It is well known that the standard (linear) knapsack problem can be solved exactly by dynamic programming in O(nc) time, where n is the number of items and c is the capacity of the knapsack. The quadratic knapsack problem, on the other hand, is NP-hard in the strong sense, which makes it unlikely that it can be solved in pseudo-polynomial time. We show however that the dynamic programming appro...

An alternative approach towards dynamic programming (DP) is presented: Recursions. A basic deterministic model and solution function are defined and the model is generalized to include stochastic processes, with the traditional stochastic DP model as a special case. Heuristic rules are included in the models simply as restrictions on decision spaces and a small slaughter pig marketing planning ...

We present a modification of the Real-Time Dynamic Programming (rtdp) algorithm that makes it a genuine off-line algorithm for solving Stochastic Shortest-Path problems. Also, a new domainindependent and admissible heuristic is presented for Stochastic Shortest-Path problems. The new algorithm and heuristic are compared with Value Iteration over benchmark problems with large state spaces. The r...

A set of agricultural suppliers with low demands can save on long-haul transportation costs by consolidating their product. We consider a system with stochastic demand and a single consolidation point near the suppliers. We propose a look-ahead heuristic that takes advantage of economies of scale by aiming to ship larger quantities. We experimentally compare the heuristic's performance against ...

We consider the approximate solution of discrete optimization problems using procedures that are capable of magnifying the effectiveness of any given heuristic algorithm through sequential application. In particular, we embed the problem within a dynamic programming framework, and we introduce several types of rollout algorithms, which are related to notions of policy iteration. We provide cond...

In this paper, we study a real-world variant of the Vehicle Routing Problem, arising from the work of distributing products of an industrial corporation. Given information about vehicles, depots, types of products, and the location of customers, we wish to determine the minimum number of vehicles required to pick up and deliver products to customers within a time limit. Using these vehicles, we...

Dynamic Programming provides a convenient and unified framework for studying many state models used in AI but no algorithms for handling large spaces. Heuristic-search methods, on the other hand, can handle large spaces but lack a common foundation. In this work, we combine the benefits of a general dynamic programming formulation with the power of heuristic-search techniques for developing an ...

We present a linear mixed integer programming model for the time-dependent heterogeneous green vehicle routing and scheduling problem (GVRSP) with the objective of minimizing total carbon dioxide emissions and weighted tardiness. Instead of discrete time intervals, the proposed model takes the traveled distances of arcs in different time periods as decision variables to determine the travel sch...

This paper proposes Dynamic Multiple Depots Vehicle Routing (DMDVR) to explore the feasible solution of routing transportation between PI-hubs and retailers in same cluster. The this research is constructed by daily forecasting demand a commodity crop, Pineapple, from Thailand’s northern region. Each route composed starting hub, number retailers, an ending hub. authors propose Mixed Integer Lin...

Actor-critic based online reinforcement learning control has been proved to be promising method for of aerial vehicles. However, it is difficult guarantee high-level success rate initial training and tune the large amount parameters actors critics considering unstable multi-input multi-output (MIMO) aircraft. In order facilitate simplify actor critic aircraft, classic stability augmentation sys...