Solving large 0–1 multidimensional knapsack problems by a new simplified binary artificial fish swarm algorithm

The artificial fish swarm algorithm has recently been emerged in continuous global optimization. It uses points of a population in space to identify the position of fish in the school. Many real-world optimization problems are described by 0-1 multidimensional knapsack problems that are NP-hard. In the last decades several exact as well as heuristic methods have been proposed for solving these problems. In this paper, a new simpli ed binary version of the artificial fish swarm algorithm is presented, where a point/ fish is represented by a binary string of 0/1 bits. Trial points are created by using crossover and mutation in the different fi sh behavior that are randomly selected by using two user de ned probability values. In order to make the points feasible the presented algorithm uses a random heuristic drop item procedure followed by an add item procedure aiming to increase the profit throughout the adding of more items in the knapsack. A cyclic reinitialization of 50% of the population, and a simple local search that allows the progress of a small percentage of points towards optimality and after that refines the best point in the population greatly improve the quality of the solutions. The presented method is tested on a set of benchmark instances and a comparison with other methods available in literature is shown. The comparison shows that the proposed method can be an alternative method for solving these problems.The authors wish to thank three anonymous referees for their comments and valuable suggestions to improve the paper. The first author acknowledges Ciˆencia 2007 of FCT (Foundation for Science and Technology) Portugal for the fellowship grant C2007-UMINHO-ALGORITMI-04. Financial support from FEDER COMPETE (Operational Programme Thematic Factors of Competitiveness) and FCT under project FCOMP-01-0124-FEDER-022674 is also acknowledged

Heuristic procedure neural networks for the CMST problem

Scope and Purpose – For solving combinatorial optimization problems, neural networks have traditionally been outperformed by traditional heuristic techniques developed specifically for the problem in question. This research is a step toward integrating the problem specific knowledge embedded in a traditional heuristic with the adaptive capabilities of neural networks. This is accomplished by creating a neural network topological design that embeds the steps of the traditional heuristic. The neural network learning then improves upon the performance of the embedded heuristic by modifying the neural weights attached to the embedded heuristic. Abstract- Combinatorial optimization problems are by nature very difficult to solve, and the Capacitated Minimum Spanning Tree problem is one such problem. Much work has been done in the management sciences to develop heuristic solution procedures that suboptimally solve large instances of the Capacitated Minimum Spanning Tree problem in a reasonable amount of time. The Capacitated Minimum Spanning Tree problem is used in this paper to develop and demonstrate a hybrid neural network methodology that incorporates heuristic methods into the neural network topological design. The heuristic procedure is embedded into the neural network topological design, and an iterative improvement process is performed using the neural network. The semi-relaxed energy function of the problem is used to develop a neural network weight adjustment procedure that modifies the problem costs. In three-quarters (75%) of our experiments, the hybrid neural networks produced better results than any of the traditional procedures tested. 1

Naval Wholesale Inventory Optimization

The article of record as published may be found at https://doi.org/10.1007/978-3-030-28565-4_15The U.S. Naval Supply Systems Command (NAVSUP), Weapon Systems Support, manages an inventory of approximately 400,000 maritime and aviation line items valued at over $20 billion. This work describes NAVSUP’s Wholesale Inventory Optimization Model (WIOM), which helps NAVSUP’s planners establish inventory levels. Under certain assumptions, WIOM determines optimal reorder points (ROPs) to minimize expected shortfalls from fill rate targets and deviations from legacy solutions. Each item’s demand is modeled probabilistically, and negative expected deviations from target fill rates are penalized with nonlinear terms (conveniently approximated by piecewise linear functions). WIOM’s solution obeys a budget constraint. The optimal ROPs and related expected safety stock levels are used by NAVSUP’s Enterprise Resource Planning system to trigger requisitions for procurement and/or repair of items based on forecasted demand. WIOM solves cases with up to 20,000 simultaneous items using both a direct method and Lagrangian relaxation. In particular, this proves to be more efficient in certain cases that would otherwise take many hours to produce a solution