Solving non-convex/non-smooth economic load dispatch problems via an enhanced particle swarm optimization

Economic load dispatch (ELD) problems have been an important issue in optimal operation and planning of power system. Characterized by non-convex/non-smooth properties and various practical constraints, the ELD problems are difficult to solve using conventional optimization techniques. In this paper, an improved orthogonal design particle swarm optimization (IODPSO) algorithm is presented for solving the single-area and multi-area ELD problems with nonlinear characteristics of the generators, such as valve-point effects, prohibited operating zones, ramp rate limits and multiple fuels. In the IODPSO algorithm, an orthogonal designed method is used to construct a promising exemplar. Multiple auxiliary vector generating strategies are proposed to enhance the efficiency and effectiveness of orthogonal design operations. A tent chaotic map is employed for the adaptation of the acceleration coefficients, thus improving the proposed algorithm's robustness and global search capabilities. In addition, we designed a repair method to handle the practical constraints. Six cases of ELD problems with different characteristics are utilized to benchmark the proposed algorithm. Experimental results demonstrate that IODPSO algorithm is a promising approach for solving the non-convex/non-smooth ELD problems.     

The application of one rank cuckoo search algorithm for solving economic load dispatch problems

In this paper, a one rank cuckoo search algorithm (ORCSA) is proposed for solving economic load dispatch (ELD) problems. The main objective of the ELD problem is to minimize total cost of thermal generators while satisfying power balance constraint, prohibited operating zones, ramp rate constraints and operating limits of generators. Moreover, the generating units considered in this paper have different characteristics such as quadratic fuel cost function, nonconvex fuel cost function and multiple fuel options. The proposed ORCSA method has been developed by performing two modifications on the original cuckoo search algorithm (CSA) to improve optimal solution quality and computational time. The first modification is to merge new solution generated from both Lévy flights and replacement a fraction of egg together and to evaluate and rank the solutions at once only. A bound by best solution mechanism has been used in the second modification for properly handling the inequality constraints. The proposed ORCSA method has been tested on different systems with different characteristics of thermal units and constraints. The results obtained by ORCSA have been compared to those from other methods available in the literature and the result comparison has indicated that the ORCSA method can obtain better solution quality than many other methods. Therefore, the proposed ORCSA can be a very effective and efficient method for solving ELD problems.     

An improved bacterial foraging algorithm for combined static/dynamic environmental economic dispatch

Economic dispatch is carried out at the energy control center to find out the optimal output of thermal generating units such that power balance criterion is met, unit operating limits are satisfied and the fuel cost is minimized. With growing environmental awareness and strict government regulations throughout the world, it has become essential to optimize not only the total fuel cost but also the harmful emissions, both, under static as well as dynamic conditions. The static environment economic dispatch finds the optimal output of generating units for a fixed load demand at a given time, while the dynamic environmental economic dispatch schedules the output of online generators with changing power demands over a certain time period (normally one day) so as to minimize these two conflicting objectives, simultaneously. In this paper, the price penalty factor approach is employed for simultaneous minimization of cost and emission. The generator ramp rate constraints, non-convex and discontinuous nature of cost function and the large number of generators in practical power plants, make this problem very difficult to solve. Here, a fuzzy ranking approach is employed to identify the solution which offers the best compromise between cost and emission objectives.     

A hybrid differential evolution algorithm based on particle swarm optimization for nonconvex economic dispatch problems

This paper presents the design and application of an efficient hybrid heuristic search method to solve the practical economic dispatch problem considering many nonlinear characteristics of power generators, and their operational constraints, such as transmission losses, valve-point effects, multi-fuel options, prohibited operating zones, ramp rate limits and spinning reserve. These practical operation constraints which can usually be found at the same time in realistic power system operations make the economic load dispatch problem a nonsmooth optimization problem having complex and nonconvex features with heavy equality and inequality constraints.The proposed approach combines in the most effective way the properties of two of the most popular evolutionary optimization techniques now in use for power system optimization, the Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms. To improve the global optimization property of DE, the PSO procedure is integrated as additional mutation operator.The effectiveness of the proposed algorithm (termed DEPSO) is demonstrated by solving four kinds of ELD problems with nonsmooth and nonconvex solution spaces. The comparative results with some of the most recently published methods confirm the effectiveness of the proposed strategy to find accurate and feasible optimal solutions for practical ELD problems.     

Application of a new multi-agent Hybrid Co-evolution based Particle Swarm Optimisation methodology in ship design

In this paper, a multiple objective ‘Hybrid Co-evolution based Particle Swarm Optimisation’ methodology (HCPSO) is proposed. This methodology is able to handle multiple objective optimisation problems in the area of ship design, where the simultaneous optimisation of several conflicting objectives is considered. The proposed method is a hybrid technique that merges the features of co-evolution and Nash equilibrium with a ε-disturbance technique to eliminate the stagnation. The method also offers a way to identify an efficient set of Pareto (conflicting) designs and to select a preferred solution amongst these designs. The combination of co-evolution approach and Nash-optima contributes to HCPSO by utilising faster search and evolution characteristics. The design search is performed within a multi-agent design framework to facilitate distributed synchronous cooperation. The most widely used test functions from the formal literature of multiple objectives optimisation are utilised to test the HCPSO. In addition, a real case study, the internal subdivision problem of a ROPAX vessel, is provided to exemplify the applicability of the developed method.     

Efficient multiple objective optimal control of dynamic systems with integer controls

In practical optimal control problems both integer control variables and multiple objectives can be present. The current paper proposes a generic and efficient solution strategy for these multiple objective mixed-integer optimal control problems (MO-MIOCPs) based on deterministic approaches. Hereto, alternative scalar multiple objective optimisation techniques as normal boundary intersection and normalised normal constraint are used to convert the original problem into a series of parametric single objective optimisation problems. These single objective mixed-integer optimal control problems are then efficiently solved through direct multiple shooting techniques which exploit convex relaxations of the original problem. Moreover, these relaxations enable to quickly approximate the final solution to any desired accuracy (without the need of solving integer problems). Consequently, the set of Pareto optimal solutions of the MO-MIOCP can be accurately obtained in highly competitive computation times. The proposed method is illustrated on (i) a testdrive case study with a complex car model which includes different gears and conflicting minimum time–minimum fuel consumption objectives, and (ii) a jacketed tubular reactor case study with conflicting conversion, heat recovery and installation costs.     

Automotive engine power performance tuning under numerical and nominal data

Modern automotive engines are controlled by an electronic control unit (ECU), and engine power performance is significantly affected by the selection of both ECU parameters and engine components. The engine performance tuning is usually done by a trial-and-error method. In the current literature, very little research has considered the selection of engine parts because engine parts are complicated objects that are usually represented as nominal data. These data are meaningless values in terms of computation. This paper presents a novel multiple-input/output least-squares support vector machine plus one-of-n remapping method for modelling engine power performance using both numerical (ECU parameters) and nominal data (candidate engine parts). The Quasi-Newton method, a genetic algorithm and particle swarm optimisation are then applied to the engine model to determine the optimal engine setup automatically. A simple binary code synthesis rule is also proposed to optimise the nominal variable. Both experimental and simulation results show that the proposed methodology can successfully yield an optimal engine setup.     

电力系统经济负荷分配的混合粒子群优化算法

为解决电力系统中的经济负荷分配问题,提出一种将约束优化与粒子群优化算法相结合的混合算法,同时引入直接搜索方法。使得混合后的粒子群优化算法不但具有高效的全局搜索能力,而且具有较强的局部搜索能力,避免陷入局部最优,提高求解精度。对两个实例进行测试,与其他智能算法的结果比较,证明提出的算法可以有效找到可行解,避免陷入局部最优,实现问题的快速求解。     

Fast Pareto set generation for nonlinear optimal control problems with multiple objectives

Many practical engineering problems involve the determination of optimal control trajectories for given multiple and conflicting objectives. These conflicting objectives typically give rise to a set of Pareto optimal solutions. To enhance real-time decision making efficient approaches are required for determining the Pareto set in a fast and accurate way. Hereto, the current paper integrates efficient multiple objective scalarisation strategies (e.g., Normal Boundary Intersection and Normalised Normal Constraint) with fast deterministic approaches for dynamic optimisation (e.g., Single and Multiple Shooting). All techniques have been implemented as an easy-to-use add-on module of the automatic control and dynamic optimisation toolkit ACADO (both freely available at ). Several algorithmic synergies (e.g., hot-start initialisation strategies) are exploited for an additional speed-up. The features of ACADO Multi-Objective are discussed and its use is illustrated on different multiple objective optimal control problems arising in several engineering disciplines.     

On Optimal Design of Treasury Bonds

In this paper we develop a methodology for the study and the optimal design of the Italian medium, long-term Treasury securities. The aim is the determination of the optimal characteristics (coupon, maturity, etc.) of their future issues. Interest rate risk is examined in a way consistent with the issuer's perspective. When it is impossible to apply some form of duration matching to manage the net asset and the liability portfolio, the minimisation of the cost of the debt and the stability of the debt service payments could be considered as the objectives of the debt issuer. A new model is proposed for the optimal issue of interest rate sensitive securities. The model is formulated as a bilevel optimisation problem in which the issuer minimises his loss function and the investor maximises the expected utility of his portfolio.     

Distributed primal-dual optimisation method with uncoordinated time-varying step-sizes

This paper is concerned with the distributed optimisation problem over a multi-agent network, where the objective function is described by a sum of all the local objectives of agents. The target of agents is to collectively reach an optimal solution while minimising the global objective function. Under the assumption that the information exchange among agents is depicted by a sequence of time-varying undirected graphs, a distributed optimisation algorithm with uncoordinated time-varying step-sizes is presented, which signifies that the step-sizes of agents are not always uniform per iteration. In light of some reasonable assumptions, this paper fully conducts an explicit analysis for the convergence rate of the optimisation method. A striking feature is that the algorithm has a geometric convergence rate even if the step-sizes are time-varying and uncoordinated. Simulation results on two numerical experiments in power systems show effectiveness and performance of the proposed algorithm.     

A new optimal approach for multiple optimisation objectives grid resource allocation and scheduling

The article considers the resource allocation and scheduling problem in a grid computing environment. The article proposes system optimisation scheduling (SOS) that provides a potential solution of joint optimisation of objectives for both the resource and application layer, which combine both application-oriented and resource-oriented scheduling benefits. Grid systems will strive to find an optimal relation between user satisfaction and resource utilisation. Utility functions are used to express grid user's Quality of Service requirement, resource provider's benefit function and system's objectives. In order to verify the efficiency of the proposed scheduling algorithm, we compare the performance of application optimisation scheduling, resource optimisation scheduling, SOS with a traditional Round-Robin algorithm. The simulations study the effect of the request rate and task-to-resource ratio on the different scheduling algorithm.     

Estimation of distribution and differential evolution cooperation for large scale economic load dispatch optimization of power systems

Economic Load Dispatch (ELD) is an important and difficult optimization problem in power system planning. This article aims at addressing two practically important issues related to ELD optimization: (1) analyzing the ELD problem from the perspective of evolutionary optimization; (2) developing effective algorithms for ELD problems of large scale. The first issue is addressed by investigating the fitness landscape of ELD problems with the purpose of estimating the expected performance of different approaches. To address the second issue, a new algorithm named “Estimation of Distribution and Differential Evolution Cooperation” (ED-DE) is proposed, which is a serial hybrid of two effective evolutionary computation (EC) techniques: estimation of distribution and differential evolution. The advantages of ED-DE over the previous ELD optimization algorithms are experimentally testified on ELD problems with the number of generators scaling from 10 to 160. The best solution records of classical 13 and 40-generator ELD problems with valve points, and the best solution records of 10, 20, 40, 80 and 160-generator ELD problems with both valve points and multiple fuels are updated in this work. To further evaluate the efficiency and effectiveness of ED-DE, we also compare it with other state-of-the-art evolutionary algorithms (EAs) on typical function optimization tasks.     

Security constrained optimal power flow solution using new adaptive partitioning flower pollination algorithm

In this paper, a flexible power system planning strategy using a novel population-based metaheuristic algorithm inspired by the pollination process of flowers named adaptive flower pollination algorithm (APFPA) has been proposed. The proposed power system planning strategy implemented and successfully applied for solving the security optimal power flow (OPF) considering faults at critical generating unit. The main particularity of the proposed variant is that the control variables are optimized based on an adaptive and flexible structure. Also the performances of the standard FPA is improved by dynamically adjusting their control parameters, this allows creating diversity and balance between exploration and exploitation during search process. The robustness of the proposed planning strategy, is demonstrated on the IEEE 30-Bus, and IEEE 57-Bus tests power system for different objectives such as fuel cost, power losses, and voltage deviation. Considering the quality of the obtained results compared with various recent methods reported in the literature, the proposed strategy seems to be a competitive tool for solving with accuracy the security OPF considering critical situations.     

Solution of economic load dispatch using hybrid chemical reaction optimization approach

In this paper, a new and efficient optimization technique based on hybridization of chemical reaction optimization (CRO) with differential evolution (DE) is developed and demonstrated to solve the ELD problem with thermal cost function having valve point loading effect together with and without multiple fuel options and with and without considering prohibited operating zone and ramp rate constraint. When valve-point effects, multi-fuel operations and the constraints of prohibited operating zone and ramp rate are taken into account, ELD problem become more complex than conventional ELD problem. To show the priority of the proposed algorithm, it is implemented on six different test systems for solving ELD problems. Comparative studies are carried out to examine the effectiveness of the proposed HCRO-DE approach with conventional DE, CRO and the other algorithms reported in the literature. The simulation results show that the proposed HCRO-DE method is capable of obtaining better quality solutions than DE, CRO and the other well popular optimization techniques.     

Airline planning benchmark problems—Part I:: Characterising networks and demand using limited data

This paper is the first of two papers entitled “Airline Planning Benchmark Problems”, aimed at developing benchmark data that can be used to stimulate innovation in airline planning, in particular, in flight schedule design and fleet assignment. While optimisation has made an enormous contribution to airline planning in general, the area suffers from a lack of standardised data and benchmark problems. Current research typically tackles problems unique to a given carrier, with associated specification and data unavailable to the broader research community. This limits direct comparison of alternative approaches, and creates barriers of entry for the research community. Furthermore, flight schedule design has, to date, been under-represented in the optimisation literature, due in part to the difficulty of obtaining data that adequately reflects passenger choice, and hence schedule revenue. This is Part I of two papers taking first steps to address these issues. It does so by providing a framework and methodology for generating realistic airline demand data, controlled by scalable parameters. First, a characterisation of flight network topologies and network capacity distributions is deduced, based on the analysis of airline data. Then a multi-objective optimisation model is proposed to solve the inverse problem of inferring OD-pair demands from passenger loads on arcs. These two elements are combined to yield a methodology for generating realistic flight network topologies and OD-pair demand data, according to specified parameters. This methodology is used to produce 33 benchmark instances exhibiting a range of characteristics. Part II extends this work by partitioning the demand in each market (OD pair) into market segments, each with its own utility function and set of preferences for alternative airline products. The resulting demand data will better reflect recent empirical research on passenger preference, and is expected to facilitate passenger choice modelling in flight schedule optimisation.     

Large scale economic dispatch of power systems using oppositional invasive weed optimization

This paper presents an evolutionary hybrid algorithm of invasive weed optimization (IWO) merged with oppositional based learning to solve the large scale economic load dispatch (ELD) problems. The oppositional invasive weed optimization (OIWO) is based on the colonizing behavior of weed plants and empowered by quasi opposite numbers. The proposed OIWO methodology has been developed to minimize the total generation cost by satisfying several constraints such as generation limits, load demand, valve point loading effect, multi-fuel options and transmission losses. The proposed algorithm is tested and validated using five different test systems. The most important merit of the proposed methodology is high accuracy and good convergence characteristics and robustness to solve ELD problems. The simulation results of the proposed OIWO algorithm show its applicability and superiority when compared with the results of other tested algorithms such as oppositional real coded chemical reaction, shuffled differential evolution, biogeography based optimization, improved coordinated aggregation based PSO, quantum-inspired particle swarm optimization, hybrid quantum mechanics inspired particle swarm optimization, modified shuffled frog leaping algorithm with genetic algorithm, simulated annealing based optimization and estimation of distribution and differential evolution algorithm.     

Internal pressure and counterpunch action design in Y-shaped tube hydroforming processes: A multi-objective optimisation approach

In sheet metal forming most of the problems are multi-objective problems, generally characterised by conflicting objectives. A classical approach to investigate such kind of problems is focused on a combination of multiple objectives into a unique objective function to be optimised. Actually, in metal forming processes optimisation two main phases have to be developed in order to reach an optimal solution: the former is the modelling phase (definition of the design variables and objective function) and the latter concerns the computational aspect (numerical simulations or experiment to be developed). In this paper, an integration between numerical simulations, response surface methodology and Pareto optimal solution search techniques was applied in order to design a complex Y shaped tube hydroforming. In particular, the calibration of internal fluid pressure and counterpunch action was investigated with the aim to achieve three different quality objectives: minimization of thinning, reduction of underfilling and accuracy of the final fillet radius at the bulge zone corner.     

An adaptive differential evolutionary algorithm incorporating multiple mutation strategies for the economic load dispatch problem

As growing the demand for electrical energy, economic load dispatch (ELD) has become one of the most important and complex issues in the operation of power systems. Owing to the confined optimum convergence and the additional constraints, it does not proficient to crack such problems by the predictable optimization algorithms. In this paper, a self-adaptable differential evolution algorithm integrating with multiple mutation strategies (ADE-MMS) is proposed for the ELD problems. In order to improve the exploration and exploitation capabilities of the original differential evolution algorithm (DE), ADE-MMS has three extensions to DE. Firstly, four types of advanced vectors generated by the different methods are employed in the mutation strategies. Secondly, a self-adaptable selection mechanism for the multiple mutation strategies is implemented in the iterations. Thirdly, the main control parameters are updated according to the fitness value under the tolerance threshold. Additionally, an effective repair method is proposed to handle the equality constraints of the ELD problems. ADE-MMS not only improve the convergence speed of the original DE but also keep equilibrium state between the exploration and the exploration. A tolerance threshold for the main control parameters makes the original DE more adaptive. Moreover, the modified equality constraints handling method is benefit to meet the equality constraints and minimize the impact on the algorithm. The performances of four DE algorithms are tested on the ten ELD problems with diverse complexities. Experimental results and comparisons with other recently reported ELD algorithms confirm that ADE-MMS is capable of obtaining excellent and feasible solutions. It reveal that ADE-MMS has good potential to solvating the ELD problems.     

Nonconvex economic load dispatch using an efficient real-coded genetic algorithm

An efficient optimisation procedure based on real-coded genetic algorithm (RCGA) is proposed for the solution of economic load dispatch (ELD) problem with continuous and nonsmooth/nonconvex cost function and with various constraints being considered. The effectiveness of the proposed algorithm has been demonstrated on different systems considering the transmission losses and valve point loading effect in thermal units. The proposed algorithm is equipped with an effective constraint handling technique, which eliminates the need for penalty parameters. For the purpose of comparison, the same problem has also been solved using binary-coded genetic algorithm (BCGA) and three other popular RCGAs. In the proposed RCGA, simulated binary crossover and polynomial mutation are used against the single point crossover and bit-flipping mutation in BCGA. It has been observed from the test results that the proposed RCGA is more efficient in terms of thermal cost minimisation and execution time for ELD problem with continuous search space than BCGA and some other popular RCGAs.