Step Cost Function Research Articles

Causal Necessity as a Narrative Planning Step Cost Function

Narrative planning generates a sequence of actions which must achieve the author's goal for the story and must be composed only of actions that make sense for the characters who take them. A causally necessary action is one that would make the plan impossible to execute if it were left out. We hypothesize that action sequences which are solutions to narrative planning problems are more likely to feature causally necessary actions than those which are not solutions. In this paper, we show that prioritizing sequences with more causally necessary actions can lead to solutions faster in ten benchmark story planning problems.

GRASP and VNS approaches for a vehicle routing problem with step cost functions

GRASP and VNS approaches for a vehicle routing problem with step cost functions

Step cost functions in a fleet size and mix vehicle routing problem with time windows

The vehicle routing problem is a traditional combinatorial problem with practical relevance for a wide range of industries. In the literature, several specificities have been tackled by dedicated methods in order to better reflect real-world situations. Following this trend, this article addresses the fleet size and mix vehicle routing problem with time windows in which companies hire a third-party logistics company. The shipping charges considered in this work are calculated using step cost functions, in which values are determined according to the type of vehicle and the total distance traveled, with fixed values for predefined distance ranges. A mixed integer linear programming model is introduced and two sequential insertion heuristics are proposed. The introduced methods are examined through a computational comparative analysis in small-sized instances with known optimal solution, 168 benchmark instances from the literature, and 3 instances based on a real-world problem from the civil construction industry. The numerical experiments show that the proposed methods are efficient and show good performance in different scenarios.

An exact approach for the multicommodity network optimization problem with a step cost function

We investigate the Multicommodity Network Optimization Problem with a Step Cost Function (MNOP-SCF) where the available facilities to be installed on the edges have discrete step-increasing cost and capacity functions. This strategic long-term planning problem requires installing at most one facility capacity on each edge so that all the demands are routed and the total installation cost is minimized. We describe a path-based formulation that we solve exactly using an enhanced constraint generation based procedure combined with columns and new cuts generation algorithms. The main contribution of this work is the development of a new exact separation model that identifies the most violated bipartition inequalities coupled with a knapsack-based problem that derives additional cuts. To assess the performance of the proposed approach, we conducted computational experiments on a large set of randomly generated instances. The results show that it delivers optimal solutions for large instances with up to 100 nodes, 600 edges, and 4950 commodities while in the literature, the best developed approaches are limited to instances with 50 nodes, 100 edges, and 1225 commodities.

Discrete-to-continuous transition in quantum phase estimation

We analyze the problem of quantum phase estimation where the set of allowed phases forms a discrete $N$ element subset of the whole $[0,2\pi]$ interval, $\varphi_n = 2\pi n/N$, $n=0,\dots N-1$ and study the discrete-to-continuous transition $N\rightarrow\infty$ for various cost functions as well as the mutual information. We also analyze the relation between the problems of phase discrimination and estimation by considering a step cost functions of a given width $\sigma$ around the true estimated value. We show that in general a direct application of the theory of covariant measurements for a discrete subgroup of the $U(1)$ group leads to suboptimal strategies due to an implicit requirement of estimating only the phases that appear in the prior distribution. We develop the theory of sub-covariant measurements to remedy this situation and demonstrate truly optimal estimation strategies when performing transition from a discrete to the continuous phase estimation regime.

New mathematical model for the bi-objective inventory routing problem with a step cost function: A multi-objective particle swarm optimization solution approach

• Transportation costs are assumed to behave as a step cost function. • A novel bi-objective mathematical model is proposed to consider this assumption. • Despite this assumption, this type of function is not considered in the IRP. • An efficient multi-objective particle swarm optimization algorithm is presented. • The algorithm's efficiency compared with the augmented ε-constraint method. Inventory management and satisfactory distribution are among the most important issues considered by distribution companies. One of the key objectives is the simultaneous optimization of the inventory costs and distribution expenses, which can be addressed according to the inventory routing problem (IRP). In this study, we present a new transport cost calculation pattern for the IRP based on some real cases. In this pattern, the transportation cost is calculated as a function of the load carried and the distance traveled by the vehicle based on a step cost function. Furthermore, previous methods usually aggregate the inventory and transportation costs to formulate them as a single objective function, but in non-cooperative real-life cases, the inventory-holding costs are paid by retailers whereas the transportation-related costs are paid by the distributor. In this study, we separate these two cost elements and introduce a bi-objective IRP formulation where the first objective is to minimize the inventory-holding cost and the second is minimizing the transportation cost. We also propose an efficient particle representation and employ a multi-objective particle swarm optimization algorithm to generate the non-dominated solutions for the inventory allocation and vehicle routing decisions. Finally, in order to evaluate the performance of the proposed algorithm, the results obtained were compared with those produced using the augmented ε-constraint method, thereby demonstrating the practical utility of the proposed multi-objective model and the proposed solution algorithm.

Direct target localization and deghosting in active radar network

Recently proposed, the one step localization approach for active sensor network estimates the target location directly from the sensor raw signals, as opposed to the classical decentralized two steps approach where intermediate signal processing (e.g., measurement estimation, detection) is performed on each sensor node. A composite multiple hypothesis test based on the generalized maximum likelihood (GML) rule is proposed to cope with the sidelobes of the one step cost function that may cause detection and localization of ghost targets. The proposed method has been verified both on synthetic and real data.

Exact solution of multicommodity network optimization problems with general step cost functions

We describe an exact solution procedure, based on the use of standard LP software, for multicommodity network optimization problems with general discontinuous step-increasing cost functions. This class of problems includes the so-called single-facility and multiple-facility capacitated network loading problems as special cases. The proposed procedure may be viewed as a specialization of the well-known BENDERS partitioning procedure, leading to iteratively solving an integer 0–1 linear programming relaxed subproblem which is progressively augmented through constraint generation. We propose an improved implementation of the constraint generation principle where, at each step, several (O( N)) new constraints are included into the current problem, thanks to which the total number of iterations is greatly reduced (never exceeding 15 in all the test problems treated). We report on systematic computational experiments for networks up to 20 nodes, 37 links and cost functions with an average six steps per link.

Single step versus multistep performance criteria for steady state SISO systems

It is shown that the positive weighting of expended control energy can give an unstable controller design if the uncontrolled system is unstable and a single step cost function is used. Multistep performance criteria avoid this problem.