alns 4.0.0

A flexible implementation of the adaptive large neighbourhood search (ALNS) algorithm.

This package offers a general, well-documented and tested implementation of the adaptive large neighbourhood search (ALNS) meta-heuristic, based on the description given in Pisinger and Ropke (2010). It may be installed in the usual way as

pip install alns

Examples

If you wish to dive right in, the examples/ directory contains example notebooks showing how the ALNS library may be used. These include:

• The travelling salesman problem (TSP), here. We solve an instance of 131 cities to within 2% of optimality, using simple destroy and repair heuristics with a post-processing step.
• The cutting-stock problem (CSP), here. We solve an instance with 180 beams over 165 distinct sizes to within 1.35% of optimality in only a very limited number of iterations.
• The resource-constrained project scheduling problem, here. We solve an instance with 90 jobs and 4 resources to within 4% of the best known solution, using a number of different operators and enhancement techniques from the literature.

Finally, the features notebook gives an overview of various options available in the alns package (explained below). In the notebook we use these different options to solve a toy 0/1-knapsack problem. The notebook is a good starting point for when you want to use different schemes, acceptance or stopping criteria yourself. It is available here.

How to use

The alns package exposes two classes, ALNS and State. The first may be used to run the ALNS algorithm, the second may be subclassed to store a solution state - all it requires is to define an objective member function, returning an objective value.

The ALNS algorithm must be supplied with a weight scheme, an acceptance criterion, and a stopping criterion.

Weight scheme

The weight scheme determines how to select destroy and repair operators in each iteration of the ALNS algorithm. Several have already been implemented for you, in alns.weights:

• SimpleWeights. This weight scheme applies a convex combination of the existing weight vector, and a reward given for the current candidate solution.
• SegmentedWeights. This weight scheme divides the iteration horizon into segments. In each segment, scores are summed for each operator. At the end of each segment, the weight vector is updated as a convex combination of the existing weight vector, and these summed scores.

Each weight scheme inherits from WeightScheme, which may be used to write your own.

Acceptance criterion

The acceptance criterion determines the acceptance of a new solution state at each iteration. An overview of common acceptance criteria is given in Santini et al. (2018). Several have already been implemented for you, in alns.accept:

• HillClimbing. The simplest acceptance criterion, hill-climbing solely accepts solutions improving the objective value.
• RecordToRecordTravel. This criterion accepts solutions when the improvement meets some updating threshold.
• SimulatedAnnealing. This criterion accepts solutions when the scaled probability is bigger than some random number, using an updating temperature.

Each acceptance criterion inherits from AcceptanceCriterion, which may be used to write your own.

Stoppping criterion

The stopping criterion determines when ALNS should stop iterating. Several commonly used stopping criteria have already been implemented for you, in alns.stop:

• MaxIterations. This stopping criterion stops the heuristic search after a given number of iterations.
• MaxRuntime. This stopping criterion stops the heuristic search after a given number of seconds.

Each stopping criterion inherits from StoppingCriterion, which may be used to write your own.

References

• Pisinger, D., and Ropke, S. (2010). Large Neighborhood Search. In M. Gendreau (Ed.), Handbook of Metaheuristics (2 ed., pp. 399-420). Springer.
• Santini, A., Ropke, S. & Hvattum, L.M. (2018). A comparison of acceptance criteria for the adaptive large neighbourhood search metaheuristic. Journal of Heuristics 24 (5): 783-815.