Nonlinear Multi-objective Optimization Problem Research Articles

Pareto Optimization or Cascaded Weighted Sum: A Comparison of Concepts

Looking at articles or conference papers published since the turn of the century, Pareto optimization is the dominating assessment method for multi-objective nonlinear optimization problems. However, is it always the method of choice for real-world applications, where either more than four objectives have to be considered, or the same type of task is repeated again and again with only minor modifications, in an automated optimization or planning process? This paper presents a classification of application scenarios and compares the Pareto approach with an extended version of the weighted sum, called cascaded weighted sum, for the different scenarios. Its range of application within the field of multi-objective optimization is discussed as well as its strengths and weaknesses.

Game Theoretic Framework for Future Generation Networks Modelling and Optimization

A new cost efficient automated planning and optimization method is proposed for OFDMA future-generation cellular networks targeting throughput maximization. The mathematical formulation is a non-linear multi-objective optimization problem subject to minimum interference, cost and similar resource constraints at each cell within a defined heterogeneous traffic environment. The fundamental objective is to maximize the individual cell throughput without deteriorating it over other cells, which results in a throughput equilibrium maximization over multiple cells. This implicitly implies traffic and co-channel interference congestion avoidance across the network whilst maintaining both cost efficiency and quality of service (QoS) policies. Optimal solution existence is subject to the network size, traffic and computational complexity constraints which converges to a throughput equilibrium or alternatively to the well known Nash Equilibrium (NE).

Multiobjective genetic algorithm conjunctive use optimization for production, cost, and energy with dynamic return flow

Many real water resources optimization problems involve conflicting objectives for which the main goal is to find a set of optimal solutions on, or near to the Pareto front. E-constraint and weighting multiobjective optimization techniques have shortcomings, especially as the number of objectives increases. Multiobjective Genetic Algorithms (MGA) have been previously proposed to overcome these difficulties. Here, an MGA derives a set of optimal solutions for multiobjective multiuser conjunctive use of reservoir, stream, and (un)confined groundwater resources. The proposed methodology is applied to a hydraulically and economically nonlinear system in which all significant flows, including stream-aquifer-reservoir-diversion-return flow interactions, are simulated and optimized simultaneously for multiple periods. Neural networks represent constrained state variables. The addressed objectives that can be optimized simultaneously in the coupled simulation–optimization model are: (1) maximizing water provided from sources, (2) maximizing hydropower production, and (3) minimizing operation costs of transporting water from sources to destinations. Results show the efficiency of multiobjective genetic algorithms for generating Pareto optimal sets for complex nonlinear multiobjective optimization problems.

Application of Parallel Chaos Optimization Algorithm for Plug-in Hybrid Electric Vehicle Design

Plug-in hybrid electric vehicles (PHEVs) have been offered as alternatives that could greatly reduce fuel consumption relative to conventional vehicles. A successful PHEV design requires not only optimal component sizes but also proper control strategy. In this paper, a global optimization method, called parallel chaos optimization algorithm (PCOA), is used to optimize simultaneously the PHEV component sizes and control strategy. In order to minimize the cost, energy consumption (EC), and emissions, a multiobjective nonlinear optimization problem is formulated and recast as a single objective optimization problem by weighted aggregation. The driving performance requirements of the PHEV are considered as the constraints. In addition, to evaluate the objective function, the optimization process is performed over three typical driving cycles including Urban Dynamometer Driving Schedule (UDDS), Highway Fuel Economy Test (HWFET), and New European Driving Cycle (NEDC). The simulation results show the effectiveness of the proposed approach for reducing the fuel cost, EC and emissions while ensuring that the vehicle performance has not been sacrificed.

Optimization of Distribution Network

Distribution network is the design of closed loop, open loop operation,which segment equipped with a normally closed and normally open switch contact switch,By changing these disconnect switches and contact switch status, the structure of the distribution network reconfiguration, you can achieve a balanced load, reducing network losses and improve voltage quality role.Distribution Network Reconfiguration in mathematics is a multi-objective high-dimensional nonlinear optimization problem, has a great solution space, using the general optimization method is difficult to obtain a good solution.Existing optimization methods such as optimal flow pattern method, branch exchange method, particle swarm optimization, genetic algorithms, computational efficiency and optimization results in other aspects worthy of improvement.

Optimal energy management of a micro-grid with renewable energy resources and demand response

With the introduction of smart energy grids and extensive penetration of renewable energy resources in distribution networks, Micro-Grids (MGs), which are comprised of various alternative energy resources and Advanced Metering Infrastructure (AMI) systems for better implementation of DR programs, are effectively employed. The design and development of Smart Energy Management Systems (SEMSs) for MGs are interesting and attractive research problems. In this paper a new SEMS architecture is presented to solve the multi-objective operation management and scheduling problem in a typical MG while considering different energy resource technologies, Plug-in Hybrid Electric Vehicles (PHEVs) and DR programs. The energy management problem is formulated as a constrained mixed integer nonlinear multi-objective optimization problem, in which the MG's total operating cost and net emissions must be minimized simultaneously. Three different optimization algorithms are used to solve the above mentioned problem and their outputs (Pareto optimal solutions) for the same problem are compared and analyzed.

Fuzzy Based Multi-Objective Evolutionary Algorithm for Optimal Location of FACTS Devices in a Power System

This paper presents a Multi Objective Evolutionary Algorithm (MOEA) to solve nonlinear power system optimization problem. The optimization is done with three variables; choice, location and rating of FACTS devices. The targeted technical objectives are; to control the power flow, increase the transmission line capability to its maximum thermal limits, to keep the voltages within limits while minimizing losses. The parameters of objectives are optimized independently and then the formulation of a nonlinear constrained multi-objective optimization problem is done while carrying out concurrent optimization taking two and three objectives. A Fuzzy min max approach is incorporated to reduce the best solution out of non dominated Pareto optimal set. Assessments have been done on IEEE 14 and IEEE 30 bus system for different loading conditions with two devices SVC and TCSC modeled in steady state and the results affirm the potency of the propound approach.

A New Scalarization Technique to Approximate Pareto Fronts of Problems with Disconnected Feasible Sets

We introduce and analyze a novel scalarization technique and an associated algorithm for generating an approximation of the Pareto front (i.e., the efficient set) of nonlinear multiobjective optimization problems. Our approach is applicable to nonconvex problems, in particular to those with disconnected Pareto fronts and disconnected domains (i.e., disconnected feasible sets). We establish the theoretical properties of our new scalarization technique and present an algorithm for its implementation. By means of test problems, we illustrate the strengths and advantages of our approach over existing scalarization techniques such as those derived from the Pascoletti–Serafini method, as well as the popular weighted-sum method.

A new ant algorithm solving the combined economic and emission dispatch problem

This paper presents a new approach to the Combined Economic and Emission Dispatch (CEED) problem, using the Continuous Ant System (C-ANT) algorithm. The CEED problem is a multi-objective nonlinear optimization problem with constraints. This problem is one of the fundamentals issues in power system operations. The paper focuses on the emission of nitrogen oxides (NO x ), because its control is significant in electric power planning. A new ant algorithm (C-ANT) is proposed for solving the CEED problem. The CEED problem is converted into a single optimization problem using a price penalty factor h. To show its efficiency and effectiveness, the proposed C-ANT algorithm is applied to a six-generator test system. The load demand of the system is 500 and 900 MW. Results show the applicability and efficiency of the proposed C-ANT algorithm. With respect to the applicability of the algorithm, the fact that it has been designed to accommodate continuous intervals in problem space distinguishes it from other similar algorithmic approaches.

Research Status and Progress on Anti-ship Missile Path Planning

Path planning is one of the multi-objective non-linear optimization problems with multiple constraints. The problem of anti-ship missile path planning (ASMPP) and its approaches are reviewed in this work. Firstly, the research status of ASMPP problem domains is analyzed. It includes unification and specification of correlative nomenclature about ASMPP, the problem boundary and definition, and the characteristics of ASMPP. Secondly, the research progress of problem model is analyzed. Thirdly, the research progress of ASMPP methods based on geometry principle and intelligent optimization algorithms is analyzed. Fourthly, the research progress of cooperative path planning methods of anti-ship missiles launched from multiple platforms is analyzed and summarized. Finally, a brief conclusion of the key problems and the development trend of ASMPP are elaborated.

Multiobjective scatter search approach with new combination scheme applied to solve environmental/economic dispatch problem

The environmental/economic dispatch (EED) is an important daily optimization task in the operation of many power systems. It involves the simultaneous optimization of fuel cost and emission objectives which are conflicting ones. The EED problem can be formulated as a large-scale highly constrained nonlinear multiobjective optimization problem. In recent years, many metaheuristic optimization approaches have been reported in the literature to solve the multiobjective EED. In terms of metaheuristics, recently, scatter search approaches are receiving increasing attention, because of their potential to effectively explore a wide range of complex optimization problems. This paper proposes an improved scatter search (ISS) to deal with multiobjective EED problems based on concepts of Pareto dominance and crowding distance and a new scheme for the combination method. In this paper, we have considered the standard IEEE (Institute of Electrical and Electronics Engineers) 30-bus system with 6-generators and the results obtained by proposed ISS algorithm are compared with the other recently reported results in the literature. Simulation results demonstrate that the proposed ISS algorithm is a capable candidate in solving the multiobjective EED problems.

Optimal VAR control for improvements in voltage profiles and for real power loss minimization using Biogeography Based Optimization

In this paper, a Biogeography Based Optimization (BBO) technique is introduced to solve multi-constrained optimal reactive power flow (ORPF) problem in power system. ORPF is a multi-objective nonlinear optimization problem that minimizes the bus voltage deviation and real power loss. The feasibility of the proposed algorithm is demonstrated for IEEE 30-bus system and IEEE 118-bus system. A comparison of simulation results reveals optimization efficacy of the proposed scheme over other well established population based optimization techniques like conventional particle swarm optimization (PSO), general passive congregation PSO (GPAC), local passive congregation PSO (LPAC), coordinated aggregation (CA) and interior point based OPF (IP-OPF).

A new method for decision making in multi-objective optimization problems

Many engineering sectors are challenged by multi-objective optimization problems. Even if the idea behind these problems is simple and well established, the implementation of any procedure to solve them is not a trivial task. The use of evolutionary algorithms to find candidate solutions is widespread. Usually they supply a discrete picture of the non-dominated solutions, a Pareto set. Although it is very interesting to know the non-dominated solutions, an additional criterion is needed to select one solution to be deployed. To better support the design process, this paper presents a new method of solving non-linear multi-objective optimization problems by adding a control function that will guide the optimization process over the Pareto set that does not need to be found explicitly. The proposed methodology differs from the classical methods that combine the objective functions in a single scale, and is based on a unique run of non-linear single-objective optimizers.

Solving nonlinear multi-objective optimization problems with fuzzy relation inequality constraints regarding Archimedean triangular norm compositions

We propose an approach to solve a nonlinear multi-objective problem subject to fuzzy relation inequalities with max-Archimedean-t-norm composition by a genetic algorithm. The additive generator of Archimedean t-norms is utilized to reform the existent genetic algorithm to solve the constrained nonlinear multi-objective optimization problems. We consider thoroughly the feasible set of the fuzzy relation inequality systems in three possible cases, namely "?", "?" and the combination of them. In general, their feasible sets are nonconvex which are completely determined by one vector as their maximum solution and a finite number of minimal solutions. The maximum and minimal solutions are formulated by using the additive generator. Additionally, we present some conditions for each case under which the problem can be reduced. Finally, each reduced problem is solved by the genetic algorithm and the efficiency of the proposed method is shown by some numerical examples.

Efficient Satellite Scheduling Based on Improved Vector Evaluated Genetic Algorithm

Satellite scheduling is a typical multi-peak, many-valley, nonlinear multi-objective optimization problem. How to effectively implement the satellite scheduling is a crucial research in space areas.This paper mainly discusses the performance of VEGA (Vector Evaluated Genetic Algorithm) based on the study of basic principles of VEGA algorithm, algorithm realization and test function, and then improves VEGA algorithm through introducing vector coding, new crossover and mutation operators, new methods to assign fitness and hold good individuals. As a result, the diversity and convergence of improved VEGA algorithm of improved VEGA algorithm have been significantly enhanced and will be applied to Earth-Mars orbit optimization. At the same time, this paper analyzes the results of the improved VEGA, whose results of performance analysis and evaluation show that although VEGA has a profound impact upon multi-objective evolutionary research, multi-objective evolutionary algorithm on the basis of Pareto seems to be a more effective method to get the non-dominated solutions from the perspective of diversity and convergence of experimental result. Finally, based on Visual C + + integrated development environment, we have implemented improved vector evaluation algorithm in the satellite scheduling.

A robust optimization approach for real-time multiple source drinking water blending problem

Although many optimization methods can be applied to real-time multiple source drinking water blending problems, the field still lacks an approach to rapidly produce a robust optimal solution by simultaneously optimizing multiple objectives. This paper develops a fuzzy multiple response surface methodology (FMRSM) to achieve this objective. In the FMRSM, experimental data are fitted to mean response surface models while the residuals (the error between the predicted response of the mean model and the measured data of the real system) are fitted to standard deviation models. Fuzzy linear programming using the min-operator approach is applied to optimize the multiple objectives. Six scenarios are designed based on data from a real-time multiple source drinking water blending operation. The results show the FMRSM is a robust, computationally efficient optimization approach. The FMRSM could be extended to other real-time multi-objective non-linear optimization problems.

Multiobjective firefly algorithm for continuous optimization

Design problems in industrial engineering often involve a large number of design variables with multiple objectives, under complex nonlinear constraints. The algorithms for multiobjective problems can be significantly different from the methods for single objective optimization. To find the Pareto front and non-dominated set for a nonlinear multiobjective optimization problem may require significant computing effort, even for seemingly simple problems. Metaheuristic algorithms start to show their advantages in dealing with multiobjective optimization. In this paper, we extend the recently developed firefly algorithm to solve multiobjective optimization problems. We validate the proposed approach using a selected subset of test functions and then apply it to solve design optimization benchmarks. We will discuss our results and provide topics for further research.

A comprehensive method for optimal power management and design of hybrid RES-based autonomous energy systems

The power management strategy (PMS) plays an important role in the optimum design and efficient utilization of hybrid energy systems. The power available from hybrid systems and the overall lifetime of system components are highly affected by PMS. This paper presents a novel method for the determination of the optimum PMS of hybrid energy systems including various generators and storage units. The PMS optimization is integrated with the sizing procedure of the hybrid system. The method is tested on a system with several widely used generators in off-grid systems, including wind turbines, PV panels, fuel cells, electrolyzers, hydrogen tanks, batteries, and diesel generators. The aim of the optimization problem is to simultaneously minimize the overall cost of the system, unmet load, and fuel emission considering the uncertainties associated with renewable energy sources (RES). These uncertainties are modeled by using various possible scenarios for wind speed and solar irradiation based on Weibull and Beta probability distribution functions (PDF), respectively. The differential evolution algorithm (DEA) accompanied with fuzzy technique is used to handle the mixed-integer nonlinear multi-objective optimization problem. The optimum solution, including design parameters of system components and the monthly PMS parameters adapting climatic changes during a year, are obtained. Considering operating limitations of system devices, the parameters characterize the priority and share of each storage component for serving the deficit energy or storing surplus energy both resulted from the mismatch of power between load and generation. In order to have efficient power exploitation from RES, the optimum monthly tilt angles of PV panels and the optimum tower height for wind turbines are calculated. Numerical results are compared with the results of optimal sizing assuming pre-defined PMS without using the proposed power management optimization method. The comparative results present the efficacy and capability of the proposed method for hybrid energy systems.

Efficient Constellation Design Based on Improved Non-dominated Sorting Genetic Algorithm-II

Constellation design is a typical multiple peaks, multiple valleys and non-linear multi-objective optimization problem. How to design satellite constellation is one of the key sectors of research in the aerospace field. In this paper, in order to improve the global convergence and diversity performance of traditional constellation optimization algorithm, multi-parent arithmetic crossover and SBX crossover operator of NSGA-II are used to improve searching capability of this algorithm. Meanwhile, Gaussian mutation and Cauchy mutation, with diversity of population, make the algorithm get better behaviors in convergence and diversity of finding solutions. Based on the methods, an improvement NSGA-II is presented to design constellation in the paper. The algorithm uses fixed length chromosome representation. Real coding is adopted for that the problem has both integer continuous variables. Combining the coverage assessment criterions, an orbit parameters optimization framework based on non-dominated sorting genetic algorithm (NSGA-II) was proposed. This method is applied to a detailed example, and result shows that a group of Pareto solutions with good spread can be achieved, which gives strong support to constellation scheme determination.

A Hybrid GA-SQP Algorithm for Analog Circuits Sizing

This study presents a hybrid algorithm obtained by combining a genetic algorithm (GA) with successive quadratic sequential programming (SQP), namely GA-SQP. GA is the main optimizer, whereas SQP is used to refine the results of GA, further improving the solution quality. The problem formulation is done in the framework named RUNE (fRamework for aUtomated aNalog dEsign), which targets solving nonlinear mono-objective and multi-objective optimization problems for analog circuits design. Two circuits are presented: a transimpedance amplifier (TIA) and an optical driver (Driver), which are both part of an Optical Network-on-Chip (ONoC). Furthermore, convergence characteristics and robustness of the proposed method have been explored through comparison with results obtained with SQP algorithm. The outcome is very encouraging and suggests that the hybrid proposed method is very efficient in solving analog design problems.