A multiobjective evolutionary algorithm based on decomposition with normal boundary intersection for traffic grooming in optical networks

Traffic grooming in optical networks is the process of multiplexing and demultiplexing low-speed traffic streams onto high-speed wavelengths. The research in the domain of traffic grooming mainly focuses on minimizing number of SONET add/drop multiplexers (SADMs) in SONET/WDM rings and it has been shown that they can potentially be reduced by careful assignment of low-speed traffic streams onto high-speed wavelengths. However, the cost of the network not only depends on the number of SADMs, but also the number of wavelengths and the grooming ratio. It is often the case that all of them cannot be minimized simultaneously. In this article, the problem of minimization of cost of a SONET/WDM unidirectional ring has been modeled as a multiobjective optimization problem which simultaneously minimizes the number of SADMs, the number of wavelengths, and the grooming ratio. A popular multiobjective genetic algorithm (NSGA-II) has been used as the underlying optimization tool. The resultant set of near-Pareto-optimal solutions contains a number of nondominated solutions, which the user can judge relatively and pick up the most promising one according to the problem requirements. Performance of the proposed algorithm has been demonstrated on different network topologies.

Optical networks can benefit from multipath routing by routing traffic over diverse fiber links to fulfill bandwidth requirements, balance network load and improve resource utilization. This paper focuses on the effectiveness of multipath routing on aggregating residual bandwidth of the established lightpaths using dynamic traffic grooming. An optimization model based on Integer Linear Programing (ILP) is formulated to leverage multipath routing and grooming to serve connection requests with known duration, in a scenario where the dynamic traffic can demand bandwidth either larger or smaller than a single wavelength capacity. The impact of a balancing policy, referred to as Holding Time Balancing (HTBalancing), on multipath routing with traffic grooming in optical networks is also investigated. Numerical results show that the proposed optimization model can achieve a lower bandwidth blocking and a better load balancing with HTBalancing policy, when compared with single path routing. The proposed relaxation algorithm can effectively find near optimal solutions, and be applied in realistic scenarios.

Traffic Grooming in optical networks is one if the most important and hot problems in the area of optical network. In the static traffic grooming problem, we introduce the concept of QoS (Quality of Service); in order to minimize the network cost utilization rate and to maximize the QoS degree of the users at the same time, we apply the intelligent computing algorithm -QIA( the quantum-based Immune Algorithm) to the framework to solve the problem.

The Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) is a popular algorithm for solving Multi-Objective Problems (MOPs). The main component of MOEA/D is to decompose a MOP into easier sub-problems using a set of weight vectors. The choice of the number of weight vectors significantly impacts the performance of MOEA/D. However, the right choice for this number varies, given different MOPs and search stages. We adaptively change the number of vectors by removing unnecessary vectors and adding new ones in empty areas of the objective space. Our MOEA/D variant uses the Consolidation Ratio to decide when to change the number of vectors and to decide where to add or remove these weighted vectors. We investigate the effects of this adaptive MOEA/D against MOEA/D with a poorly chosen set of vectors, a MOEA/D with fine-tuned vectors and MOEA/D with Adaptive Weight Adjustment on two commonly used benchmark functions. We analyse the algorithms in terms of hypervolume, IGD and entropy performance. Our results show that the proposed method is equivalent to MOEA/D with fine-tuned vectors and superior to MOEA/D with poorly defined vectors. Thus, our adaptive mechanism mitigates problems related to the choice of the number of weight vectors in MOEA/D, increasing the final performance of MOEA/D by filling empty areas of the objective space and avoiding premature stagnation of the search progress.

Less attention has been given to energy aware optical counterparts, compared to the research in energy-aware wireless and ethernet networks. In this paper, we consider energy-aware traffic grooming problems in optical networks for both static and dynamic cases. Rather than simply considering a logical architecture of an optical node, we specifically look further into the modular physical architecture. We show that by reusing already active physical components during request allocations, we can significantly reduce the total number of active components and, hence, total energy consumption in the network, especially when traffic load is low. Since energy usage is an important element of operational expenditure, this approach provides the financial motivation for service providers along with the desired environmental motivation. We present a mathematical formulation of the problems, propose auxiliary graph based heuristics, and justify our cases compared to traditional approaches, based on simulation results.

Traffic grooming in optical networks employing wavelength division multiplexing (WDM) has gained prominence due to the prevailing disparity between the user requirement and wavelength capacity. Nodes in an optical network get upgraded to the latest grooming technology slowly with time. Hence, WDM grooming networks are expected to employ heterogeneous grooming architectures. In this paper, we develop an analytical model to evaluate the blocking performance of WDM grooming networks with heterogeneous grooming capabilities. We demonstrate the accuracy of the analytical model by comparing the analytical results with that of the simulation. We observe that analytical models with and without precise knowledge of the grooming architectures predict similar performance. The proposed analytical model can be employed by resource placement algorithms that identify a set of nodes and links that need to be upgraded when the resources are limited.

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.

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.

In this paper, we propose a parallel multiobjective approach based on the honey bees' behaviour for grooming low-speed traffic requests onto high-capacity optical channels. This problem of grooming low-speed traffic requests is known in the literature as the traffic grooming problem. This problem in mesh optical networks is an NP-hard problem, in which the solution time raises exponentially when the network size increases; therefore, the use of metaheuristics and parallelism jointly is a great option in order to reduce the prohibitive runtime. The parallel approach is implemented for shared-memory architectures by using OpenMP. In our experiments, we have measured the speedup and efficiency of the method with 1, 2, 4, 8 and 16 cores when dealing with three optical networks: small (6-node network, 6 nodes), medium (National Science Foundation, 14 nodes) and large (Nippon Telegraph and Telephone, 55 nodes). Furthermore, we present a comparative study with traditional methods and other multiobjective metaheuristics published in the literature; in which we show the advantages of our multiobjective proposal.

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.

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.

To obtain propellant formulations with superior comprehensive and robustness performance, the study establishes a multi-objective optimization model that accounts for uncertainties. The model adopts a bi-layer structure. The inner layer computes performance bounds to construct uncertainty intervals, which are subsequently transformed into deterministic performance via interval order relations. The outer layer optimizes component mass fractions using MOEA/D (Multi-objective Evolutionary Algorithm Based on Decomposition) to maximize the deterministic performance. The study leverages Large Language Models (LLMs) as pre-trained optimizers to automate the operator design of MOEA/D. Designers can identify formulations that satisfy the performance requirements and robustness criteria by adjusting uncertainty levels and MOEA/D weight coefficients. The results on ZDTs and UFs demonstrate that MOEA/D-LLM achieves approximately a 4.0% improvement in hypervolume values compared to MOEA/D. Additionally, the NEPE propellant optimization case shows that MOEA/D-LLM improves the computational speed by about 13.05% and enhances hypervolume values by around 2.7% compared to MOEA/D. The specific impulse increases by 1.11%, the generation of aluminum oxide and hydrogen chloride decreases by approximately 18.43% and 16.40%, respectively, and the impact sensitivity is reduced by about 1.67%.

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.

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

A triple‐objective optimal design method for AC filters in high voltage direct current (HVDC) system based on an improved multi‐objective evolutionary algorithm based on decomposition (MOEA/D) is proposed. A triple‐objective optimisation mathematical model including total harmonic distortion (THD) on AC side voltage, investment cost of AC filters and telephone harmonic form factor (THFF) is established. An improved MOEA/D is proposed to realise the triple‐objective optimal design for AC filters more efficiently. The improved MOEA/D adds a particular mutation operator, which can not only to prevent MOEA/D from getting stuck at local optimum but also accelerate the convergence to the optimum solution while the algorithm approaches the neighbourhood of the optimum solution. A three‐dimensional fuzzy evaluation system is designed to select the optimum solution of the triple‐objective optimisation. A case of ±500 kV HVDC system is simulated. Taking the ±500 kV HVDC system as the prototype system, a dynamic simulation experimental platform of the rectification system of the direct current transmission system with AC filters is designed and established based on the similarity principle. Both the simulation and experimental results verify that the proposed method have excellent performance.