“…KP is one of the most widely studied and experimented discrete programming problems. It offers many practical applications in diverse areas, such as project selection [2], resource distribution [3], investment decision making [4] and network interdiction problem [5].…”
This paper presents a novel binary monarch butterfly optimization (BMBO) method, intended for addressing the 0-1 knapsack problem (0-1 KP). Two tuples, consisting of real-valued vectors and binary vectors, are used to represent the monarch butterfly individuals in BMBO. Real-valued vectors constitute the search space, whereas binary vectors form the solution space. In other words, monarch butterfly optimization works directly on real-valued vectors, while solutions are represented by binary vectors. Three kinds of individual allocation schemes are tested in order to achieve better performance. Toward revising the infeasible solutions and optimizing the feasible ones, a novel repair operator, based on greedy strategy, is employed. Comprehensive numerical experimentations on three types of 0-1 KP instances are carried out. The comparative study of the BMBO with four state-of-the-art classical algorithms clearly points toward the superiority of the former in terms of search accuracy, convergent capability and stability in solving the 0-1 KP, especially for the high-dimensional instances.
“…KP is one of the most widely studied and experimented discrete programming problems. It offers many practical applications in diverse areas, such as project selection [2], resource distribution [3], investment decision making [4] and network interdiction problem [5].…”
This paper presents a novel binary monarch butterfly optimization (BMBO) method, intended for addressing the 0-1 knapsack problem (0-1 KP). Two tuples, consisting of real-valued vectors and binary vectors, are used to represent the monarch butterfly individuals in BMBO. Real-valued vectors constitute the search space, whereas binary vectors form the solution space. In other words, monarch butterfly optimization works directly on real-valued vectors, while solutions are represented by binary vectors. Three kinds of individual allocation schemes are tested in order to achieve better performance. Toward revising the infeasible solutions and optimizing the feasible ones, a novel repair operator, based on greedy strategy, is employed. Comprehensive numerical experimentations on three types of 0-1 KP instances are carried out. The comparative study of the BMBO with four state-of-the-art classical algorithms clearly points toward the superiority of the former in terms of search accuracy, convergent capability and stability in solving the 0-1 KP, especially for the high-dimensional instances.
“…Boland et al implemented a version of their model with "lazy" constraints but found that this did not improve performance for their model instances. Peeta et al (2010) address a pre-disaster planning problem that seeks to strengthen a highway network whose links are subject to random failures due to a disaster. Each link may be either operational or non-functional after the disaster.…”
Stochastic programming with recourse usually assumes uncertainty to be exogenous. Our work presents modelling and application of decision-dependent uncertainty in mathematical programming including a taxonomy of stochastic programming recourse models with decision-dependent uncertainty. The work includes several ways of incorporating direct or indirect manipulation of underlying probability distributions through decision variables in two-stage stochastic programming problems. Two-stage models are formulated where prior probabilities are distorted through an affine transformation or combined using a convex combination of several probability distributions. Additionally, we present models where the parameters of the probability distribution are first-stage decision variables. The probability distributions are either incorporated in the model using the exact expression or by using a rational approximation. Test instances for each formulation are solved with a commercial solver, BARON, using selective branching.
“…Chang (2003) develop a performance measure based on accessibility to evaluate the functionality of an urban transportation system in the aftermath of a disaster. Peeta et al (2010) study a shortest-path based model to decide which links to strengthen in a highway network that are subject to random failures.…”
This paper focuses on the problem of identifying optimal protection strategies to reduce the impact of flooding on a road network. We propose a dynamic mixed-integer programming model that extends the classic concept of road network protection by shifting away from single-arc fortifications to a more general and realistic approach involving protection plans that cover multiple components. We also consider multiple disruption scenarios of varying magnitude. To efficiently solve large problem instances, we introduce a customised GRASP heuristic. Finally, we provide some analysis and insights from a case study of the Hertfordshire road network in the East of England.Results show that optimal protection strategies mainly involve safeguarding against flooding events that are small and likely to occur, whereas implementing higher protection standards are not considered cost-effective.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.