In this paper a League Championship Algorithm (LCA) is developed for structural optimization where the optimization variables are of discrete type and the set of the values possibly obtained by each variable is also given. LCA is a relatively new metaheuristic Algorithm inspired from sport Championship process. In LCA, each individual can choose to approach to or retreat from other individuals in the population. This makes it able to provide a good balance between exploration and exploitation tasks in course of the search. To check the suitability and effectiveness of LCA for structural optimization, five benchmark problems are adopted and the performance of LCA is investigated and deeply compared with other approaches. Numerical results indicate that the proposed LCA method is very promising for solving structural optimization problems with discrete variables.

The multi-period portfolio optimization models were introduced to overcome the weaknesses of the single-period models via considering a dynamic optimization system. However, due to the nonlinear nature of the problem and rapid growth of the size complexity with increasing the number of periods and scenarios, this study is devoted to developing a novel League Championship Algorithm (LCA) to maximize the portfolio’ s mean-variance function subject to different constraints. A Vector Auto Regression model is also developed to estimate the return on risky assets in different time periods and to simulate different 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 indicate that the quality of portfolios, in terms of the mean-variance measure, obtained by LCA is 10 to 20 percent better than those of the commercial software. This sounds promising that our method can be a suitable tool for solving a variety of portfolio optimization problems.

Inverse heat conduction problems, which are one of the most important groups of problems, are often ill-posed and complicated problems, and their optimization process has lots of local extrema. This paper provides a novel computational procedure based on finite differences method and League Championship Algorithm to solve a one-dimensional inverse heat conduction problem. At the beginning, we use the Crank-Nicolson semi-implicit finite difference scheme to discretize the problem domain and solve the direct problem which is a second-order method in time and unconditionally stable. The consistency, stability and convergence of the method are investigated. Then we employ a new optimization method known as League Championship Algorithm to estimate the unknown boundary condition from some measured temperature on the line. League Championship Algorithm is a recently proposed probabilistic Algorithm for optimization in continuous environments, which tries to simulate a Championship environment wherein several teams with different abilities play in an artificial League for several weeks or iterations. To confirm the efficiency and accuracy of the proposed approach, we give some examples for the engineering applications. Results show an excellent agreement between the solution of the proposed numerical Algorithm and the exact solution.

There are many numerous methods for solving large-scale problems in which some of them are very flexible and efficient in both linear and non-linear cases. League Championship Algorithm is such Algorithm which may be used in the mentioned problems. In the current paper, a new play-off approach will be adapted on League Championship Algorithm for solving large-scale problems. The proposed Algorithm will be used for solving large-scale solving support vector machine model which is a quadratic optimization problem and cannot be solved in a non polynomial time using exact Algorithms or optimally using traditional heuristic ones in large scale sizes. The efficiency of the new Algorithm will be compared to traditional one in terms of the optimality and time measures. The superiority of the Algorithm can be compared versus older version.

This paper addresses a practical but complicated version of Just in Time (JIT) problem in which a set of available jobs with known processing times and due dates are processed on a single machine and delivered in batches of arbitrary size. A new mathematical model is developed to minimize the non-convex sum of earliness-tardiness and delivery costs criteria. Due to the limitations imposed by the large size complexity of the proposed model and its nonlinear nature, we use the recently proposed League Championship Algorithm (LCA) to solve arbitrary test problem instances of the problem on hand. Since LCA works in continuous space, we use several representational schemes to map the solutions generated by LCA to discrete space and compare the output of the Algorithm under each mapping scenario. To measure how effective LCA is in comparison with the mathematical modeling approach and other heuristic methods, we use the Lingo system and a discrete version of the Imperialistic Competitive Algorithm (ICA) as the comparator Algorithms, respectively. Experimental results show that LCA is strongly efficient and dominates the comparator Algorithms. At the same time, the time saved by LCA to report the final output is significant, which recommends the use of this Algorithm for other practical optimization problems.