The Role of Metaheuristics as Solutions Generators

Abstract

Optimization problems are ubiquitous nowadays. Many times, their corresponding computational models necessarily leave out of consideration several characteristics and features of the real world, so trying to obtain the optimum solution can not be enough for a problem solving point of view. The aim of this paper is to illustrate the role of metaheuristics as solutions’ generators in a basic problem solving framework. Metaheuristics become relevant in two modes: firstly because every run (in the case of population based techniques) allows to obtain a set of potentially good solutions, and secondly, if a reference solution is available, one can set up a new optimization problem that allows to obtain solutions with similar quality in the objectives space but maximally different structure in the design space. Once a set of solutions is obtained, an example of an a posteriori analysis to rank them according with decision maker’s preferences is shown. All the problem solving framework steps, emphasizing the role of metaheuristics are illustrated with a dynamic version of the tourist trip design problem (for the first mode), and with a perishable food distribution problem (for the second one). These examples clearly show the benefits of the problem solving framework proposed. The potential role of the symmetry concept is also explored.

The Fifteen Puzzle—A New Approach through Hybridizing Three Heuristics Methods

“…However, our implementation of the BA* algorithm with the three heuristics does not find optimal solutions for most of the Fifteen Puzzle instances, the difference between the solution length found by BA* and the optimal solution for each puzzle instance does not increase when the puzzle instance requires more moves to optimally reach the goal. Nowadays, metaheuristic optimization algorithms are widely used for solving complex problems [33], [34], [35]. One of the algorithms that have been recently used to obtain non-optimal solutions to the Fifteen Puzzle problems was a metaheuristic algorithm Artificial Bee Colony (ABC) [36].…”

A Critical Analysis of a Tourist Trip Design Problem with Time-Dependent Recommendation Factors and Waiting Times

“…As we have seen, adding new features to a model in order to make it more realistic may complicate its solving process. However, in cases where those features are indeed justified, a feasible alternative would be to obtain a set of solutions to a simpler model and include such features a posteriori in the way proposed in [25]. Now, for most test instances the optimal overall interest is available in both models, thus paving the way to explore the use of metaheuristic algorithms to solve them.…”