Cost Vector Research Articles

Capacity inverse minimum cost flow problems under the weighted Hamming distance

Given a network N(V, A, u, c) and a feasible flow \(x^0\), the inverse minimum cost flow problem is to modify the capacity vector or the cost vector as little as possible to make \(x^0\) form a minimum cost flow of the network. The modification can be measured by different norms. In this paper, we consider the capacity inverse minimum cost flow problems under the weighted Hamming distance, where we use the weighted Hamming distance to measure the modification of the arc capacities. Both the sum-type and the bottleneck-type cases are considered. For the former, it is shown to be APX-hard due to the weighted feedback arc set problem. For the latter, we present a strongly polynomial algorithm which can be done in \(O(n\cdot m^2)\) time.

Lower bound sets for biobjective shortest path problems

This article considers the problem of calculating the set of all Pareto-optimal solutions in one-to-one biobjective shortest path problems with positive cost vectors. The efficiency of multiobjective best-first search algorithms can be improved with the use of consistent informed lower bounds. More precisely, the use of the ideal point as a lower bound has recently been shown to effectively increase search performance. In theory, the use of lower bounds that better approximate the Pareto frontier using sets of vectors (bound sets), could further improve performance. This article describes a lower bound set calculation method for biobjective shortest path problems. Improvements in search efficiency with lower bound sets of increasing precision are analyzed and discussed.

Some Differential Estimates in Linear Programming

This paper proposes two sets of formulas for the sensitivity analysis of the optimal value function of a parametric linear programming problem. The first one evaluates the changes of the optimal value with respect to perturbations of the right-hand side vector in the constraint system and of the cost vector. The second one gives a lower bound and an upper bound for the Dini directional derivative of the optimal value function.

Sharing the costs of cleaning a river: the Upstream Responsibility rule

The cleaning up of waste present in transboundary rivers, which requires the cooperation of different authorities, is a problematic issue, especially when responsibility for the discharge of the waste is not well-defined. Following Ni and Wang (2007) we assume that a river is a segment divided into several regions from upstream to downstream. We show that when the transfer rate of the waste is unknown, the clean-up cost vector provides useful information for estimating some limits in regard to the responsibility of each region. We propose a cost allocation rule, the Upstream Responsibility rule, which takes into account these limits in distributing costs “fairly” and we provide an axiomatic characterization of this rule via certain properties based on basic ideas concerning the responsibility of regions.

On the lattice programming gap of the group problems

Given a full-dimensional lattice Λ⊂Zk and a cost vector l∈Q>0k, we are concerned with the family of the group problems (0.1)min{l⋅x:x≡r(modΛ),x≥0},r∈Zk. The lattice programming gapgap(Λ,l) is the largest value of the minima in (0.1) as r varies over Zk. We show that computing the lattice programming gap is NP-hard when k is a part of input. We also obtain lower and upper bounds for gap(Λ,l) in terms of l and the determinant of Λ.

EUCALYPT: efficient tree reconciliation enumerator.

BackgroundPhylogenetic tree reconciliation is the approach of choice for investigating the coevolution of sets of organisms such as hosts and parasites. It consists in a mapping between the parasite tree and the host tree using event-based maximum parsimony. Given a cost model for the events, many optimal reconciliations are however possible. Any further biological interpretation of them must therefore take this into account, making the capacity to enumerate all optimal solutions a crucial point. Only two algorithms currently exist that attempt such enumeration; in one case not all possible solutions are produced while in the other not all cost vectors are currently handled. The objective of this paper is two-fold. The first is to fill this gap, and the second is to test whether the number of solutions generally observed can be an issue in terms of interpretation.ResultsWe present a polynomial-delay algorithm for enumerating all optimal reconciliations. We show that in general many solutions exist. We give an example where, for two pairs of host-parasite trees having each less than 41 leaves, the number of solutions is 5120, even when only time-feasible ones are kept. To facilitate their interpretation, those solutions are also classified in terms of how many of each event they contain. The number of different classes of solutions may thus be notably smaller than the number of solutions, yet they may remain high enough, in particular for the cases where losses have cost 0. In fact, depending on the cost vector, both numbers of solutions and of classes thereof may increase considerably. To further deal with this problem, we introduce and analyse a restricted version where host switches are allowed to happen only between species that are within some fixed distance along the host tree. This restriction allows us to reduce the number of time-feasible solutions while preserving the same optimal cost, as well as to find time-feasible solutions with a cost close to the optimal in the cases where no time-feasible solution is found.ConclusionsWe present Eucalypt, a polynomial-delay algorithm for enumerating all optimal reconciliations which is freely available at http://eucalypt.gforge.inria.fr/.Electronic supplementary materialThe online version of this article (doi:10.1186/s13015-014-0031-3) contains supplementary material, which is available to authorized users.

Experimental control of Triatoma infestans in poor rural villages of Bolivia through community participation.

BackgroundTriatoma infestans is the main vector of Chagas disease in the southern cone countries. Present control strategies based on indoor and outdoor residual insecticide spraying are not sufficient to control disease transmission, particularly in Bolivia. Techniques based on the management of the human environment may be good alternatives or supplements.MethodsSocial and entomological surveys were carried out in four villages of Bolivia situated in the dry inter-Andean Valleys and the Chaco region. Risk factors for house infestation by T. infestans were identified, and an eco-health intervention based on education and community participation was carried out to reduce the risks of house infestation. It consisted of implementing simple and low cost vector control techniques such as coating of mud walls, cleaning activities and removal of poultry that enter rooms to lay eggs.ResultsThe eco-health intervention significantly reduced the number of infested bedrooms, the mean abundance of T. infestans in bedrooms and beds, especially in the Chaco region. Mud wall coating was well accepted and could be proposed as a supplementary tool to the National Program of Chagas Disease Control to enhance the effects of insecticide sprayings.ConclusionsEven if cleaning activities were still neglected, community participation proved to be effective in reducing house infestation.

Multi-objective nonlinear predictive control of process systems: A dual-mode tracking control approach

There typically exist different and often conflicting control objectives, e.g., reference tracking, robustness and economic performance, in many chemical processes. The current work considers the multi-objective control problems of continuous-time nonlinear systems subject to state and input constraints and multiple conflicting objectives. We propose a new multi-objective nonlinear model predictive control (NMPC) design within the dual-mode paradigm, which guarantees stability and constraint satisfaction. The notions of utopia point and compromise solution are used to reconcile the confliction of the multiple objectives. The designed controller minimizes the distance of its cost vector to a vector of independently minimized objectives, i.e., the steady-state utopia point. Recursive feasibility is established via a particular terminal region formulation while stabilizing the closed-loop system to the compromise solution via the dual-mode control principle. In order to derive the terminal region as large as possible, a terminal control law with free-parameters is constructed by using the control Lyapunov functions (CLFs) technique. Two examples of multi-objective control of a CSTR and a free-radical polymerization process are used to illustrate the effectiveness of the new multi-objective NMPC and to compare their performance.

A linear fractional optimization over an integer efficient set

Mathematical optimization problems with a goal function, have many applications in various fields like financial sectors, management sciences and economic applications. Therefore, it is very important to have a powerful tool to solve such problems when the main criterion is not linear, particularly fractional, a ratio of two affine functions. In this paper, we propose an exact algorithm for optimizing a linear fractional function over the efficient set of a Multiple Objective Integer Linear Programming (MOILP ) problem without having to enumerate all the efficient solutions. We iteratively add some constraints, that eliminate the undesirable (not interested) points and reduce, progressively, the admissible region. At each iteration, the solution is being evaluated at the reduced gradient cost vector and a new direction that improves the objective function is then defined. The algorithm was coded in MATLAB environment and tested over different instances randomly generated.

Inverse Optimization in Countably Infinite Linear Programs

Given the objective coefficients and a feasible solution for a linear program, inverse optimization involves finding a new vector of objective coefficients that (i) is as close as possible to the original vector; and (ii) would make the given feasible solution optimal. This problem is well-studied for finite-dimensional linear programs. We develop a duality-based inverse optimization framework for countably infinite linear programs (CILPs) -- problems that include a countably infinite number of variables and constraints. Using the standard weighted absolute sum metric to quantify distance between cost vectors, we provide conditions under which constraints in the inverse optimization problem can be reformulated as a countably infinite set of linear constraints. We propose a convergent algorithm to solve the resulting infinite-dimensional mathematical program. This algorithm involves solving a sequence of finite-dimensional linear programs. We apply these results to inverse optimization in infinite-horizon non-stationary Markov decision processes.

An evolutionary algorithm for multi-criteria inverse optimal value problems using a bilevel optimization model

Given a linear program, a desired optimal objective value, and a set of feasible cost vectors, one needs to determine a cost vector of the linear program such that the corresponding optimal objective value is closest to the desired value. The problem is always known as a standard inverse optimal value problem. When multiple criteria are adopted to determine cost vectors, a multi-criteria inverse optimal value problem arises, which is more general than the standard case. This paper focuses on the algorithmic approach for this class of problems, and develops an evolutionary algorithm based on a dynamic weighted aggregation method. First, the original problem is converted into a bilevel program with multiple upper level objectives, in which the lower level problem is a linear program for each fixed cost vector. In addition, the potential bases of the lower level program are encoded as chromosomes, and the weighted sum of the upper level objectives is taken as a new optimization function, by which some potential nondominated solutions can be generated. In the design of the evolutionary algorithm some specified characteristics of the problem are well utilized, such as the optimality conditions. Some preliminary computational experiments are reported, which demonstrates that the proposed algorithm is efficient and robust.

On multi-objective economic predictive control for cyclic process operation

In recent literature, a utopia-tracking strategy has been proposed for multi-objective model predictive control. This strategy tracks a vector of independently minimized objectives, evaluated at steady-state operation (the utopia point). The approach in the present work is based on the premise that cyclic process operation may in some cases outperform, on average, steady-state operation. We therefore concern ourselves with optimizing average performance for one cyclic period of operation. A dynamic utopia-tracking strategy is proposed, which generalizes steady-state utopia-tracking to systems which are optimally operated cyclically. The proposed control law minimizes the distance of its cost vector to a vector of independently minimized objectives, evaluating average cyclic performance (the dynamic utopia point). Recursive feasibility is established for a cyclic terminal state constraint formulation, however, conditions for stability are not given. The theoretical concepts are illustrated for a simple acetylene hydrogenation case, and a more complex oil production optimization case. The simulation study indicates novel operational insight for the oil production optimization case, by illustrating how simultaneous optimization of two objectives results in cyclic operation with improved performance.

Pareto Frontier for the time–energy cost vector to an Earth–Moon transfer orbit using the patched-conic approximation

In this work, we present a study about the determination of the optimal time–energy cost vector, i.e., flight time and total \({\Delta }V\) (velocity change) spent in an orbital transfer of a spacecraft from an Earth circular parking orbit to a circular orbit around the Moon. The method used to determine the flight time and total \({\Delta }V\) is based on the well-known approach of patched conic in which the three-body problem that involves Earth, Moon and spacecraft is decomposed into two ‘two bodies’ problems, i.e., Earth–spacecraft and Moon–spacecraft. Thus, the trajectory followed by the spacecraft is a composition of two parts: The first one, when the spacecraft is within the Earth’s sphere of influence; The second one, when the spacecraft enters into the Moon’s sphere of influence. Therefore, the flight time and total \({\Delta }V\) to inject the spacecraft into the lunar trajectory and place it around the Moon can be determined using the expressions for the two-body problem. In this study, we use the concept of Pareto Frontier to find a set of parameters in the geometry of patched-conic solution that minimizes simultaneously the flight time and total \({\Delta }V\) of the mission. These results present different possibilities for performing an Earth–Moon transfer where two conflicting objectives are optimized.

Note on the Inverse Metric Traveling Salesman Problem Against the Minimum Spanning Tree Algorithm

ABSTRACT In this paper, we consider an interesting variant of the inverse minimum traveling salesman problem. Given an in-stance ( G , w ) of the minimum traveling salesman problem defined on a metric space, we fix a specified Hamiltonian cycle HC 0 . The task is then to adjust the edge cost vector w to w ' so that the new cost vector w ' satisfies the triangle inequality condition and HC 0 can be returned by the minimum spanning tree algorithm in the TSP-instance defined with w '. The objective is to minimize the total deviation between the original and the new cost vectors with respect to the L 1 -norm. We call this problem the inverse metric traveling salesman problem against the minimum spanning tree algorithm and show that it is closely related to the inverse metric spanning tree problem. Keywords: Combinatorial Optimization, Inverse Optimization, TSP, Minimum Spanning Tree Algorithm * Corresponding Author, E-mail: yerimchung@yonsei.ac.kr 1. INTRODUCTION In (Chung, 2010; Chung and Demange, 2012), some variant of the inverse optimization problem is defined with respect to a specific algorithm. For a combinatorial optimization problem, we are given an instance

Regret bounded by gradual variation for online convex optimization

Recently, it has been shown that the regret of the Follow the Regularized Leader (FTRL) algorithm for online linear optimization can be bounded by the total variation of the cost vectors rather than the number of rounds. In this paper, we extend this result to general online convex optimization. In particular, this resolves an open problem that has been posed in a number of recent papers. We first analyze the limitations of the FTRL algorithm as proposed by Hazan and Kale (in Machine Learning 80(2---3), 165---188, 2010) when applied to online convex optimization, and extend the definition of variation to a gradual variation which is shown to be a lower bound of the total variation. We then present two novel algorithms that bound the regret by the gradual variation of cost functions. Unlike previous approaches that maintain a single sequence of solutions, the proposed algorithms maintain two sequences of solutions that make it possible to achieve a variation-based regret bound for online convex optimization. To establish the main results, we discuss a lower bound for FTRL that maintains only one sequence of solutions, and a necessary condition on smoothness of the cost functions for obtaining a gradual variation bound. We extend the main results three-fold: (i) we present a general method to obtain a gradual variation bound measured by general norm; (ii) we extend algorithms to a class of online non-smooth optimization with gradual variation bound; and (iii) we develop a deterministic algorithm for online bandit optimization in multipoint bandit setting.

Bottleneck combinatorial optimization problems with uncertain costs and the OWA criterion

In this paper a class of bottleneck combinatorial optimization problems with uncertain costs is discussed. The uncertainty is modeled by specifying a discrete scenario set containing a finite number of cost vectors, called scenarios. In order to choose a solution the Ordered Weighted Averaging aggregation operator (OWA for short) is applied. The OWA operator generalizes traditional criteria in decision making under uncertainty such as the maximum, minimum, average, median, or Hurwicz criterion. New complexity and approximation results in this area are provided. These results are general and remain valid for many problems, in particular for a wide class of network problems.

A New Local Search Algorithm for Binary Optimization

We develop a new local search algorithm for binary optimization problems, whose complexity and performance are explicitly controlled by a parameter Q, measuring the depth of the local search neighborhood. We show that the algorithm is pseudo-polynomial for general cost vector c, and achieves a w2/(2w-1) approximation guarantee for set packing problems with exactly w ones in each column of the constraint matrix A, when using Q = w2. Most importantly, we find that the method has practical promise on large, randomly generated instances of both set covering and set packing problems, as it delivers performance that is competitive with leading general-purpose optimization software (CPLEX 11.2).

Multicost Routing Approach in Wireless Ad hoc Networks

Problem statement: A Wireless ad hoc network is a collection of autonomous movable nodes that communicate with each other over wireless links without any static infrastructure. In these networks there is no fixed topology because of the mobility of nodes, interference, multipath propagation and path loss. A variety of routing protocols and algorithm with varying network settings are analyzed to link between the nodes and communicate packets to their destinations. Most of these algorithms are single cost, in the logic that they consign a scalar cost parameter to every link and compute the path that has minimum cost. Although multicost routing, a vector of cost parameters is consigned to each link and the cost vector of a path is well-defined based on the cost vectors of the links that embrace it. Adjustable transmission power control of the nodes with multi cost routing algorithm can support optimizeto acquire the reduced interference and improve the ad hoc network performance. Approach: The link and path of the wireless network is consigned with several cost parameters. Hop count, total interference, node link delay, residual energy of a node and the node transmission power are the cost parameters assigned for link and path of the ad hoc networks. Multicost parameters are combined in different optimization function with respect to various routing algorithm. Results: Simulation and optimization shows multicost SUM/MIN Energy-Interference algorithm with variable transmission power can lead to decrease the interference and improves the overall network performance. Conclusion: The function optimized for wireless ad hoc networks that the Multicost SUM/MIN Energy-Interference algorithm achieves improved performance over than the single cost algorithm.

On accuracy, robustness and tolerances in vector Boolean optimization

A Boolean programming problem with a finite number of alternatives where initial coefficients (costs) of linear payoff functions are subject to perturbations is considered. We define robust solution as a feasible solution which for a given set of realizations of uncertain parameters guarantees the minimum value of the worst-case relative regret among all feasible solutions. For the Pareto optimality principle, an appropriate definition of the worst-case relative regret is specified. It is shown that this definition is closely related to the concept of accuracy function being recently intensively studied in the literature. We also present the concept of robustness tolerances of a single cost vector. The tolerance is defined as the maximum level of perturbation of the cost vector which does not destroy the solution robustness. We present formulae allowing the calculation of the robustness tolerance obtained for some initial costs. The results are illustrated with several numerical examples.

MODELLING THE BID AND ASK PRICES OF ILLIQUID CDSs

CDS (credit default swap) contracts that were initiated some time ago frequently have spreads and/or maturities that are not available on the current market of CDSs, and are thus illiquid. This article introduces an incomplete-market approach to valuing illiquid CDSs that, in contrast to the risk-neutral approach of current market practice, allows a dealer who buys an illiquid CDS from an investor to determine ask and bid prices (which differ) in such a way as to guarantee a minimum positive expected rate of return on the deal. An alternative procedure, which replaces the expected rate of return by an analogue of the Sharpe ratio, is also discussed. The approach to pricing just described belongs to the good-deal category of approaches, since the dealer decides what it would take to make an appropriate expected rate of return, and sets the bid and ask prices accordingly. A number of different hedges are discussed and compared within the general framework developed in the article. The approach is implemented numerically, and example plots of important quantities are given. The paper also develops a useful result in linear programming theory in the case that the cost vector is random.