Stochastic optimization over the Pareto front by the augmented weighted Tchebychev program

В этой статье мы предлагаем новый алгоритм для решения многоцелевых задач стохастического целочисленного линейного программирования (MOSILP). Мы оптимизируем данную стохастическую линейную функцию φ по полному набору эффективных решений MOSILP, которые были преобразованы в эквивалентную детерминированную задачу с использованием неопределенных предположений, вводимых лицом, принимающим решения. Для этой цели мы применяем двухэтапный рекурсивный подход, при котором расширенная взвешенная программа Чебышева постепенно оптимизируется для создания эффективного решения, тем самым улучшая значение вспомогательной функции φ . Предлагаемый здесь подход определяет и решает последовательность целочисленных линейных программ с нарастающими ограничениями, так что на каждом этапе алгоритма генерируется новое эффективное решение. Для иллюстрации представлен числовой пример In this paper, we propose a novel algorithm to deal with multi-objective stochastic integer linear programming problems (MOSILP). Given a stochastic linear function φ , we will optimize it over the full set of efficient solutions of a MOSILP. We convert the latter into an equivalent deterministic problem using uncertain aspirations which are inputs specified by the decision maker. For this purpose, we adopt a 2-stage recourse approach where an augmented weighted Tchebychev program is progressively optimized to generate an efficient solution, the value of the utility function φ is improved to enumerate all efficient solutions. The approach proposed here defines and solves a sequence of progressively more constrained integer linear programs, so that a new efficient solution is generated at each step of the algorithm. A numerical example is presented for illustration

Assessing forest management strategies under a mountain pine beetle attack in Alberta: exploring the impacts

We explore how forest resource managers can respond to a potential outbreak of mountain pine beetle ( Dendroctonus ponderosae Hopkins, 1902) by assessing how well different forest management strategies achieve various management objectives over time. Strategies include targeting at-risk stands as well as increasing harvest levels. Outcomes are evaluated on the basis of volume flows, net revenues, and the age class structure of the ending inventory. We use a spatially and temporally explicit model to simulate forest management outcomes and consider two different scenarios, one in which the attack occurs early and one where it is delayed. The model utilizes a planning with recourse approach in which the firm can reevaluate its harvesting schedule following the attack. We use company data from west-central Alberta for a 40-year planning exercise. The timing of the attack resulted in small differences in timber supply. However, most strategies performed better financially under an early attack, which limits the harvest of marginal stands. Increasing harvest levels performed better in economic terms but resulted in a very young growing stock with little old forest. The success of any strategy is linked to the timing of the attack and how it affects the growing stock, subsequently impacting timber and revenue flows.