An Interval Analysis Method for Uncertain Multi-Objective Optimization of Solid Propellant Formulations

Multiobjective evolutionary algorithms based on decomposition (MOEA/D) decompose a multiobjective optimization problem (MOP) into a group of subproblems and optimizes them at the same time. The reproduction method in MOEA/D, which generates offspring solutions, has crucial effect on the performance of algorithm. As the difficulties of MOPs increases, it requires much higher efficiency for the reproduction methods in MOEA/D. However, for the complex optimization problems whose PS shape is complicated, the original reproduction method used in MOEA/D might not be suitable to generate excellent offspring solutions. In order to improve the property of the reproduction method for MOEA/D, this paper proposes an external archive matching strategy which selects solutions’ most matching archive solutions as parent solutions. The offspring solutions generated by this strategy can maintain a good convergence ability. To balance convergence and diversity, a perturbed learning scheme is used to extend the search space of the solutions. The experimental results on three groups of test problems reveal that the solutions obtained by MOEA/D-EAM have better convergence and diversity than the other four state-of-the-art algorithms.

In optimization problems it is often necessary to perform an optimization based on more than one objective. The goal of the multiobjective optimization is usually to find an approximation of the Pareto front which contains solutions that represent the best possible trade-offs between the objectives. In a multiobjective scenario it is important to both improve the solutions in terms of the objectives and to find a wide variety of available options. Evolutionary algorithms are often used for multiobjective optimization because they maintain a population of individuals which directly represent a set of solutions of the optimization problem. multiobjective evolutionary algorithm based on decomposition (MOEA/D) is one of the most effective multiobjective algorithms currently used in the literature. This paper investigates several methods which increase the selective pressure to the outside of the Pareto front in the case of the MOEA/D algorithm. Experiments show that by applying greater selective pressure in the outwards direction the quality of results obtained by the algorithm can be increased. The proposed methods were tested on nine test instances with complicated Pareto sets. In the tests the new methods outperformed the original MOEA/D algorithm.

Although a number of multiobjective evolutionary algorithms have been proposed over the last two decades, not much effort has been made to deal with variable linkages in multiobjective optimization. Recently, we have suggested a general framework of multiobjective evolutionary algorithms based on decomposition (MOEA/D) [1]. MOEA/D decomposes a MOP into a number of scalar optimization subproblems by a conventional decomposition method. The optimal solution to each of these problems is a Pareto optimal solution to the MOP under consideration. An appropriate decomposition could make these individual Pareto solutions evenly distribute along the Pareto optimal front. MOEA/D aims at solving these scalar optimization subproblems simultaneously. In this paper, we propose, under the framework of MOEA/D, a multiobjective differential evolution based decomposition (MODE/D) for tackling variable linkages. Our experimental results show that MODE/D outperforms several other MOEAs on several test problems with variable linkages.

A Multiobjective Optimization Problem (MOP) requires the optimization of several objective functions simultaneously, usually in conflict with each other. One of the most efficient algorithms for solving MOPs is MOEA/D (Multiobjective Evolutionary Algorithm Based on Decomposition), which decomposes a MOP into single-objective optimization subproblems and solves them using information from neighboring subproblems. MOEA/D variants with other evolutionary operators have emerged over the years, improving their efficiency in various MOPs. Recently, the IWOA (Improved Whale Optimization Algorithm) was proposed, an optimization algorithm bioinspired by the whale hunting method hybridized with Differential Evolution, which presented excellent results in single-objective optimization problems. This work proposes the MOEA/D-IWOA algorithm, which associates characteristics of the evolutionary operators of the IWOA to MOEA/D. Computational experiments were accomplished to analyze the performance of the MOEA/D-IWOA in benchmark MOPs suites. The results were compared with those obtained by the MOEA/D, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Third Evolution Step of Generalized Differential Evolution (GDE3), Improving the Strength Pareto Evolutionary Algorithm (SPEA2), and Indicator-Based Evolutionary Algorithm (IBEA) algorithms in the Hypervolume and Inverted Generational Distance Plus (IGD+) indicators. The MOEA/D-IWOA proved to be competitive, with a good performance profile, in addition to presenting the best results in some POMs.

Given that the definition of the multi-objective optimization problem is raised when number of objectives is increased in number at the optimization problem, where not only the number of objectives but also the computational resources which are needed to solve the problem, is also more desired. Therefore, novel approaches had required to solve multi-objective optimization problem in a reasonable time. One of this novel approach is utilization of the decomposition method with the evolutionary algorithm/operator. This algorithm was called multi-objective evolutionary algorithm based on decomposition (MOEA/D). Later on, variants have been proposed to improve the performance of the MOEA/D algorithm. However, a general comparison between these variants has needed for demonstrate the performance of these algorithm. For this reason, in this research the variants of MOEA/D algorithms have implemented on benchmark problems (DTLZ and MaF) and the performances has compared with each other. Two metrics had selected to evaluate/compare the performances of the variants. The metrics are IGD and Spread metrics. The results at the end of the implementations suggest that adaptive weighting idea is the most promising idea to increase the performance of the MOEA/D algorithm.

There are a large number of multi-objective optimization problems in real-world applications, like in games, that need to be solved in real time. In order to meet this pressing need, we suggests a method of parallelizing the multi-objective evolutionary algorithm based on decomposition (MOEA/D). Furthermore, a novel task decomposition strategy and scalarizing method without the ideal point are proposed for meeting the requirements of real-time and precision of the game. By combining the novel scalarizing function and GPU-based CUDA technology with the MOEA/D, a parallel MOEA/D for real-time multi-objective optimization problems is developed, namely P-MOEA/D. Experimental studies on ZDT and DTLZ benchmark problems suggest that the P-MOEA/D algorithm is efficient and fast.

A decomposition based memetic algorithm for multi-objective vehicle routing problem with time windows

Constrained multiobjective optimization arises in many real-life applications, and is therefore gaining a constantly growing attention of the researchers. Constraint handling techniques differ in the way infeasible solutions are evolved in the evolutionary process along with their feasible counterparts. Our recently proposed threshold based penalty function gives a chance of evolution to infeasible solutions whose constraint violation is less than a specified threshold value. This paper embeds the threshold based penalty function in the update and replacement scheme of multi-objective evolutionary algorithm based on decomposition (MOEA/D) to find tradeoff solutions for constrained multiobjective optimization problems (CMOPs). The modified algorithm is tested on CTP-series test instances in terms of the hypervolume metric (HV-metric). The experimental results are compared with the two well-known algorithms, NSGA-II and IDEA. The sensitivity of algorithm to the adopted parameters is also checked. Empirical results demonstrate the effectiveness of the proposed penalty function in the MOEA/D framework for CMOPs

Learning of fuzzy parameters for system modeling using evolutionary algorithms is an interesting topic. In this paper, two optimal design and tuning of Interval type-2 fuzzy logic system are proposed using hybrid learning algorithms. The consequent parameters of the interval type-2 fuzzy logic system in both the hybrid algorithms are tuned using Kalman filter. Whereas the antecedent parameters of the system in the first hybrid algorithm is optimized using the multi-objective particle swarm optimization (MOPSO) and using the multi-objective evolutionary algorithm Based on Decomposition (MOEA/D) in the second hybrid algorithm. Root mean square error and maximum absolute error as the two accuracy objective are utilized to find the Pareto-optimal solution with the MOPSO and MOEA/D respectively. The proposed hybrid multi-objective designs of the interval type-2 fuzzy logic system are utilized to the prediction of solar photovoltaic output. It is observed that MOEA/D outperforms MOPSO in this case in terms of quality of results and its diversity. Finally, one point is selected from the obtained Pareto front and its performance is illustrated.

The Markowitz mean-variance (MV) model is the basis of modern portfolio theory, the goal of which is to choose an optimal set of weights with the maximum expected return for a given level of risk. However, the MV model assumes that returns are normally distributed, which ignores the asymmetry of returns in real life. The mean-variance-skewness (MVS) portfolio framework introduces the skewness of the return as an extension of the classical MV model. Because of the increasing conflicting objective functions, the multi-objective portfolio optimization problem is more difficult to solve. This paper investigates the use of a multi-objective evolutionary algorithm based on decomposition (MOEA/D) for solving the portfolio optimization problem in the stock market. The results show that MOEA/D can produce Pareto fronts efficiently with three objectives to be optimized.

A new approach in multi-objective evolutionary optimization is decomposition. Decomposition is a basic method in old multi-objective optimization which in evolutionary multiobjective optimization, has not been widely used. Using this method, a multi-objective optimization problem is converted into a number of scalar subproblems, and all the subproblems are simultaneously optimized. In this paper, the performance and efficiency of the algorithm MOEA/D (multi-objective evolutionary algorithm based on decomposition) with the performance of two algorithms NSGA-II and MOPSO (evolution optimization methods based on dominance) for solving constrained portfolio optimization in Tehran Stock Exchange, has been compared. Portfolio return and its risk, has been considered as the optimization objectives and CvaR has been considered as a risk measure. The results indicate the high potential of these algorithms for constrained portfolio optimization. Also, the results indicate that the optimization algorithm based on decomposition has lower computational complexity, and Pareto front is more extensive than the other two methods. (Abstract)

Multi-objective Estimation of Distribution Algorithms (MOEDAS) have been successfully applied to solve Multi-objective Optimization Problems (MOPs) since they are able to model dependencies between variables of the problem and then sample new solutions to guide the search to promising areas. A state-of-the-art optimizer for single-objective continuous functions that also uses probabilistic modeling is the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Different variants of CMA-ES have been proposed for MOPs however most of them are based on Pareto dominance as the main selection criterion. Recently, a new multi-objective CMA-ES called MOEA/D-CMA was proposed combining the strengths of CMA-ES with those of the multi-objective evolutionary algorithm based on decomposition (MOEA/D). Nowadays, however, researchers on MOEAs agree that combining Pareto and decomposition can be beneficial for the search on MOPs. As a result, a new MOEA has been proposed, called MOEA/DD. This algorithm modifies the MOEA/D by including a new Pareto dominance update mechanism that brings more diversity into the search. In this study, we extend the MOEA/D-CMA by replacing its update mechanism by the one of MOEA/DD. The hypothesis is that this update mechanism will improve the performance of MOEA/D-CMA as it improved MOEA/D. MOEA/D-CMA and MOEA/DD-CMA are implemented and evaluated through an experimental study. The experimental study involves two well-known families of benchmark problems whose objective numbers scale from two to fifteen. Then, an extensive statistical analysis of the results is made to extract sound, statistically supported conclusions about the performance of the algorithms as the number of objectives scales.

A new resource allocation strategy based on the relationship between subproblems for MOEA/D

Wireless sensor networks design requires high quality location assignment and energy efficient power assignment for maximizing the network coverage and lifetime. Classical deployment and power assignment approaches optimize these two objectives individually or by combining them together in a single objective or by constraining one and optimizing the other. In this article a multi-objective deployment and power assignment problem (DPAP) is formulated and a multi-objective evolutionary algorithm based on decomposition (MOEA/D) is specialized. Following the MOEA/D's framework the above multiobjective optimization problem (MOP) is decomposed into many scalar single objective problems. The sub-problems are solved simultaneously by using neighborhood information. Additionally, unique problem-specific, parameter-rising, genetic operators and local search heuristics were designed specifically for the DPAP. In addition, a new encoding scheme is designed to represent a WSN based on the DPAP's design variables. Simulation results show that MOEA/D provides a high quality set of alternative solutions without any prior knowledge on the objectives preference.

Rapid growth in data and computational demands has driven the widespread adoption of heterogeneous computing systems that combine different processing units, such as CPUs, GPUs, and FPGAs. Efficient scheduling of tasks in these systems is essential to optimize resource utilization, reduce power consumption, and meet performance requirements. However, the complexities of managing multiple tasks, diverse machine architectures, and conflicting objectives make scheduling in these environments an NP-hard problem. This study reformulates the traditional scheduling model as a multi-objective optimization problem focusing on minimizing makespan and maximizing parallelization across heterogeneous systems. Multi-Objective Evolutionary Algorithms based on Decomposition (MOEA/D) have effectively solved these complex scheduling challenges. MOEA/D offers a flexible and powerful approach for handling multi-objective scheduling tasks in a heterogeneous computing environment. This paper explores how MOEA/D can be combined with other metaheuristics to further improve task scheduling and balance competing performance objectives. The effectiveness of the approach is demonstrated through 28 validation scenarios. The algorithm’s performance is evaluated using four scientific workflows: structured as (FFT and Montage) and unstructured as (Molecular-A and Molecular-B). Performance evaluation is performed using appropriate metrics, specifically hypervolume and inverted generational distance plus, to assess the quality of the solutions. Experimental results demonstrate that the GRASP-MOEA/D hybrid approach outperforms all competitors in structured workflows, achieving the best schedule by minimizing makespan and maximizing resource utilization within a reasonable runtime. For unstructured workflows, GSA-MOEA/D achieves the best performance in 75% of cases, while SA-MOEA/D is the best in 37.5% of cases. However, GSA-MOEA/D and SA-MOEA/D face significant computational overhead as workflow size increases. In particular, GRASP-MOEA/D is the second-best performer in most unstructured workflow scenarios, making it a strong alternative to effectively solve these scheduling challenges.