dimension for sorting v (default is 0)
//
// Undefined behavior if:
//   - v[i].size() != maxima.size() for any i
//   - abs(maxima[i]) != 1
//   - obj > 2
template <typename C, typename M>
void nondlib::inplace::filterDimSweep3D(std::vector<C> &v, M const& maxima, size_t obj = 0);

Multidimensional divide-and-conquer algorithm for filter operation in any number of dimensions

// Parameters:
//   v - Point set to be filtered
//   maxima - A random access container denoting whether minimization or
//            maximization should be considered for each objective
//   base - base case for the algorithm, either 2 or 3 (default is 3)
//
// Undefined behavior if:
//   - v[i].size() != maxima.size() for any i
//   - abs(maxima[i]) != 1
template <typename C, typename M>
void nondlib::inplace::filterDivConqD(std::vector<C> &v, M const& maxima, size_t base = 3);

Dimension-sweep algorithm for update operation and any number of dimensions

// Parameters:
//   v - Nondominated point set to be updated
//   maxima - A random access container denoting whether minimization or
//            maximization should be considered for each objective
//   p - point to be inserted into set v (if not dominated) with a type that is
//       random access container and that can be used to construct a type C
//       container
//
// Returns: a boolean denoting whether or not the nondominated set v was updated
//       
// Undefined behavior if:
//   - v[i].size() != maxima.size() for any i
//   - p.size() != maxima.size()
//   - abs(maxima[i]) != 1
template <typename C, typename M, typename P>
bool nondlib::inplace::updateMaximaND(std::vector<C> &v, M const& maxima, P &&p);

Not-in-place functions

The not-in-place versions of the library are implemented under the nondlib::notinplace namespace using the same function names and parameters. The two main differences are that point set v is passed as a const reference, and that the filtered/updated set is returned from the function as a vector. Example for the filterQuadD function:

// Parameters:
//   v - Objective point set to be filtered
//   maxima - A random access container denoting whether minimization or
//            maximization should be considered for each objective
//
// Returns: The filtered nondominated set. 
//
// Undefined behavior if:
//   - v[i].size() != maxima.size() for any i
//   - abs(maxima[i]) != 1
template <typename C, typename M>
std::vector<C> nondlib::inplace::filterQuadD(std::vector<C> const& v, M const& maxima);

How to cite

Duarte M. Dias, Alexandre D. Jesus, Luís Paquete, A software library for archiving nondominated points, GECCO 2021 (to appear).