Metaheuristics for Stochastic Problems

Abstract

A large number of publications have been written about metaheuristics and their use in solving deterministic optimization problems. As metaheuristic techniques become more widespread in the production of decision support systems, it is clear that they also need to cope with problems, based on real‐world applications, that contain noise and uncertainty. An increasing amount of work is being put into the study of metaheuristics for stochastic problems, and into how metaheuristics must be adapted to efficiently handle different sources of stochasticity. We give examples of how metaheuristics have been used to solve stochastic problems, thereby illustrating the additional considerations that are required in this context.

Composing Vessel Fleets for Maintenance at Offshore Wind Farms by Solving a Dual-Level Stochastic Programming Problem Using GRASP

“…Restrictions regarding weather conditions are enforced through constraints (17). The time of completing a task is found by applying constraints (18) and constraints (19). Finally, the domains of the variables are given by constraints ( 20)- (23).…”

“…While there are man-hours left (t p f v > 0) and there are maintenance tasks available (line 13), the maintenance task with the highest cost per man-hour left is selected, the vessel is assigned to this task, and the number of man-hours left both for the maintenance task and vessel type is updated (lines 14-17). If t f m = 0, then maintenance task m is completed, removed from the set M p f , and the variable γ p f m is set to 1 (lines [18][19][20]. If all vessels of type v are assigned in the current period, it is removed from the set V p (lines [24][25][26].…”

“…At the same time, it may be the first time that GRASP has been used to solve any MFSMP [1,8], and only the second application of any metaheuristic to a dual-level stochastic problem [10,16]. The surveys of metaheuristics for stochastic problems by Bianchi et al [17], Gutjahr [18], and Hvattum and Esbensen [19] provide further evidence that GRASP has very rarely been used to solve problems with uncertainty. On the other hand, other metaheuristics have been tested in settings with uncertainty recently, such as genetic algorithms, particle swarm optimization, and bee colony algorithms [20]; tabu search [21]; differential evolution [22]; and invasive weed optimization [23].…”

On modification of population-based search algorithms for convergence in stochastic combinatorial optimization

“…simulated annealing, [8] ant colony optimization, [9] etc., including a recent work by Hannah and Powell [10] in a genetic algorithm context by modifying 'evolutionary policy iteration' for Markov decision processes into a sample-based algorithm for SCOPs (see also two recent surveys [4,11] on heuristic stochastic optimization algorithms). We stress that this paper's focus is on studying general frameworks of converting any population-based algorithm, especially designed for solving COPs, into a sample-based one for solving SCOPs by using some techniques that Downloaded by [New York University] at 12:36 07 June 2015…”

Weighted proximity search

“…Heuristic strategies are of vital importance to obtain good quality solutions for problems that cannot be solved to optimality within a reasonable time. Several heuristic strategies exploring different lines of thought have been proposed in the literature Extended author information available on the last page of the article (Boussaïd et al 2013;Hvattum and Esbensen 2011). One of those lines consists of searching for better solutions by exploring neighborhoods of given reference solutions.…”