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Late Acceptance Hill Climbing in Python

Project description

Late Acceptance Hill Climbing

Implementation of Late Acceptance Hill Climbing (LAHC) algorithm by Burke and Bykov [Burke2017] in python.


Either download the repository to your computer and install, e.g. by pip

pip install .

or install directly from the python package index.

pip install lahc


The package provides a base class for subclassing to a specific problem. The move and energy methods must be implemented by the user before the algorithm is applied.

The user controls the algorithm by adjusting a single algorithmic parameter, the history length, and the termination criteria for the algorithm. See subsection on each of the topics below.

The search is started by calling the run method.

The example is a good place to start using of the package.

The implementation relies heavily on copying the state. The default copy strategy (copy_strategy='deepcopy') relies on the STL copy.deepcopy method which works for most data structures, but is typically quite slow. Large performance gains can be easily obtained by adapting a different copying strategy, see the documentation of the copy_state method.

The history length

The behaviour of the LAHC algorithm is governed by a single parameter, the history length. To alter the history length of the algorithm, adjust the history_length parameter of the class.

If the history length is set to one, the LAHC algorithm is equivalent to a greedy Hill Climbing algorithm. Increasing the history length generally improves the solution quality, but also increases the time to convergence.

Selection of the history length should therefore be based on requirements for the quality of the solution and time available for the analysis.

A useful characteristic of the LAHC heuristic is that the runtime to convergence is roughly proportional to the history length. The runtime at any history length can therefore be estimated after applying the algorithm at a few different history lengths.

As a general recommendation, start at a low history length and gradually increase it to determine the runtime and variation in the estimated results. Select a shorter history length that allows multiple runs in the time allocated for simulations rather than a longer history length with a single run.

Termination criteria

The algorithm terminates when the terminate_search method evaluates to True or when a interupt signal (Ctrl-C) is sent to the process.

The default behaviour of the terminate_search method is to terminate the algorithm when a minimum number of attempts has been made and the algorithm has not been able to improve the solution for a certain number of steps. The minimum number of steps and necessary number of idle iterations can be adjusted with the steps_minimum and steps_idle_fraction parameters, respectively.

The default value of the steps_idle_fraction (0.02) is generally a good choice for a variety of problems, but the default steps_minimum value (100000) may have to be adjusted depending on the problem. As a general recommendation, the user should reduce the steps_minimum parameter if the algorithm consistently terminates at steps_minimum after running for a long period without improving the solution.


Both the structure and parts of the source code for the LateAcceptanceHillClimber class is copied from the Annealer class in the simanneal python project. All contributions from the simanneal project is hereby gratefully acknowledged. Check out the simanneal project at

which implements the widely used and sucessful Simulated Annealing metaheuristic.


Please open an issue for support.


Please contribute using Github Flow. Create a branch, add commits, and open a pull request.


[BURKE2017]E. K. Burke, Y. Bykov, The late acceptance Hill-Climbing heuristic. European Journal of Operational Research. 258, 70–78 (2017).

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