Mahdi Moeini

Robust investment strategies with discrete asset choice constraints using DC programming

In this article, we are concerned with robust investment strategies for the portfolio management problem. We extend the classical Markowitz framework with discrete asset choice constraints to worst-case portfolio selection with rival risk and return scenario specifications. Robustness is ensured by considering the optimal strategy in view of multiple rival scenarios and evaluating the portfolio simultaneously with the worst-case scenario. Discrete constraints, such as buy-in thresholds and cardinality, represent the investors choice on the assets. Portfolio allocation with discrete asset choice constraints is a non-convex and NP-hard problem. A local deterministic optimization approach based on difference of convex (DC) functions programming is introduced and a DC algorithm (DCA) is developed to solve min–max mean–variance portfolio optimization problem. The computational results using historical data show that the DCA is more efficient than the standard methods and often provides a global solution.

DC programming approach for portfolio optimization under step increasing transaction costs

We address a class of particularly hard-to-solve portfolio optimization problems, namely the portfolio optimization under step increasing transaction costs. The step increasing functions are approximated, as closely as desired by a difference of polyhedral convex functions. Then we apply the difference of convex functions algorithm (DCA) to the resulting polyhedral DC program. For testing the efficiency of the DCA we compare it with CPLEX and the branch and bound algorithm proposed by Konno et al.

Portfolio selection under downside risk measures and cardinality constraints based on DC programming and DCA

In this paper, we consider the case of downside risk measures with cardinality and bounding constraints in portfolio selection. These constraints limit the amount of capital to be invested in each asset as well as the number of assets composing the portfolio. While the standard Markowitz’s model is a convex quadratic program, this new model is a NP-hard mixed integer quadratic program. Realizing the computational intractability for this class of problems, especially large-scale problems, we first reformulate it as a DC program with the help of exact penalty techniques in Difference of Convex functions (DC) programming and then solve it by DC Algorithms (DCA). To check globality of computed solutions, a global method combining the local algorithm DCA with a Branch-and-Bound algorithm is investigated. Numerical simulations show that DCA is an efficient and promising approach for the considered problem.

Long-Short Portfolio Optimization Under Cardinality Constraints by Difference of Convex Functions Algorithm

In the matter of Portfolio selection, we consider an extended version of the Mean-Absolute Deviation (MAD) model, which includes discrete asset choice constraints (threshold and cardinality constraints) and one is allowed to sell assets short if it leads to a better risk-return tradeoff. Cardinality constraints limit the number of assets in the optimal portfolio and threshold constraints limit the amount of capital to be invested in (or sold short from) each asset and prevent very small investments in (or short selling from) any asset. The problem is formulated as a mixed 0–1 programming problem, which is known to be NP-hard. Attempting to use DC (Difference of Convex functions) programming and DCA (DC Algorithms), an efficient approach in non-convex programming framework, we reformulate the problem in terms of a DC program, and investigate a DCA scheme to solve it. Some computational results carried out on benchmark data sets show that DCA has a better performance in comparison to the standard solver IBM CPLEX.

Location and relocation problems in the context of the emergency medical service systems: a case study

In this paper, we address the dynamic emergency medical service (EMS) systems. A dynamic location model is presented for locating and relocating a fleet of ambulances. The proposed model can control the movements and locations of ambulances in order to provide a better coverage of the demand points. The model can keep this ability under different fluctuation patterns that may happen during a given period of time. A number of numerical experiments have been carried out by using some real-world data sets. They have been collected through the French EMS system at the Hospital Henri Mondor, France. Finally, we present a comparison between the results of the introduced model and the outputs of a classical EMS dynamic location model. According to the observations, the introduced model provides a better coverage of the EMS demands.

A Novel Efficient Approach for Solving the Art Gallery Problem

In this paper, we consider the Art Gallery Problem (AGP) that asks for the minimum number of guards placed in a polygon to oversee the whole polygon. The AGP is known to be NP-hard even for very restricted special cases. This paper describes a primal-dual algorithm based on continuous optimization techniques for solving large-scale instances of the Art Gallery Problem. More precisely, the algorithm is a combination of methods from computational geometry, linear programming (LP), and Difference of Convex functions (DC) programming. The structure of the algorithm permits to provide lower and upper bounds on the minimum number of guards. In order to evaluate the algorithm, we measure its performance by solving some standard test instances including some non-orthogonal polygons with holes.

A Variable Neighborhood Search heuristic for the maximum ratio clique problem

Abstract Consider a graph in which every vertex has two non-negative weights. In this graph, the maximum ratio clique problem (MRCP) searches for a maximal clique that maximizes a fractional function defined by the ratio of the sums of vertex weights. It has been proved that MRCP is NP-hard and, consequently, it is difficult to solve MRCP by exact methods. Due to this fact, we present the first heuristic approach, i.e., a multi-start Variable Neighborhood Search (MS-VNS) algorithm. In order to verify the performance of our MS-VNS, we use standard instances and according to our observations, our MS-VNS approach provides high-quality solutions in a short computation time. Furthermore, on most of the instances, our algorithm outperforms the classical methods that have already been used for solving MRCP.

The Maximum Ratio Clique Problem: A Continuous Optimization Approach and Some New Results

In this paper, we are interested in studying the maximum ratio clique problem (MRCP) that is a variant of the classical maximum weight clique problem. For a given graph, we suppose that each vertex of the graph is weighted by a pair of rational numbers. The objective of MRCP consists in finding a maximal clique with the largest ratio between two sets of weights that are assigned to its vertices. It has been proven that the decision version of this problem is NP-complete and it is hard to solve MRCP for large instances. Hence, this paper looks for introducing an efficient approach based on Difference of Convex functions (DC) programming and DC Algorithm (DCA) for solving MRCP. Then, we verify the performance of the proposed method. For this purpose, we compare the solutions of DCA with the previously published results. As a second objective of this paper, we identify some valid inequalities and evaluate empirically their influence in solving MRCP. According to the numerical experiments, DCA provides promising and competitive results. Furthermore, the introduction of the valid inequalities improves the computational time of the classical approaches.

Portfolio Selection Under Buy-In Threshold Constraints Using DC Programming and DCA

In matter of portfolio selection, we consider a generalization of the Markowitz mean-variance model which includes buy-in threshold constraints. These constraints limit the amount of capital to be invested in each asset and prevent very small investments in any asset. The new model can be converted into a NP-hard mixed integer quadratic programming problem. The purpose of this paper is to investigate a continuous approach based on DC programming and DCA (DC algorithms) for solving this new model. DCA is a local continuous approach to solve a wide variety of nonconvex programs for which it provided quite often a global solution and proved to be more robust and efficient than standard methods. Preliminary comparative results of DCA and a classical branch-and-bound algorithm is presented. These results show that DCA is an efficient and promising approach for the considered portfolio selection problem

A Heuristic for Solving the Maximum Dispersion Problem

In this paper, we investigate solving the Maximum Dispersion Problem (MaxDP). For a given set of weighted objects, the MaxDP consists in partitioning this set into a predefined number of groups, such that the overall dispersion of elements, assigned to the same group, is maximized. Furthermore, each group has a target weight and the total weight of each group must be within a specific interval around the target weight. It has been proven that the MaxDP is NP-hard and, consequently, difficult to solve by classical exact methods. In this work, we use variants of Variable Neighborhood Search (VNS) for solving the MaxDP. In order to evaluate the efficiency of VNS, we carried out some numerical experiments on randomly generated instances. The results of the VNS is compared with the solutions provided by the solver Gurobi. According to our results, the VNS gives high quality solutions for small instances and, in solving large instances, it provides some decent solutions for all instances; however, Gurobi fails to provide any solution for some of them.