The Multi-Depot Vehicle Routing Problem (MDVRP) is a real-world model of the simplistic Vehicle Routing Problem (VRP) that considers how to satisfy multiple customer demands from numerous depots. This paper introduces a hybrid 2-stage approach based on two population-based algorithms - Ant Colony Optimization (ACO) that mimics ant behaviour in nature and the Imperialist Competitive Algorithm (ICA) that is based on geopolitical relationships between countries. In the proposed hybrid algorithm, ICA is responsible for customer assignment to the depots while ACO is routing and sequencing the customers. The algorithm is compared to non-hybrid ACO and ICA as well as four other state-of-the-art methods across 23 common Cordreau's benchmark instances. Results show clear improvement over simple ACO and ICA and demonstrate very competitive results when compared to other rival algorithms.

The multidimensional knapsack problem is a well-known constrained optimization problem with many real-world engineering applications. In order to solve this NPhard problem, a new modified Imperialist Competitive Algorithm with Constrained Assimilation (ICAwICA) is presented. The proposed algorithm introduces the concept of colony independence - a free will to choose between classical ICA assimilation to empire's imperialist or any other imperialist in the population. Furthermore, a constrained assimilation process has been implemented that combines classical ICA assimilation and revolution operators, while maintaining population diversity. This work investigates the performance of the proposed algorithm across 101 Multidimensional Knapsack Problem (MKP) benchmark instances. Experimental results show that the algorithm is able to obtain an optimal solution in all small instances and presents very competitive results for large MKP instances.

Prediction of crop yield is essential for food security policymaking, planning, and trade. The objective of the current study is to propose novel crop yield prediction models based on hybrid machine learning methods. In this study, the performance of the artificial neural networks-imperialist competitive algorithm (ANN-ICA) and artificial neural networks-gray wolf optimizer (ANN-GWO) models for the crop yield prediction are evaluated. According to the results, ANN-GWO, with R of 0.48, RMSE of 3.19, and MEA of 26.65, proved a better performance in the crop yield prediction compared to the ANN-ICA model. The results can be used by either practitioners, researchers or policymakers for food security.

This paper presents an implementation of the Imperialist Competitive Algorithm (ICA) for solving the fuzzy random portfolio selection problem where the asset returns are represented by fuzzy random variables. Portfolio Optimization is an important research field in modern finance. By using the necessity-based model, fuzzy random variables reformulate to the linear programming and ICA will be designed to find the optimum solution. To show the efficiency of the proposed method, a numerical example illustrates the whole idea on implementation of ICA for fuzzy random portfolio selection problem.