Multi-objective optimization

Increasing economy’s resistance against the menace of sanctions, various risks, shocks, and internal and external threats are one of the main national policies which can be implemented through bank investments. Investment project selection is a complex and multi-criteria decision-making process that is influenced by multiple and often some conflicting objectives. This paper studies portfolio investment decisions in Iranian Banks. The main contribution of this paper is the creation of a project portfolio selection model that facilitates how Iranian banks would make investment decisions on proposed projects to satisfy bank profit maximization and risk minimization, while focus on national policies such as Resistance Economy Policies. The considered problem is formulated as a multi-objective integer programming model. A framework called Multi-Objective Electromagnetism-like (MOEM) algorithm, is developed to solve this NP-hard problem. To further enhance MOEM, a local search heuristic based on simulated annealing is incorporated in the algorithm. In order to demonstrate the efficiency and reliability of the proposed algorithm, a number of test are performed. The MOEM results are compared with two well-known multi-objective genetic algorithms in the literature, i.e. Non-dominated Sorting Genetic Algorithm (NSGA-II) and Strength Pareto Evolutionary Algorithm (SPEA-II) based on some comparison metrics. Also, these algorithms are compared with an integer linear programming formulation for small instances. Computational experiments indicate the superiority of the MOEM over existing algorithms.

In the current paper, we have assimilated fuzzy techniques and optimization techniques, namely differential evolution, to put forward a modern archive-based fuzzy evolutionary algorithm for multi-objective optimization using clustering. The current work account for the application of a cluster associated approach. Specific quantitative cluster validity measures, i.e., J-measure and Xie-Beni, have been referenced to carry out the appropriate partitioning. The proposed algorithm introduces a new form of strategy which attempts to benefit the feasible search domain of the algorithm by minimizing the analysis and exploration of less beneficial search scope. This clustering method yields a group of trade-off solutions on the ultimate optimal pare to front. Eventually, these solutions are united and maintained in an archive for further evaluation. The current work summarizes and organizes an archive concerned with excellent and diversified solutions in an effort to outline comprehensive non-dominated solutions. The degree of efficiency is revealed with respect to partitioning on gene expression and real-life datasets. The proposed algorithm seeks to reduce the function assessment analysis and maintains a very small working population size. The effectiveness of the proposed method is presented in comparison with some state-of-art methods.

As we are looking for knowledge of stock future returns in portfolio optimization, we are practically faced with two principal concepts: Uncertainty and Information about variables. This paper attempts to introduce a pragmatic bi-objective investment model based on uncertainty, instead of probability space and information theory, instead of variance and other moments as a risk measure for portfolio optimization. Not only is uncertainty space expected to be more in line with investment theory, but also, applying and learning this approach seems more straightforward and practical for novice investors. The proposed model simultaneously maximizes the uncertain mean of stock returns and minimizes uncertain entropy as a measure of portfolio risk. The uncertain zigzag distribution has been used for variables to avoid the complexity of fitting distributions for data. This uncertain mean-entropy portfolio optimization (UMEPO) has been solved by three meta-heuristic methods of multi-objective optimization: NSGA-II, MOPS, and MOICA. Finally, it was observed that the optimal portfolio obtained from the proposed model has a higher return and a lower entropy as a risk measure compared to the same model in the probability space.