Multi-objective Optimization Problem Research Articles

Collaborative Video Caching in the Edge Network using Deep Reinforcement Learning

With the enormous growth in mobile data traffic over the 5G environment, Adaptive BitRate (ABR) video streaming has become a challenging problem. Recent advances in Mobile Edge Computing (MEC) technology make it feasible to use Base Stations (BSs) intelligently by network caching, popularity-based video streaming, etc. Additional computing resources on the edge node offer an opportunity to reduce network traffic on the backhaul links during peak traffic hours. More recently, it has been found in the literature that collaborative caching strategies between neighbouring BSs (i.e., MEC servers) make it more efficient to reduce backhaul traffic and network congestion and thus improve the viewer experience substantially. In this work, we propose a Reinforcement Learning (RL) based collaborative caching mechanism where the edge servers cooperate to serve the requested content from the end-users. Specifically, this research aims to improve the overall cache hit rate at the MEC, where the edge servers are clustered based on their geographic locations. The said task is modelled as a multi-objective optimization problem and solved using an RL framework. In addition, a novel cache admission and eviction policy is defined by calculating the priority score of video segments in the clustered MEC mesh network.

Optimization Design of High-Dimensional Parameters MIMO Antenna in Semantic-Based Mobile Applications

To ensure the quality of semantic communication, an optimization scheme for multiple-input and multiple-output (MIMO) antenna design using in semantic-based mobile is proposed and verified. The scheme is based on a modified algorithm MOEA/D-BH, which integrates the black-hole (BH) algorithm into multi-objective EA based on decomposition (MOEA/D). By introducing controllable absorption distance and neighborhood learning mechanism, MOEA/D-BH can deal with high-dimension parameters well in a multi-objective optimization problem. Thus, in a limited design space, a satisfied antenna can be optimized by proposed scheme efficiently. This can be a feasible candidate scheme for MIMO antenna design. A single-band and dual-band MIMO antenna, which are applied for semantic-based mobile system, are optimized by proposed scheme sharing the same model. Both the data of simulation and measurement show good electrical and MIMO performances in the working frequency band. Thus not only the performance of the semantic communication definitely improved, but also it provides useful exploration for the development of intelligent semantic mobile systems.

Multi-objective trajectory planning for industrial robots using a hybrid optimization approach

Abstract In this paper, a hybrid approach organized in four phases is proposed to solve the multi-objective trajectory planning problem for industrial robots. In the first phase, a transcription of the original problem into a standard multi-objective parametric optimization problem is achieved by adopting an adequate parametrization scheme for the continuous robot configuration variables. Then, in the second phase, a global search is performed using a population-based search metaheuristic in order to build a first approximation of the Pareto front (PF). In the third phase, a local search is applied in the neighborhood of each solution of the PF approximation using a deterministic algorithm in order to generate new solutions. Finally, in the fourth phase, results of the global and local searches are gathered and postprocessed using a multi-objective direct search method to enhance the quality of compromise solutions and to converge toward the true optimal PF. By combining different optimization techniques, we intend not only to improve the overall search mechanism of the optimization strategy but also the resulting hybrid algorithm should keep the robustness of the population-based algorithm while enjoying the theoretical properties of convergence of the deterministic component. Also, the proposed approach is modular and flexible, and it can be implemented in different ways according to the applied techniques in the different phases. In this paper, we illustrate the efficiency of the hybrid framework by considering different techniques available in various numerical optimization libraries which are combined judiciously and tested on various case studies.

A line search technique for a class of multi-objective optimization problems using subgradient

A line search technique for a class of multi-objective optimization problems using subgradient

Solving Convex Multi-Objective Optimization Problems via a Capable Neural Network Scheme

A neural network architecture is constructed to solve Convex Multi-objective Programming Problem (CMPP). By using the weighted sum method, a single-objective optimization problem related to the CMPP is formulated, in which the scalar objective is summation of weighted original objective functions. The Pareto Optimal Solution (POS) is given by using different values of weights. A neural network framework is then designed for solving the obtained convex problem. Based on employing Lyapunov theory, the proposed model is established to be stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the convex programming problem with different values of weights. The computer simulations shows the feasibility and the efficiency of the suggested model.

A GPU-accelerated adaptation of the PSO algorithm for multi-objective optimization applied to artificial neural networks to predict energy consumption

Optimization research often confronts the challenge of developing time consuming processes. This article introduces an innovative approach that leverages the computational power of Graphics Processing Units (GPUs) to speed up that optimization process. We present an innovative adaptation of Particle Swarm Optimisation (PSO) to meet the requirements of multiobjective optimization problems. This approach aims to leverage the strengths of a multi-objective approach to perform energy consumption prediction using neural networks. By employing GPU parallel techniques, our method not only speeds up the optimization process but also enhances the efficiency of neural network training execution. The main advantage of our approach lies in its dual ability to simultaneously optimizing neural network architectures by determining the minimum number of hidden neurons and fitting the weights of the networks in order to achieve the lowest error. Preliminary results suggest a notable enhancement in prediction accuracy of forecasting electric energy consumption, as a result of optimizing the architecture and parameters of the neural network using the proposed method. This PSO adaptation stands out for its ability to address complex problems, increase efficiency and produce accurate predictions, making it a novel solution in Machine Learning heuristic methods for application in the solution of advanced prediction problems with time constraints from time series.

Dual-stage and dual-population cooperative evolutionary algorithm for solving constrained multiobjective problems

During the search process, the characteristics of the feasible regions encountered by the population continually change in Constrained Multiobjective Optimization Problems (CMOPs). This variability poses a challenge for traditional evolutionary algorithms, which often struggle to adapt to the diverse problem characteristics of the encountered feasible regions. To overcome this limitation, we propose a Dual-Stage and Dual-Population Cooperative Evolutionary Algorithm (DDCEA) to address CMOPs characterized by diverse feasible regions. DDCEA employs a dual-stage mechanism to adapt the offspring generation strategy and establishes two distinct populations to evaluate offspring using constraint-sensitive and constraint-free strategies. Comparative analyses reveal that DDCEA surpasses chosen state-of-the-art CMOEAs in adapting to the changing feasible regions and then approximating the constrained Pareto fronts.

Medical Support Vehicle Location and Deployment at Mass Casualty Incidents

Anticipating and planning for the urgent response to large-scale disasters is critical to increase the probability of survival at these events. These incidents present various challenges that complicate the response, such as unfavorable weather conditions, difficulties in accessing affected areas, and the geographical spread of the victims. Furthermore, local socioeconomic factors, such as inadequate prevention education, limited disaster resources, and insufficient coordination between public and private emergency services, can complicate these situations. In large-scale emergencies, multiple demand points (DPs) are generally observed, which requires efforts to coordinate the strategic allocation of human and material resources in different geographical areas. Therefore, the precise management of these resources based on the specific needs of each area becomes fundamental. To address these complexities, this paper proposes a methodology that models these scenarios as a multi-objective optimization problem, focusing on the location-allocation problem of resources in Mass Casualty Incidents (MCIs). The proposed case study is Mexico City in a earthquake post-disaster scenario, using voluntary geographic information, open government data, and historical data from the 19 September 2017 earthquake. It is assumed that the resources that require optimal location and allocation are ambulances, which focus on medical issues that affect the survival of victims. The designed solution involves the use of a metaheuristic optimization technique, along with a parameter tuning technique, to find configurations that perform at different instances of the problem, i.e., different hypothetical scenarios that can be used as a reference for future possible situations. Finally, the objective is to present the different solutions graphically, accompanied by relevant information to facilitate the decision-making process of the authorities responsible for the practical implementation of these solutions.

Various duality models associated with some constrained robust nonlinear optimal control problems

This paper deals with various duality results for a new class of constrained robust nonlinear control problems. Concretely, we introduce a minimisation problem associated with a vector of functionals of multiple integral type. In addition, the considered multi-objective controlled optimisation problem is governed by several mixed constraints generated by partial derivatives of second order and uncertain data. For this new class of control problems, we establish and characterise Wolfe, Mond-Weir and mixed type robust dual models. To this aim, by using the notion of convex multiple integral functional, generated by a controlled second-order Lagrangian with uncertain data, and the concept of robust weak efficient solution to the problem under study, we build a new mathematical context to state and prove the duality theorems.

A deep reinforcement learning algorithm framework for solving multi-objective traveling salesman problem based on feature transformation

As a special type of multi-objective combinatorial optimization problems (MOCOPs), the multi-objective traveling salesman problem (MOTSP) plays an important role in practical fields such as transportation and robot control. However, due to the complexity of its solution space and the conflicts between different objectives, it is difficult to obtain satisfactory solutions in a short time. This paper proposes an end-to-end algorithm framework for solving MOTSP based on deep reinforcement learning(DRL). By decomposing strategies, solving MOTSP is transformed into solving multiple single-objective optimization subproblems. Through linear transformation, the features of the MOTSP are combined with the weights of the objective function. Subsequently, a modified graph pointer network(GPN) model is used to solve the decomposed subproblems. Compared with the previous DRL model, the proposed algorithm can solve all the subproblems using only one model without adding weight information as input features. Furthermore, our algorithm can output a corresponding solution for each weight, which increases the diversity of solutions. In order to verify the performance of our proposed algorithm, it is compared with four classical evolutionary algorithms and two DRL algorithms on several MOTSP instances. The comparison shows that our proposed algorithm outperforms the compared algorithms both in terms of training time and the quality of the resulting solutions.

Sizing and energy management of grid-connected hybrid renewable energy systems based on techno-economic predictive technique

This study intends to construct and optimally run a grid-connected hybrid renewable energy system (HRES) powering a residential building. A special techno-economic multi-objective optimization technique is used for sizing the HRES. In addition, an energy management strategy (EMS) is established as a distinct multi-objective optimization problem to minimize degradation and operating costs while improving system performance. A Bi-level mixed integer non-linear programming (BMINLP) is the framework used to formulate the two-optimization problems. Sizing problem is characterized by the higher level, on contrast; the nested EMS problem within the constraints of the size problem is presented on the lower level. For this investigation, the problem is executed via the MATLAB program. The global optimization toolbox is applied via the Multi-Objective Genetic Algorithm (MOGA) to solve the sizing optimization. While the EMS is executed using the "Intlinprg" mixed integer linear programming (MILP) solver. The technical and economic performance parameters such as degradation, renewable energy fraction (REF), operating, maintenance, and investment costs are evaluated in this study. The primary results reveal that the summer week encounters the lowest total cost and the highest REF, at roughly 99484 $ and 60%, respectively. Furthermore, the investigation shows that the lowest degradation value attained in the same week with approximately 50.

A two-stage direction-guided evolutionary algorithm for large-scale multiobjective optimization

Large-scale multiobjective optimization problems (LSMOPs) have exponential growth in the search space as the decision variables increase, and the vast search space poses a challenge to the performance of multiobjective evolutionary algorithms (MOEAs). Many current large-scale MOEAs need to consume a large amount of computational resources to get good performance. This paper proposes a two-stage direction-guided evolutionary algorithm for large-scale multiobjective optimization (LMOEA-S2D) to balance the performance and computational resource overhead. The algorithm exploits the Pareto-optimality property of domination and the diversity-preserving property of decomposition to optimize the performance in the two stages, respectively, and designs a corresponding direction-guided mechanism to improve search efficiency. LMOEA-S2D designs global direction search and local direction search in the domination-based stage for efficient exploitation to accelerate population convergence. To promote greater population diversity, a hybrid direction search was devised to aid diversity exploration in the decomposition-based stage, and this facilitates even distribution of candidate solutions across the Pareto optimal frontier. LMOEA-S2D is compared with five state-of-the-art large-scale MOEAs on some large-scale multiobjective test suites with 100 to 5,000 decision variables. The experimental results show that LMOEA-S2D significantly outperformed all compared algorithms under limited computational resources.

Reinforcement learning-based differential evolution algorithm for constrained multi-objective optimization problems

Many real-world problems can be established as Constrained Multi-objective Optimization Problems (CMOPs). It is still challenging to automatically set efficient parameters for Constrained Multi-Objective Evolutionary Algorithms (CMOEAs) to solve these CMOPs. A Reinforcement Learning-based Multi-Objective Differential Evolution (RLMODE) algorithm is proposed, in which the main parameters are dynamically adjusted. During the evolution process, the offspring generated is evaluated and compared with its corresponding parents, the relationship between the offspring and parent can adjust the parameters of RLMODE by the Reinforcement Learning (RL) technique. The feedback mechanism can produce the most appropriate parameters for RLMODE, which pushes the population towards feasible regions. The proposed RLMODE is evaluated on thirty functions and compared with some popular CMOEAs. The performance indicator IGD has revealed that the proposed RLMODE is competitive. Then, they are applied to solve the UAV path planning problem with three objectives and a constraint. The real application has further demonstrated the superiority of the proposed RLMODE.

A Synergistic Multi-Objective Evolutionary Algorithm with Diffusion Population Generation for Portfolio Problems

When constructing an investment portfolio, it is important to maximize returns while minimizing risks. This portfolio optimization can be considered as a multi-objective optimization problem that is solved by means of multi-objective evolutionary algorithms. The use of multi-objective evolutionary algorithms (MOEAs) provides an effective approach for dealing with the complex data involved in multi-objective optimization problems. However, current MOEAs often rely on a single strategy to obtain optimal solutions, leading to premature convergence and an insufficient population diversity. In this paper, a new MOEA called the Synergistic MOEA with Diffusion Population Generation (DPG-SMOEA) is proposed to address these limitations by integrating MOEAs with diffusion models. To train the diffusion model, a mixed memory pool strategy is optimized, which collects improved solutions from the MOEA/D-AEE, an optimized MOEA, as training samples. The trained model is then used to generate offspring. Considering the cold-start mechanism of the diffusion model, particularly during the training phase where it is not suitable for generating initial offspring, this paper adjusts and optimizes the collaborative strategy to enhance the synergy between the diffusion model and MOEA/D-AEE. Experimental validation of the DPG-SMOEA demonstrates the advantages of using diffusion models in low-dimensional and relatively continuous data analysis. The results show that the DPG-SMOEA performs well on the low-dimensional Hang Seng Index test dataset, while achieving average performance on other high-dimensional datasets, consistent with theoretical predictions. Overall, the DPG-SMOEA achieves better results compared to MOEA/D-AEE and other multi-objective optimization algorithms.

Reference path for ships in ports and waterways based on optimal control

In the context of maritime transportation, waterborne shipping has developed quickly and attracted significant attention. This paper aims to propose a ship path planning model based on optimal control to provide reference paths for ships, prioritizing navigational efficiency and safety considerations. Based on the optimal control, the ship path planning problem is transformed into a multi-objective optimization problem, taking into account the speed constraints of ships during navigation. Then, the cost function based on the multi-objective optimization is constructed. Dynamic programming and numerical simulation are utilized to solve the value function, which is inducted to generate reference paths for ships. In addition, a case study including 12 Origin-Destination (OD) pairs in the Port of Rotterdam is conducted to generate reference paths. The simulation results showed that the model is proven to have high applicability in generating reference paths of ships navigating within the confines of port waters. By enhancing navigational safety and efficiency, the model could be used to provide invaluable guidance to both the bridge team and pilotage work.

Multi-Objective Optimization of a Multi-Cavity, Significant Wall Thickness Difference Extrusion Profile Mold Design for New Energy Vehicles.

With the rapid development of the new energy vehicle market, the demand for extruded profiles for battery trays, mainly characterized by significant wall thickness differences in multiple chambers, is increasing, posing new challenges to production and quality control. This study examines the multi-objective optimization problem in the design process of aluminum profile dies with multi-cavity profiles and significant wall thickness differences. Using QFORM-extrusion professional aluminum extrusion finite element analysis software and the response surface analysis method, the standard deviation of the velocity (SDV), standard deviation of the pressure (SDP), and thick wall hydrostatic pressure (TWHP) on the profile section at the die exit are optimized. By analyzing the functional relationship between the key die structure parameters (the height of the baffle plates, the length of the bearing, and the height of the false mandrel) and the optimization objective, the optimal combination scheme of die structure parameters was obtained using the NSGA2 (non-dominated sorting genetic algorithm-2) multi-objective genetic optimization algorithm. The results show that, compared with the initial design scheme, the standard deviation of profile section velocity was reduced by 5.33%, the standard deviation of pressure was reduced by 11.16%, and the thick wall hydrostatic pressure was increased by 26.47%. The die designed and manufactured using this scheme successfully completed the hot extrusion production task, and the profile quality met the predetermined requirements, thus verifying the effectiveness of this study in optimizing the design of a multi-cavity aluminum profile die with significant differences in wall thickness for complex structures.

Using Genetic Algorithms and Core Values of Cooperative Games to Solve Fuzzy Multiobjective Optimization Problems

A new methodology for solving the fuzzy multiobjective optimization problems is proposed in this paper by considering the fusion of cooperative game theory and genetic algorithm. The original fuzzy multiobjective optimization problem needs to be transformed into a scalar optimization problem, which is a conventional optimization problem. Usually, the assignments of suitable coefficients to the corresponding scalar optimization problem are subjectively determined by the decision makers. However, these assignments may cause some biases by their subjectivity. Therefore, this paper proposes a mechanical procedure to avoid this subjective biases. We are going to formulate a cooperative game using the α-level functions of the multiple fuzzy objective functions. Under this setting, the suitable coefficients can be determined mechanically by involving the core values of the cooperative game, which is formulated using the multiple fuzzy objective functions. We shall prove that the optimal solutions of the transformed scalar optimization problem are indeed the nondominated solutions of fuzzy multiobjective optimization problem. Since the core-nondominated solutions will depend on the coefficients that are determined by the core values of cooperative game, there will be a lot of core-nondominated solutions that will also depend on the corresponding coefficients. In order to obtain the best core-nondominated solution, we shall invoke the genetic algorithms by evolving the coefficients.

A Multi-Objective Optimization Problem Solving Method Based on Improved Golden Jackal Optimization Algorithm and Its Application

The traditional golden jackal optimization algorithm (GJO) has slow convergence speed, insufficient accuracy, and weakened optimization ability in the process of finding the optimal solution. At the same time, it is easy to fall into local extremes and other limitations. In this paper, a novel golden jackal optimization algorithm (SCMGJO) combining sine–cosine and Cauchy mutation is proposed. On one hand, tent mapping reverse learning is introduced in population initialization, and sine and cosine strategies are introduced in the update of prey positions, which enhances the global exploration ability of the algorithm. On the other hand, the introduction of Cauchy mutation for perturbation and update of the optimal solution effectively improves the algorithm’s ability to obtain the optimal solution. Through the optimization experiment of 23 benchmark test functions, the results show that the SCMGJO algorithm performs well in convergence speed and accuracy. In addition, the stretching/compression spring design problem, three-bar truss design problem, and unmanned aerial vehicle path planning problem are introduced for verification. The experimental results prove that the SCMGJO algorithm has superior performance compared with other intelligent optimization algorithms and verify its application ability in engineering applications.

A novel multi-population evolutionary algorithm based on hybrid collaboration for constrained multi-objective optimization

Multi-population-based methods are widely employed for solving constrained multiobjective optimization problems (CMOPs). The population collaboration strategy is a critical part of multi-population algorithms, and different collaboration strategies perform well on different complex CMOPs. However, these single-population collaboration strategies are still challenging to adapt to various CMOPs with different characteristics. To address this issue, we propose a novel tri-population hybrid collaboration evolutionary algorithm called TP-HCEA, which includes a constraint-relaxed population (denoted as mainpop), a constraint-ignored auxiliary population (denoted as auxpop1), and an auxiliary population (denoted as auxpop2) for the original CMOP, to search optimal solutions in the feasible region. Specifically, due to the different complementarities of the two auxiliary populations, mainpop collaborates with auxpop1 and auxpop2 in a dynamic choice between strong and weak cooperation. The effectiveness of TP-HCEA is validated through comparative analysis with seven state-of-the-art algorithms in four CMOP benchmark suites and nine real-world problems.

Multi-objective optimization for low hydrogen consumption and long useful life in fuel cell emergency power supply systems

The power system using hydrogen fuel cells (FCs) as the primary energy source holds significant potential for applications in emergency fields such as post-disaster relief and outdoor power supply. The operational environment of the FC emergency power supply system (FCEPSS) is challenging, with long continuous operation time, difficulties in hydrogen supply, high maintenance costs, and, accordingly, requirements for hydrogen consumption and useful life of FCs are heightened. Hence, this paper proposes a multi-objective energy management strategy (EMS) for FCEPSS. First, the structure of FCEPSS is designed based on the demand analysis in emergency scenarios. Then, the hydrogen consumption and life degradation models of FCEPSS are established. Aiming at the multi-objective optimization problem of minimizing hydrogen consumption and life degradation value in the FCEPSS, an improved multi-objective optimization algorithm is proposed. This paper converts complex constraints into the penalty term and incorporates it as one of the objectives, constructing a three-objective optimization model. To enhance the solution of multi-objective optimization problems, an improved strategy based on relaxation-tightening and three-objective sorting is proposed. Combining the fast non-dominated sorting genetic algorithm-II and the above improved strategy, an improved multi-objective optimization algorithm (IMOOA) is constructed. In the simulation, the advantages of the proposed IMOOA algorithm are verified. In the experimental part, compared with the logical threshold strategy, the proposed strategy saves 0.60% of hydrogen consumption and reduces 5.65% of life degradation within 24 h, respectively. Finally, the superiority of the multi-objective EMS utilizing the IMOOA is demonstrated.