An Effective League Championship Algorithm for the Stochastic Multi-Period Portfolio Optimization Problem

Abstract

The Multi-Period Portfolio Optimization (MPPO) models have been introduced to overcome the weaknesses of the single-period models via considering a dynamic optimization system. However, considering the nonlinear nature of the problem and rapid growth of the size complexity with increase in the number of periods and scenarios, this study is devoted to developing a novel League Championship Algorithm (LCA) to maximize the mean variance function of the portfolio subject to di erent constraints. A Vector Auto-Regression (VAR) model was developed to estimate the return on risky assets in di erent time periods and to simulate di erent scenarios of the rate of return, accordingly. Besides, we proved a valid upper bound of the objective function based on the idea of using surrogate relaxation of constraints. Our computational results based on sample data collected from S&P 500 and 10-year T. bond indices indicated that the quality of portfolios, in terms of the mean variance measure, obtained by LCA was 10 to 20 percent better than that by the commercial software. It seems promising that our method can be a suitable tool for solving a variety of portfolio optimization problems.

A Mixed Integer Linear Formulation and a Grouping League Championship Algorithm for a Multiperiod‐Multitrip Order Picking System with Product Replenishment to Minimize Total Tardiness

“…Recall that picker b can be available within [Sbt, Fbt] in a given period t. e start and finish time of each trip is controlled by Constraint sets (13)- (16). Constraint (17) allows multiple replenishment of a storage location. An order should be picked before the arrival of the order, which will take its place.…”

“…To solve larger-scale problems, grouping metaheuristic algorithms are proposed based on the problem structure, and their effectiveness is investigated using numerical experiments. Two metaheuristic algorithms, namely, the league championship algorithm (LCA) [10][11][12][13][14][15][16][17][18] and particle swarm optimization (PSO), are heavily modified and applied to the problem. en, the solutions of these methods are compared with the solutions obtained using Gams/Cplex software for small-, medium-, and large-scale problems in terms of time and optimality.…”