Konstantin Pavlikov

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• PhD
• Professor (Associate) at University of Southern Denmark

Fractional and Rounded capacity inequalities are two important families of valid inequalities known for the homogeneous Capacitated Vehicle Routing Problem (CVRP). Such inequalities impose the minimum number of vehicles required to service each and every subset of customers, be it a fractional or an integer value. In case of the Heterogeneous versi...

This paper considers the well-known Travelling Salesman Problem (TSP) in its symmetric and asymmetric versions. A distinctive feature of the symmetric version of the problem is the ability to formulate it as an undirected network optimization problem using \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}...

The family of Rounded Capacity (RC) inequalities is one of the most important sets of valid inequalities for the Capacitated Vehicle Routing Problem (CVRP). This paper considers the problem of separation of violated RC inequalities and develops an exact procedure employing mixed integer linear programming. The developed routine is demonstrated to b...

The family of Rounded Capacity (RC) inequalities is one of the most important sets of valid inequalities for the Capacitated Vehicle Routing Problem (CVRP). This paper considers the problem of separation of violated RC inequalities and develops an exact procedure employing mixed integer linear programming. The developed routine is demonstrated to b...

The Weapon-Target Assignment (WTA) problem aims to assign a set of weapons to a number of assets (targets), such that the expected value of survived targets is minimized. The WTA problem is a nonlinear combinatorial optimization problem known to be NP-hard. This paper applies several existing techniques to linearize the WTA problem. One linearizati...

This paper considers the class of facility location models known as the maximum expected covering location model, in which located facilities are subject to random failures and the objective is to maximize the expected value of served (or covered) locations. We introduce a risk averse version of the problem that focuses on maximizing the conditiona...

The golf director problem introduced in Pavlikov et al. (2014) is a sports management problem which aims to find an allocation of golf players into fair teams for certain golf club competitions. The motivation for the problem is that club golf competitions are recreational events where the golf director wants to form teams that are competitive even...

We consider optimization problems of identifying critical nodes in coupled interdependent networks, that is, choosing a subset of nodes whose deletion causes the maximum network fragmentation (quantified by an appropriate metric) in the presence of deterministic or probabilistic cascading failure propagations. We use two commonly considered network...

Optimization of Value-at-Risk is an important problem both from theoretical and practical standpoints. It can be represented through a class of chance-constrained optimization problems, which are generally hard to solve. Mixed integer problem formulations with big M constants is a standard way to approach such problems, where tightness of these con...

The minimum connectivity interdiction problem seeks to remove at most k nodes from an undirected graph, such that a connectivity measure of the remaining subgraph is minimized. Examples of connectivity measures of a graph include the number of connected pairs of nodes, the size of the largest connected component, and the inverse of the number of co...

We define new distances between univariate probability distributions, based on the concept of the CVaR norm. The problem of approximation of one discrete probability distribution by another one, potentially with a smaller number of outcomes, is considered. Such problems arise in the context of scenario reduction and the approximation is performed b...

This article addresses challenges of estimating operational risk regulatory capital when a loss sample is truncated from below at a data collection threshold. Recent operational risk literature reports that the attempts to estimate loss distributions by the maximum likelihood method are not always successful under the truncation approach that accou...

This paper introduces the family of CVaR norms in , based on the CVaR concept. The CVaR norm is defined in two variations: scaled and non-scaled. The well-known and norms are limiting cases of the new family of norms. The D-norm, used in robust optimization, is equivalent to the non-scaled CVaR norm. We present two relatively simple definitions of...

The notion of drawdown is central to active portfolio management. Conditional Drawdown-at-Risk (CDaR) is defined as the average of a specified percentage of the largest drawdowns over an investment horizon and includes maximum and average drawdowns as particular cases. The necessary optimality conditions for a portfolio optimization problem with CD...

Club golf competitions are regular events arranged by golf directors (or professionals) for club members. Player skill levels are measured by their USGA or R&A handicaps and it is the job of the director to use the handicaps to organize teams that are, in some sense, fair. The handicap system is limited in that it does not take the variance of play...