Complex Multi-objective Problems Research Articles

A new multi-objective particle swarm optimisation algorithm based on R2 indicator selection mechanism

ABSTRACTIn recent years, Pareto-based selection mechanism has been successfully applied in dealing with complex multi-objective optimisation problems (MOPs), while indicators-based have been explored to apply in solving this problems. Therefore, a new multi-objective particle swarm optimisation algorithm based on R2 indicator selection mechanism (R2SMMOPSO) is presented in this paper. In the proposed algorithm, R2 indicator is designed as a selection mechanism for ensuring convergence and distribution of the algorithm simultaneously. In addition, an improved cosine-adjusted inertia weight balances the ability of algorithm exploitation and exploration effectively. Besides, Gaussian mutation strategy is designed to prevent particles from falling into the local optimum when the particle does not satisfy the condition of the position update formula, polynomial mutation is applied in the external archive to increase the diversity of elite solutions. The performance of the proposed algorithm is validated and compared with some state-of-the-art algorithms on a number of test problems. Experimental studies demonstrate that the proposed algorithm shows very competitive performance when dealing with complex MOPs.

Multi-objective particle swarm optimization based on cooperative hybrid strategy

A multi-objective particle swarm optimization based on cooperative hybrid strategy (CHSPSO) is presented in this paper to solve complex multi-objective problems. Most algorithms usually contain only one strategy, which makes them unable to trade off the convergence and diversity when solving the complex multi-objective problems. The proposed cooperative hybrid strategy can effectively guarantee the convergence and the diversity of the algorithm. The multi-population strategy and the dynamic clustering strategy are employed to improve the convergence and the diversity. At the same time, the life strategy and lottery probability selection strategy are used to further ensure the diversity of the population. A series of test functions are used to verify the effectiveness of CHSPSO. The performance of the proposed algorithm is compared with other evolutionary algorithms. The results show that CHSPSO can obtain a better convergence and diversity for the complex multi-objective problems.

Surrogate-based aerodynamic optimisation of compact nacelle aero-engines

Genetic algorithms are a powerful optimisation technique for the design of complex engineering systems. Although computing power continuously grows, methods purely based on expensive numerical simulations are still challenging for the optimisation of aerodynamic components at an early stage of the design process. For this reason, response surface models are typically employed as a driver of the genetic algorithm. This reduces considerably the total overhead computational cost but at the expense of an inherent prediction uncertainty. Aero-engine nacelle design is a complex multi-objective optimisation problem due to the nonlinearity of transonic flow aerodynamics. This research develops a new framework, that combines surrogate modelling and numerical simulations, for the multi-objective optimisation of aero-engine nacelles. The method initially employs numerical simulations to guide the genetic algorithm through generations and uses a combination of higher fidelity results along with evolving surrogate models to identify a set of optimum designs. This new approach has been applied to the multi-objective optimisation of civil aero-engines which are representative of future turbofan configurations. Compared to the conventional CFD in-the-loop optimisation method, the proposed algorithm successfully identified the same set of optimum nacelle designs at a 25% reduction in the computational cost. Within the context of preliminary design, the method meets the typical 5% acceptability criterion with a 65% reduction in computational cost.

Research on Optimal Operation Strategy of Multi-energy Power System Considering Complementary Coordination

Abstract Due to the obvious different characteristics of multi-energy power sources, it is necessary to take into account the economic and safety requirements of the power grid at the same time to achieve optimal operation strategy (OOS). This paper focuses on the OOS of multi-energy power system (MEPS), which contains wind power, cascade hydropower, thermal power, and pumped-storage power. Considering the complementary coordinationc characteristics of different types of energy, a completed set of day-ahead coordinated and optimized operating models of MEPS is established, with multiple optimization objectives of maximizing the safety, economy and renewable energy consumption. In order to solve this complex multi-objective problem, a three-stage solution method based on Benders decomposition is proposed. Through decoupling the safety object and economic object of MEPS, efficient solution of the OOS is achieved. The digital simulation discusses the influence of factors such as the diversity of natural scenarios and the safety requirements of the system operation, and simulation results verify the effectiveness of proposed strategy.

Research on joint optimal dispatching method for hybrid power system considering system security

Abstract Due to the clear differences in the characteristics of different power sources, it is necessary to take both the economic and security requirements of the power grid into account simultaneously to achieve an optimal operation strategy for a multienergy power system. This paper focuses on the optimal day-ahead dispatching of a hybrid power system that includes wind power, solar photovoltaic power, cascade hydropower, thermal power, and pumped-storage power. Considering the complementary characteristics of these different sources, a day-ahead joint optimal dispatching model of the multi-energy power system is established, with objectives of maximizing the security level, economic benefits and renewable energy consumption. A three-stage method based on Benders decomposition is proposed to solve this complex multiobjective problem. By decoupling the security and economic problems of the hybrid power system, an efficient solution for the scheduling strategy is achieved. The influences of factors such as the diversity of natural scenarios and the security requirements of system operation on the scheduling results are fully discussed in the case study section. The computational efficiencies of the proposed three-stage method and of the direct method are also comparatively analyzed. The simulation results verify the superiority of the proposed scheduling strategy and algorithm.

Chemotherapy appointment scheduling and daily outpatient-nurse assignment.

Chemotherapy planning and patient-nurse assignment problems are complex multiobjective decision problems. Schedulers must make upstream decisions that affect daily operations. To improve productivity, we propose a two-stage procedure to schedule treatments for new patients, to plan nurse requirements, and to assign the daily patient mix to available nurses. We develop a mathematical formulation that uses a waiting list to take advantage of last-minute cancellations. In the first stage, we assign appointments to the new patients at the end of each day, we estimate the daily requirement for nurses, and we generate the waiting list. The second stage assigns patients to nurses while minimizing the number of nurses required. We test the procedure on realistically sized problems to demonstrate the impact on the cost effectiveness of the clinic.

Computing the Mean‐Variance‐Sustainability Nondominated Surface by ev‐MOGA

Despite the widespread use of the classical bicriteria Markowitz mean‐variance framework, a broad consensus is emerging on the need to include more criteria for complex portfolio selection problems. Sustainable investing, also called socially responsible investment, is becoming a mainstream investment practice. In recent years, some scholars have attempted to include sustainability as a third criterion to better reflect the individual preferences of those ethical or green investors who are willing to combine strong financial performance with social benefits. For this purpose, new computational methods for optimizing this complex multiobjective problem are needed. Multiobjective evolutionary algorithms (MOEAs) have been recently used for portfolio selection, thus extending the mean‐variance methodology to obtain a mean‐variance‐sustainability nondominated surface. In this paper, we apply a recent multiobjective genetic algorithm based on the concept of ε‐dominance called ev‐MOGA. This algorithm tries to ensure convergence towards the Pareto set in a smart distributed manner with limited memory resources. It also adjusts the limits of the Pareto front dynamically and prevents solutions belonging to the ends of the front from being lost. Moreover, the individual preferences of socially responsible investors could be visualised using a novel tool, known as level diagrams, which helps investors better understand the range of values attainable and the tradeoff between return, risk, and sustainability.

A risk assessment based optimization method for route selection of hazardous liquid railway network

Route selection is the first and significant step for hazardous liquid railway network design project. Not only the economy, but the safety factors need to be considered for making a comprehensive analysis and determining an appropriate design plan. However, the railway network route selection is a complex multi-objective decision problem. Considering the construction cost and safety factors of hazardous liquid railway, this paper proposed a multi-objective optimization model. Considering the impact metrics, air pollution, river pollution, soil-underground water pollution, sensitive area and emergency system, a comprehensive risk assessment model was further built. The weight of each metric was decided by expert scoring. Based on index pricing method, risk factors were considered into maintenance and operation cost. Aiming at the strong non-linearity, a three-stage method was adopted to solve the problem. A virtual case and a real case with two refineries as sources and two terminals in midwestern China were studied in this paper. The construction schemes of hazardous liquid railway network in the study region were obtained by using the proposed method with considering the complex geographical and social environment. The effect of algorithm parameters on model was discussed in paper. Due to the high subjectivity of the emergency system score, the sensitivity of which was further analyzed. The practicality of the proposed method was verified through the case study.

A Hybrid Multiobjective Particle Swarm Optimization Algorithm Based on R2 Indicator

When dealing with complex multiobjective problems, particle swarm optimization algorithm is easy to fall into local optimum and lead to uneven distribution. Therefore, this paper presents a hybrid multiobjective particle swarm optimization algorithm based on R2 indicator (R2HMOPSO) for solving multiobjective optimization problem. The proposed algorithm uses the sigmoid function mapping method to adjust the inertia weight and learning factors in order to tradeoffs the exploration and exploitation process effectively. In addition, simulation binary crossover operator is designed to reinitialize the particles to improve the search capability of the algorithm and to prevent particles from falling into local optimum and premature convergence. R2 indicator is incorporated into the R2HMOPSO algorithm so as to deal with the solutions of uneven distribution on the true Pareto front. Besides, polynomial mutation is used to maintain diversity in the external archive. The improved algorithm is evaluated on standard benchmarks. By comparing it with four state-of-the-art multiobjective optimization algorithms, the simulation results show that R2HMOPSO algorithm is competitive and effective in terms of convergence and distribution.

A Review on Optimal Allocation and Sizing Techniques for DG in Distribution Systems

Distributed Generation (DG) offers the reliable and economic source of electricity to consumers. These are connected directly to the distribution system at consumer load points. Integration of DG units into an existing system has significantly high importance due to its innumerable advantages. However, Optimal DG (ODG) allocation and sizing is always a challenging task for utilities as well as consumers. The major objective of ODG allocation and sizing is to improve system overall efficiency with minimum power loss, maximum system security, voltage stability, and reliability. Analytical techniques are performing well for small and simple systems, not suitable for a system with large and complex networks. However, various meta-heuristic techniques are performing better in terms of accuracy and convergence for extensively large and complex networks. A hybrid optimization is a combination of two or more optimization techniques. This technique offers efficient and reliable global optimum solutions for complex multi-objective problems. In this context, a comprehensive literature review of DG fundamentals and the different technical approaches for DG integration into the distribution system are analyzed here. Furthermore, an attempt has been made for comparison of analytical, classical (non-heuristic), meta-heuristic and hybrid optimization techniques with respect to objective function, test system, advantages, and disadvantages. This present study will give in-depth knowledge and acts as a forthright reference for imminent investigators and investors for ODG allocation and sizing in a distribution system.Â

Power transformer optimal design using an innovative heuristic algorithm combined with mixed‐integer non‐linear programming and FEM technique

Power transformer optimal design (PTOD) is a complex multi-objective optimisation problem. Due to large variables search space, most optimisation methods proposed in literature for PTOD are prone to find local minimum instead of the global one. To prevail over the aforementioned problem, this study aims to propose a new heuristic algorithm combined with mixed-integer non-linear programming (MINLP), and also, some modifications to conventional PTOD procedure. Some promising features of the proposed method in comparison to the previously proposed methods are (i) it considers more design variables as a gene for transformer constructing chromosome (TCC), (ii) before building the main TCC, it divides the PTOD algorithm into some sub-algorithms and starts to construct some sub-chromosomes with lower number of genes as parts of the main TCC, which allows us to detect improper genes based on a sensitivity analysis and design constraints, (iii) not only it considers technical and consumer constrains, but it also take manufacturing constraints into account, (iv) MINLP is used to find global optimum point, and (v) the validity of obtained optimal solution is further assessed by presenting comprehensive finite-element method (FEM) and experimental result.

Multi-objective optimization of a plug flow reactor using a divide and conquer approach

Lower profit margins and tighter environmental constraints push chemical companies to search for sustainable development and operation. To ensure sustainable development and operation in practice, multiple and conflicting objectives (e.g., maximize production vs. minimize energy consumption) typically have to be optimized simultaneously. The frame of multi-objective optimization allows to systematically propose improvements and evaluate trade-offs between different objectives. Solving a multi-objective optimization problem yields a set of solutions called the Pareto front, in which no improvement can be made in one objective without worsening another objective. The posteriori analysis of this set by a smart filter aims to keep only the significant solutions for the decision maker who is interested in a specific level of trade-offs. However, this strategy suffers from the large overhead of insignificant solutions produced in the original set. This situation makes applying this strategy to the complex multi-objective optimal control problems time consuming. In this paper, the smart filter by Mattson et al. (2004) is compared to a novel Divide and Conquer (D&C) algorithm to obtain a Pareto front with adaptive resolution for a case study of a plug flow reactor. The new algorithm depends on obtaining the Pareto front recursively while terminating the exploration of a Pareto front segment as soon as an insignificant point is found. It is shown that the D&C algorithm produces representations with similar quality to the smart filter with higher speed and a more intuitive trade-off oriented solution procedure.

Dynamic Data Driven Adaptive Simulation Framework for Automated Control in Microgrids

In this paper, we introduce a novel dynamic data driven adaptive simulation framework for the operation and control of microgrids (MGs) that significantly accelerates the real-time computation of the resource allocation, and controls decisions to optimize the operational cost, energy surety, as well as emissions per MW. The proposed framework includes a database receiving input from electrical and environmental sensors, a fault detection algorithm that discovers liabilities and potential hazards within the MG, an agent-based simulation of the MG system, an optimal computing budget allocation-based control selection algorithm that uses the agent-based simulation to decide the best control design of the MG, and a multiobjective algorithm for optimizing the decisions of the MG given the best control design. For validating our framework, we use the structure of a realistic MG that is simulated using real-historical data. The experiments reveal that the proposed framework significantly reduces the computational burden of a considerably complex multiobjective problem.

The Multi-criteria Decision Support in Choosing the Efficient Location of Warehouses in the Logistic Network

The warehouse facilities location is a complex multi-objective decision problem. In order to determine this location one can use a different mathematical models that describe the location according to the accepted constraints and criterion functions. This paper presents the warehouses location in the logistic network. The logistic network consists of suppliers, potentially warehouses with the known location and recipients. The variety of constraints that must be considered e.g. the production capacity of suppliers, buyers, the storage capacity makes it difficult to decide on the final location of objects of the logistic network. The warehouse location problem in the logistics network is multi-criteria optimization problem that depends on quantitative and qualitative criteria. In general, the optimization criteria takes the form: minimal storage costs, transition costs of the cargo through warehouse facilities, the cost of cargo transport to the warehouse facility, etc. The complexity of the warehouse location problem dictated by the diversity of constraints and decision variables (e.g. the type of binary decision variables and the real type of variables), the search for the location of many warehouse facilities at the same time, multi-criteria aspects of the problem imposes the need for the application of an appropriate optimization algorithm adequately to the presented location problem. The genetic algorithm is a practical optimisation tool solving many difficult decision problems. It should be underlined that in complicated problems this tool does not guarantee the optimal solution, but sub-optimal. Despite that, the quality of the solution is accepted by decision-makers.

A multi-objective mixed-discrete particle swarm optimization with multi-domain diversity preservation

Among population-based optimization algorithms guided by meta-heuristics, Particle Swarm Optimization (PSO) has gained significant popularity in the past two decades, particularly due to its ease of implementation and fast convergence capabilities. This paper seeks to translate the beneficial features of PSO from solving typical continuous single-objective problems to solving multi-objective mixed-discrete problems, which is relatively a new ground for PSO application. The original Mixed-Discrete PSO (MDPSO) algorithm, which included an exclusive diversity preservation technique to significantly mitigate premature particle clustering, has been shown to be a powerful single-objective solver for highly constrained MINLP problems. This papers makes fundamental advancements to MDPSO, enabling it to solve complex multi-objective problems with mixed-discrete design variables. Specifically, in the velocity update equation for any particle, the explorative term is modified to point towards a stochastically selected non-dominated solution at that iteration ? thereby adopting the concept of multi-leader swarms. The fractional domain in the diversity preservation technique, which was previously defined in terms of the best global particle, is now formulated as a function of the extreme members in the set of intermediate Pareto optimal solutions. With this advancement, diversity preservation not only mitigates premature particle stagnation, but also promotes more uniform coverage of the Pareto frontier. The multi-objective MDPSO algorithm is tested using a set of benchmark problems and a wind farm layout optimization problem. To illustrate the competitive benefits of the new MO-MDPSO algorithm, the results are compared with those given by other popular multi-objective solvers such as NSGA-II and SPEA.

Difference Selection Strategy for Solving Complex Multi-Objective Problems

Difference Selection Strategy for Solving Complex Multi-Objective Problems

Improving multi-objective reservoir operation optimization with sensitivity-informed dimension reduction

Abstract. This study investigates the effectiveness of a sensitivity-informed method for multi-objective operation of reservoir systems, which uses global sensitivity analysis as a screening tool to reduce computational demands. Sobol's method is used to screen insensitive decision variables and guide the formulation of the optimization problems with a significantly reduced number of decision variables. This sensitivity-informed method dramatically reduces the computational demands required for attaining high-quality approximations of optimal trade-off relationships between conflicting design objectives. The search results obtained from the reduced complexity multi-objective reservoir operation problems are then used to pre-condition the full search of the original optimization problem. In two case studies, the Dahuofang reservoir and the inter-basin multi-reservoir system in Liaoning province, China, sensitivity analysis results show that reservoir performance is strongly controlled by a small proportion of decision variables. Sensitivity-informed dimension reduction and pre-conditioning are evaluated in their ability to improve the efficiency and effectiveness of multi-objective evolutionary optimization. Overall, this study illustrates the efficiency and effectiveness of the sensitivity-informed method and the use of global sensitivity analysis to inform dimension reduction of optimization problems when solving complex multi-objective reservoir operation problems.

A survey on multi-objective evolutionary algorithms for many-objective problems

Multi-objective evolutionary algorithms (MOEAs) are well-suited for solving several complex multi-objective problems with two or three objectives. However, as the number of conflicting objectives i...

A new gravitational search optimization algorithm to solve single and multiobjective optimization problems

This paper proposes a sufficient improved optimization algorithm based on gravitational search algorithm GSA to handle complex multi-objective MO optimization problems. The main idea behind the GSA is based on the Newton's law which has shown great success in recent years. Nevertheless, the existence of some deficiencies such as dependency of the algorithm on its adjusting parameters, stagnation and the probability of trapping in local optima has reduced the searching ability of the GSA. In order to overcome the above deficiencies, this paper suggests a novel mutation technique which is implemented based on four types of solutions. The first type belongs to the non-dominated solutions. The second type includes those solutions which are dominated by only one solution in the search space. Similarly, the third and the forth types belong to those solutions which are dominated by only three and four solutions respectively. After that, the initial GSA population is constructed by choosing from these four types of solutions. This procedure will let the next movement of the algorithm to reach more optimal solutions through the improvisation stage. The satisfying performance of the proposed algorithm is examined on several well-known benchmarks including both the single-objective and multi-objective optimization problems.

Implementation of a fast non-dominated sorting firefly algorithm and a vehicle simulation model for multi-objective component sizing of a power-split PHEV powertrain: a comparative numerical study

In the current investigation, the authors take advantage of a well-known emerging swarm intelligence-based metaheuristic method, i.e., firefly algorithm (FA), to cope with a tedious automotive optimisation problem, known as component sizing. As far as the authors are concerned, the presented research can be considered as one of the rare archived reports which substantiate the applicability and efficacy of metaheuristics for the component sizing of power-split plug-in hybrid electric vehicle (PHEV) powertrains. Here, the authors take one further step and formulate a complex multiobjective optimisation problem to clearly investigate the potentials of metaheuristics. It is worth pointing out that most of the existing classical optimisation approaches are unable to successfully solve a multiobjective component sizing problem, and are often trapped into local minimums and offer local Pareto solutions. Moreover, through a numerical comparative study, the superiority of the proposed fast non-dominated sorting firefly algorithm (FNSFA) over the non-dominated sorting genetic algorithm (NSGA-II) is demonstrated. The outcomes of this research encourage automotive engineers to take advantage of nature-based optimisers, e.g., FNSFA, for component sizing problems.