Asymmetric Problem Research Articles

A New Approach to Identifying a Multi-Criteria Decision Model Based on Stochastic Optimization Techniques

Many scientific papers are devoted to solving multi-criteria problems. Researchers solve these problems, usually using methods that find discrete solutions and with the collaboration of domain experts. In both symmetrical and asymmetrical problems, the challenge is when new decision-making variants emerge. Unfortunately, discreet identification of preferences makes it impossible to determine the preferences for new alternatives. In this work, we propose a new approach to identifying a multi-criteria decision model to address this challenge. Our proposal is based on stochastic optimization techniques and the characteristic objects method (COMET). An extensive work comparing the use of hill-climbing, simulated annealing, and particle swarm optimization algorithms are presented in this paper. The paper also contains preliminary studies on initial conditions. Finally, our approach has been demonstrated using a simple numerical example.

Second-Order Sliding Mode Control Design Subject to an Asymmetric Output Constraint

In this brief, a novel second-order sliding mode (SOSM) control method is developed to solve the asymmetric output constraint problem by using a power integrator and barrier Lyapunov function (BLF). The new BLF is first constructed based on the asymmetric constraint condition. A novel SOSM algorithm is then constructed for the nonlinear systems with an asymmetric output constraint. Under the proposed SOSM algorithm, the output of the resulting closed-loop system will never escape from the asymmetric constraint. Finally, a pendulum system is adopted to verify the validity of the theoretical results.

Dynamic asymmetric assignment problem in open multi-agent systems

The purpose of the work is to develop models and algorithms for optimizing matching in dynamically generated graphs of asymmetric relations in coordinated open systems of interacting agents with centralized and collective control. The dynamic asymmetric matching optimization problem arises here as a result of a compromise approximation of the mapping of the dynamic programming method onto a stream of known open assignment problems or several traveling salesmen. However, the branching alternatives presented in this way for independent tasks do not take into account the interdependence of real relationships between agents and their tasks, including their relationship to time. Ignoring the dependence of branching alternatives leads to a delay in the moment or to a loss in the quality of assignment of tasks to coordinated agents. The main idea of the proposed implementation of the principle known for effective control is to postpone the moment the final decision is made to the latest moment, taking into account the susceptibility of the system to local changes in state variables. The interdependence of states is revealed on the basis of the analysis of the correspondence of the graph of the current matching with the optimal solution on the subgraph of perfect matching. The transition between states is implemented by the incremental version of the reoptimization algorithm for solving linear problems of assigning the shortest replenishing path using the method. The space of search states is a dynamically generated bipartite sparse graph of alternatives for a combination of agents and tasks, represented by a list of arcs. To highlight the sets of changed arcs, it is proposed to supplement the weight of the arcs with the boundaries of the stability intervals of the solution, optionally formed in the background. By default, the weight of the modified arc matches the boundary of the stability interval. On each correction cycle of the lists of agents, tasks, and their associations, subsets of elements are selected for which reconsideration of matching is required. An enhanced condition for the selection of such elements is to go beyond the boundaries of the stability interval. In this case, the asymmetry of the assignment problem is taken into account by choosing the adjacency structure for the fraction of the graph with a minimum of vertices. As a result, the reaction time of procedures for solving the assignment problem is reduced by an order of magnitude.

Human Capital Evaluation in Private Equity Investment Decisions: Contemporary Practice & Challenges

This paper investigates the processes involved in human capital (HC) evaluation in the investment of organisations by private equity (PE) firms. The significance of this issue relates to both the increasing importance of the PE industry in the wider corporate environment and the increasing recognition, within business and regulatory and financial communities, that the valuation and reporting of HC as a corporate asset requires attention. We examine the issue through the conceptual frame of HC evaluation by PE as an agency problem centred on asymmetric information. Findings are discussed from twenty-three semi-structured interviews with senior representatives of nineteen different PE firms with collective experience of over 3700 investments, to elicit insights into the nature, challenges and consequences of HC evaluation. The findings reinforce the agency perspective and characterise this setting as one featuring an aggravated form of asymmetric information-based agency problem. We find that the commonly employed HC evaluation methods are regarded as suboptimal in their susceptibility to heuristics and biases and to factors such as time pressure and interpersonal dynamics, potentially resulting in flawed judgements and negative investment decisions. We provide an analysis of the most commonly-reported consequences of shortcomings in HC evaluation, and offer recommendations for future research.

Asymmetric integral barrier Lyapunov function-based adaptive tracking control considering full-state with input magnitude and rate constraint

This paper investigates the neural adaptive tracking control problem of a class of strict-feedback systems considering asymmetric full-state with input magnitude and rate constraint (MRC). By designing a dual-integral-type actual control law, the MRC on system input is transformed to be the magnitude limitations on the extended states of the original system, so the original system with both state and MRC considerations is converted to be a new system with only full-state constraint. Besides, compared with the traditional symmetric integral barrier Lyapunov function, new asymmetric integral barrier Lyapunov function is introduced to the dynamic surface-based controller design process in this paper for dealing with the asymmetric state constraint problem. It is analyzed that the original system is semi-globally uniformly ultimately bounded, and that the desired multiple constraints are never violated. The effectiveness of the control strategy is shown via numerical simulations.

A parallelised large neighbourhood search heuristic for the asymmetric two-echelon vehicle routing problem with swap containers for cargo-bicycles

Cargo-bicycles are a promising alternative to conventional vans in city logistics in response to increasing urbanisation and environmental damage caused by city traffic. The delivery structure is modelled with the well studied Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP), which uses cross-docking from vans to cargo-bicycles at so-called satellites. To reduce the extra handling effort compared to single-tier systems, swap containers are used. Furthermore, for cargo-bicycles the consideration of asymmetric distance matrices is important. Therefore, we present the Asymmetric 2E-CVRP with Swap Containers and develop an efficient Parallelised Large Neighbourhood Search heuristic, that is further improved using a first-level heuristic. The heuristic is tested using the symmetric 2E-CVRP benchmark instances from the literature, outperforms previous heuristics for large instances and finds new best-known solutions. Subsequently, the heuristic is applied to a case study in Munich with 22 newly generated instances, each containing 200 customers and asymmetric distances. The results allow quantitative insights into the cost and CO2e emissions savings of the investigated cargo-bicycle set-up compared to conventional van delivery.

A hybrid tree-based algorithm to solve asymmetric distributed constraint optimization problems

Asymmetric distributed constraint optimization problems (ADCOPs) have emerged as an important formalism in multi-agent community due to their ability to capture personal preferences. However, the existing search-based complete algorithms for ADCOPs only exploit local knowledge to calculate lower bounds, which leads to inefficient pruning and prohibits them from solving large scale problems. On the other hand, inference-based complete algorithms (e.g., DPOP) for distributed constraint optimization problems are able to aggregate the global cost promptly but cannot be directly applied into ADCOPs due to a privacy concern. Thus, in this paper, we investigate the possibility of combining inference and search to effectively solve ADCOPs at an acceptable loss of privacy. Specifically, we propose a hybrid complete ADCOP algorithm called PT-ISABB which uses a tailored inference algorithm to provide tight lower bounds and upper bounds, and a tree-based complete search algorithm to guarantee the optimality. Furthermore, we introduce two suboptimal variants of PT-ISABB based on bounded-error approximation mechanisms to enable trade-off between theoretically guaranteed solutions and coordination overheads. We prove the correctness of PT-ISABB and its suboptimal variants. Finally, the experimental results demonstrate that PT-ISABB exhibits great superiorities over other state-of-the-art search-based complete algorithms and its suboptimal variants can quickly find a solution within the user-specified bounded-error.

Asymmetric distance location model

In this note, we analyze location problems where the distance (time) to get to the destination by air is affected by winds. We propose two models: the asymmetric Weber location problem and the round-trip Weber location problem. The problems are analyzed and solved.

Solution of asymmetric discrete competitive facility location problems using ranking of candidate locations

We address a discrete competitive facility location problem with an asymmetric objective function and a binary customer choice rule. Both an integer linear programming formulation and a heuristic optimization algorithm based on ranking of candidate locations are designed to solve the problem. The proposed population-based heuristic algorithm is specially adapted for the discrete facility location problems by using their features such as geographical distances and the maximal possible utility of candidate locations, which can be evaluated in advance. The performance of the proposed algorithm was experimentally investigated by solving different instances of the model with real data of municipalities in Spain.

Comparison of Kullback-Leibler, Hellinger and LINEX with Quadratic Loss Function in Bayesian Dynamic Linear Models: Forecasting of Real Price of Oil

In this paper we intend to examine the application of Kullback-Leibler, Hellinger and LINEX loss function in Dynamic Linear Model using the real price of oil for 106 years of data from 1913 to 2018 concerning the asymmetric problem in filtering and forecasting. We use DLM form of the basic Hoteling Model under Quadratic loss function, Kullback-Leibler, Hellinger and LINEX trying to address the results if we treat the ‘over-estimation’ and ‘under-estimation’ differently. So, we drive one-step-ahead forecast for Dynamic Linear Model under quadratic, LINEX and Kullback-Leibler losses in Bayesian context. With Normal posterior distribution, our results suggest that, the LINEX loss function may provide better forecasts than conventional Quadratic loss function, Hellinger and Kullback-Leibler loss function, especially in case of having volatility and time-varying parameters. JEL classification: C11, C22, C53, C61, Q47

Heat and mass transfer and thermodynamic analysis of power-law fluid flow in a porous microchannel

Transfer of heat and mass and thermodynamic irreversibilities are investigated in a porous, parallel-plate microreactor in which the working fluid is non-Newtonian. The investigated microreactor features thick flat walls with uneven thicknesses, which can be subject to different thermal loads. The dimensionless governing equations of the resultant asymmetric problem are first derived theoretically and then solved numerically by using a finite volume technique. This results in two-dimensional solutions for the velocity, temperature and concentration fields as well as the distributions of Nusselt number and local and total entropy generations. The results clearly demonstrate the significance of the numerical value of the power-law index and departure from Newtonian behavior of the fluid. In particular, it is shown that by increasing the value of power-law index the Nusselt number on the wall decreases. This leads to the intensification of the temperature gradients in the system and therefore magnifies the local and total entropy generations. Also, it is shown that the wall thickness and thermal asymmetry can majorly affect the heat transfer process and thermodynamic irreversibility of the microreactor. It is noted that the current work is the first comprehensive study of heat transfer and entropy generation in porous micro-chemical reactor with non-Newtonian, power-law fluid.

Approximating the asymmetric p-center problem in parameterized complete digraphs

The asymmetric p-center problem (ApCP) was proved by Chuzhoy et al. (STOC’04) to be NP-hard to approximate within a factor of $$\log ^*n - \Theta (1)$$ unless $$\mathrm {NP} \subseteq \mathrm {DTIME}(n^{\log \log n})$$. This paper studies ApCP and the vertex-weighted asymmetric p-center problem (WApCP). First, we propose four classes of parameterized complete digraphs, $$\alpha $$-CD, $$(\alpha , \beta )$$-CD, $$\langle \alpha , \gamma \rangle $$-CD and $$(\alpha , \beta , \gamma )$$-CD, from the angle of the parameterized upper bound on the ratio of two asymmetric edge weights between vertices as well as on the ratio of two vertex weights, and the parameterized triangle inequality, respectively. Using the greedy approach, we achieve a $$(1 + \alpha )$$- and $$\beta \cdot (1 + \alpha )$$-approximation algorithm for the ApCP in $$\alpha $$-CD’s and $$(\alpha , \beta )$$-CD’s, respectively, as well as a $$(1 + \alpha \gamma )$$- and $$\beta \cdot (1 + \alpha \gamma )$$-approximation algorithm for the WApCP in $$\langle \alpha , \gamma \rangle $$-CD’s and $$(\alpha , \beta , \gamma )$$-CD’s, respectively.

K -center Clustering under Perturbation Resilience

The k -center problem is a canonical and long-studied facility location and clustering problem with many applications in both its symmetric and asymmetric forms. Both versions of the problem have tight approximation factors on worst case instances: a 2-approximation for symmetric k -center and an O (log * ( k ))-approximation for the asymmetric version. Therefore, to improve on these ratios, one must go beyond the worst case. In this work, we take this approach and provide strong positive results both for the asymmetric and symmetric k -center problems under a natural input stability (promise) condition called α-perturbation resilience [15], which states that the optimal solution does not change under any α-factor perturbation to the input distances. We provide algorithms that give strong guarantees simultaneously for stable and non-stable instances: Our algorithms always inherit the worst-case guarantees of clustering approximation algorithms and output the optimal solution if the input is 2-perturbation resilient. In particular, we show that if the input is only perturbation resilient on part of the data, our algorithm will return the optimal clusters from the region of the data that is perturbation resilient while achieving the best worst-case approximation guarantee on the remainder of the data. Furthermore, we prove that our result is tight by showing symmetric k -center under (2 − ϵ)-perturbation resilience is hard unless NP = RP . The impact of our results is multifaceted. First, to our knowledge, asymmetric k -center is the first problem that is hard to approximate to any constant factor in the worst case, yet can be optimally solved in polynomial time under perturbation resilience for a constant value of α. This is also the first tight result for any problem under perturbation resilience, i.e., this is the first time the exact value of α for which the problem switches from being NP-hard to efficiently computable has been found. Furthermore, our results illustrate a surprising relationship between symmetric and asymmetric k -center instances under perturbation resilience. Unlike approximation ratio, for which symmetric k -center is easily solved to a factor of 2 but asymmetric k -center cannot be approximated to any constant factor, both symmetric and asymmetric k -center can be solved optimally under resilience to 2-perturbations. Finally, our guarantees in the setting where only part of the data satisfies perturbation resilience make these algorithms more applicable to real-life instances.

Stable matchings in high dimensions via the Poisson-weighted infinite tree

Nous considérons l’appariement stable de deux processus de Poisson indépendants dans $\mathbb{R}^{d}$, sous une contrainte asymmetrique sur les couleurs. Un point bleu ne peut être apparié qu’à un point rouge, tandis qu’un point rouge peut être apparié soit à un point rouge soit à un point bleu. On ne sait pas s’il existe un choix d’intensités des processus bleu et rouge tel que tous les points sont appariés. Nous démontrons que pour toutes intensités fixes, il y a des points bleus non-appariés en dimension suffisamment elevée. En effet, si le rapport de l’intensité des points rouges à l’intensité des points bleus est $\rho $, l’intensité des points bleus non-appariés tend vers $e^{-\rho }/(1+\rho )$ quand $d\to \infty $. On établit aussi des résultats analogues pour certaines variantes à multiples couleurs. La preuve utilise un modèle d’appariement stable sur l’arbre infini pondéré de Poisson (PWIT), qui peut être analysé par des équations différentielles. Le PWIT a été utilisé dans de nombreux contextes comme limite d’échelle pour des modèles impliquant des graphes complets pondérés de variables aléatoires indépendants, mais à notre connaissance, celle-ci est la première présentation d’une application rigoureuse à l’espace euclidien en haute dimension. Finalement, on analyse le problème d’appariement asymétrique sous une métrique hiérarchique, et on démontre qu’il existe des points non-appariés pour tout choix d’intensités.

An Energy-Efficient Coverage Enhancement Strategy for Wireless Sensor Networks Based on a Dynamic Partition Algorithm for Cellular Grids and an Improved Vampire Bat Optimizer.

Sensor nodes perform missions based on the effectual invariable coverage of events, and it is commonly guaranteed by the determinate deployment for sensor nodes who deviate from the optimum site frequently. To reach the optimal coverage effect with the lowest costs is a primary goal of wireless sensor networks. In this paper, by splicing the sensing area optimally with cellular grids, the best deployment location for sensors and the required minimum number of them are revealed. The optimization problem of coverage rate and energy consumption is converted into a task assignment problem, and a dynamic partition algorithm for cellular grids is also proposed to improve the coverage effect when the number of sensors is variable. Furthermore, on the basis of solving the multi-objective problem of reducing and balancing the energy cost of sensors, the vampire bat optimizer is improved by introducing virtual bats and virtual preys, and finally solves the asymmetric assignment problem once the number of cellular grids is not equal to that of sensors. Simulation results indicate that the residual energy of sensors during redeployment is balanced notably by our strategy when compared to three other popular coverage-enhancement algorithms. Additionally, the total energy cost of sensor nodes and coverage rate can be optimized, and it also has a superior robustness when the number of nodes changes.

Applying Max-sum to asymmetric distributed constraint optimization problems

We study the adjustment and use of the Max-sum algorithm for solving Asymmetric Distributed Constraint Optimization Problems (ADCOPs). First, we formalize asymmetric factor-graphs and apply the different versions of Max-sum to them. Apparently, in contrast to local search algorithms, most Max-sum versions perform similarly when solving symmetric and asymmetric problems and some even perform better on asymmetric problems. Second, we prove that the convergence properties of Max-sum_ADVP (an algorithm that was previously found to outperform standard Max-sum and Bounded Max-sum) and the quality of the solutions it produces, are dependent on the order between nodes involved in each constraint, i.e., the inner constraint order (ICO). A standard ICO allows to reproduce the properties achieved for symmetric problems. Third, we demonstrate that a non-standard ICO can be used to balance exploration and exploitation. Our results indicate that Max-sum_ADVP with non-standard ICO and Damped Max-sum, when solving asymmetric problems, both outperform other versions of Max-sum, as well as local search algorithms specifically designed for solving ADCOPs.

Constructing Separable Non-$2\pi$-Periodic Solutions to the Navier-Lamé Equation in Cylindrical Coordinates Using the Buchwald Representation: Theory and Applications

In a previous paper [Adv. Appl. Math. Mech. 10 (2018), pp. 1025-1056], we used the Buchwald representation to construct several families of separable cylindrical solutions to the Navier-Lam\'{e} equation; these solutions had the property of being $2\pi$-periodic in the circumferential coordinate. In this paper, we extend the analysis and obtain the complementary set of separable solutions whose circumferential parts are elementary $2\pi$-aperiodic functions. Collectively, we construct eighteen distinct families of separable solutions; in each case, the circumferential part of the solution is one of three elementary $2\pi$-aperiodic functions. These solutions are useful for solving a wide variety of dynamical problems that involve cylindrical geometries and for which $2\pi$-periodicity in the angular coordinate is incompatible with the given boundary conditions. As illustrative examples, we show how the obtained solutions can be used to solve certain forced-vibration problems involving open cylindrical shells and open solid cylinders where (by virtue of the boundary conditions) $2\pi$-periodicity in the angular coordinate is inappropriate. As an addendum to our prior work, we also include an illustrative example of a certain type of asymmetric problem that can be solved using the particular $2\pi$-periodic subsolutions that ensue when there is no explicit dependence on the circumferential coordinate.

Equivalent Magnetic Circuit Model for Consequent Pole Hybrid Excitation Synchronous Machine with AC Field Control

At present, almost all hybrid excitation machines (HEMs) apply DC field current to control the air-gap flux. However, the DC field control mode results in a problem that the capability of field-weakening is not equal to that of field-strengthening. This paper briefly explains the mechanism of asymmetric bidirectional field control capability in present HEMs, proposes a consequent pole hybrid excitation synchronous (CPHES) machine with AC field control mode to solve the asymmetric problem. The structure and principles of CPHES machine are presented. Additionally, the equivalent magnetic circuit model of CPHES machine is derived to reduce the computational complexity of analyzing CPHES structure by using three-dimensional finite element analysis (3DFEA). The proposed equivalent model and 3D-FEA are compared, the results verify the proposed model is basically consistent with the 3D-FEA, and the proposed model is able to reduce the computational complexity greatly.

About the influence of the forces of interaction between the droplets on the dynamics of emulsion

The dynamics of deposition of compound droplets of the emulsion under the action of gravity is investigated. The interaction of the droplet with its inclusion is taken into account. Axisymmetric and asymmetric problems of deposition of compound droplets are considered. Expressions for the relative and absolute velocities of the compound emulsion droplets are found. Based on numerical modeling, the trajectories of the relative and absolute motion of the droplets are obtained.

On a Differential Constraint in Asymmetric Theories of the Mechanics of Growing Solids

The article deals with the problem on setting boundary conditions for asymmetric problems in the mechanics of growing solids. Firstly, we study the conditions on the growing surface that are most important from the point of view of the theory completeness. When deriving relations on the growing surface, we use the results known from the algebra of rational invariants. Geometrically and mechanically consistent differential constraints that are valid for a very wide range of materials and metamaterials are obtained on the growing surface. Several variants of constitutive equations on the growing surface of different levels of complexity are investigated. The formulated differential constraints imply the experimental identification of several defining functions. Thus, the results obtained can serve as a general basis in applied research on the mechanics of growing solids with an asymmetric stress tensor.