Introduction to linear and nonlinear programming

Multi-Criteria Decision Making (MCDM) techniques are gaining popularity in sustainable energy management. The techniques provide solutions to the problems involving conflicting and multiple objectives. Several methods based on weighted averages, priority setting, outranking, fuzzy principles and their combinations are employed for energy planning decisions. A review of more than 90 published papers is presented here to analyze the applicability of various methods discussed. A classification on application areas and the year of application is presented to highlight the trends. It is observed that Analytical Hierarchy Process is the most popular technique followed by outranking techniques PROMETHEE and ELECTRE. Validation of results with multiple methods, development of interactive decision support systems and application of fuzzy methods to tackle uncertainties in the data is observed in the published literature.

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Application of multi-criteria decision making to sustainable energy planning—A review

This paper presents a new multiobjective evolutionary algorithm for environmental/economic power dispatch (EED) problem. The EED problem is formulated as a nonlinear constrained multiobjective optimization problem. A new strength Pareto evolutionary algorithm (SPEA) based approach is proposed to handle the EED as a true multiobjective optimization problem with competing and noncommensurable objectives. The proposed approach employs a diversity-preserving mechanism to overcome the premature convergence and search bias problems. A hierarchical clustering algorithm is also imposed to provide the decision maker with a representative and manageable Pareto-optimal set. Moreover, fuzzy set theory is employed to extract the best compromise nondominated solution. Several optimization runs of the proposed approach have been carried out on a standard test system. The results demonstrate the capabilities of the proposed approach to generate well-distributed Pareto-optimal solutions of the multiobjective EED problem in one single run. The comparison with the classical techniques demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EED problem. In addition, the extension of the proposed approach to include more objectives is a straightforward process.

Environmental/economic power dispatch using multiobjective evolutionary algorithms

The potential and effectiveness of the newly developed Pareto-based multiobjective evolutionary algorithms (MOEA) for solving a real-world power system multiobjective nonlinear optimization problem are comprehensively discussed and evaluated in this paper. Specifically, nondominated sorting genetic algorithm, niched Pareto genetic algorithm, and strength Pareto evolutionary algorithm (SPEA) have been developed and successfully applied to an environmental/economic electric power dispatch problem. A new procedure for quality measure is proposed in this paper in order to evaluate different techniques. A feasibility check procedure has been developed and superimposed on MOEA to restrict the search to the feasible region of the problem space. A hierarchical clustering algorithm is also imposed to provide the power system operator with a representative and manageable Pareto-optimal set. Moreover, an approach based on fuzzy set theory is developed to extract one of the Pareto-optimal solutions as the best compromise one. These multiobjective evolutionary algorithms have been individually examined and applied to the standard IEEE 30-bus six-generator test system. Several optimization runs have been carried out on different cases of problem complexity. The results of MOEA have been compared to those reported in the literature. The results confirm the potential and effectiveness of MOEA compared to the traditional multiobjective optimization techniques. In addition, the results demonstrate the superiority of the SPEA as a promising multiobjective evolutionary algorithm to solve different power system multiobjective optimization problems.

Multiobjective evolutionary algorithms for electric power dispatch problem

Grey wolf optimizer (GWO) is one of recent metaheuristics swarm intelligence methods. It has been widely tailored for a wide variety of optimization problems due to its impressive characteristics over other swarm intelligence methods: it has very few parameters, and no derivation information is required in the initial search. Also it is simple, easy to use, flexible, scalable, and has a special capability to strike the right balance between the exploration and exploitation during the search which leads to favourable convergence. Therefore, the GWO has recently gained a very big research interest with tremendous audiences from several domains in a very short time. Thus, in this review paper, several research publications using GWO have been overviewed and summarized. Initially, an introductory information about GWO is provided which illustrates the natural foundation context and its related optimization conceptual framework. The main operations of GWO are procedurally discussed, and the theoretical foundation is described. Furthermore, the recent versions of GWO are discussed in detail which are categorized into modified, hybridized and paralleled versions. The main applications of GWO are also thoroughly described. The applications belong to the domains of global optimization, power engineering, bioinformatics, environmental applications, machine learning, networking and image processing, etc. The open source software of GWO is also provided. The review paper is ended by providing a summary conclusion of the main foundation of GWO and suggests several possible future directions that can be further investigated.

Grey wolf optimizer: a review of recent variants and applications

Stochastic economic emission load dispatch

Grey Wolf Optimizer (GWO) is a recently developed meta-heuristic search algorithm inspired by grey wolves (Canis lupus), which simulate the social stratum and hunting mechanism of grey wolves in nature and based on three main steps of hunting: searching for prey, encircling prey and attacking prey. This paper presents the application of GWO algorithm for the solution of non-convex and dynamic economic load dispatch problem (ELDP) of electric power system. The performance of GWO is tested for ELDP of small-, medium- and large-scale power systems, and the results are verified by a comparative study with lambda iteration method, Particle Swarm Optimization algorithm, Genetic Algorithm, Biogeography-Based Optimization, Differential Evolution algorithm, pattern search algorithm, NN-EPSO, FEP, CEP, IFEP and MFEP. Comparative results show that the GWO algorithm is able to provide very competitive results compared to other well-known conventional, heuristics and meta-heuristics search algorithms.

Solution of non-convex economic load dispatch problem using Grey Wolf Optimizer

Ameliorated grey wolf optimization for economic load dispatch problem

In the multiobjective framework, fuzzy decision-making methodology is exploited to decide the generation schedule of a short-range fixed-head hydrothermal problem. The multiobjective problem is formulated considering five objectives: (i) cost, (ii) NO/sub x/ emission, (iii) SO/sub 2/ emission, (iv) CO/sub 2/ emission and (v) variance of generation mismatch with the explicit recognition of statistical uncertainties in the thermal generation cost, NO/sub x/, SO/sub 2/ and CO/sub 2/ emission curves and power demand, which are random variables. The solution set of such formulated problems is non-inferior due to contradictions among the objectives taken. The weighting method is used to simulate the trade-off relation between the conflicting objectives in the non-inferior domain. Once the trade-off has been obtained, fuzzy set theory helps the system operator to choose the weighting pattern and thus the operating point that maximises the satisfaction of all the objectives. The results are demonstrated on three sample systems.

Fuzzy decision-making in stochastic multiobjective short-term hydrothermal scheduling

PSEUDO code of proposed technique.Display Omitted An optimization technique that embeds CSO and Powells search (PS) method is proposed.The proposed technique is applied to solve combined heat and power dispatch problem.CSO is having attributes of PSO and society civilization algorithm.Initially, search is performed by CSO and then PS is applied to improve the solution.The test systems having valve point loading effect and POZs constraint. An integrated technique that embeds civilized swarm optimization (CSO) and Powells pattern search (PPS) method is proposed to search economic dispatch of combined heat and power (CHP) dispatch problem. In the proposed technique, CSO is selected as global search technique and PPS is undertaken as a local search technique. Civilized swarm optimization is having attributes of particle swarm optimization (PSO) and society civilization algorithm (SCA). In CSO, mutually interacting societies forms the civilization. The positions of society particles are updated through the guidance of own leader along with their best positions. The best performing particle of CSO is further improved by PPS method based on a certain set criterion. The PPS method is based on the conjugate search direction method and does not require the gradient or Hessian matrix of the function to be optimized. The CHP dispatch problem has a mutual dependency of demand and heat-power capacity of generating units, so it requires an effective constraint handling strategy. In this work, variable reduction strategy with exterior penalty method is applied to satisfy equality constraints. The proposed technique is tested on five CHP test systems considering valve-point loading effect, prohibited operating zones constraint, and transmission losses. The obtained results are compared to the results reported in the literature and found satisfactory. Further, for verification of statistical performance of the proposed technique, t-test and Wilcoxon signed rank test is also performed.

Jaspreet Singh Dhillon

Papers

Stochastic economic emission load dispatch

Solution of non-convex economic load dispatch problem using Grey Wolf Optimizer

Ameliorated grey wolf optimization for economic load dispatch problem

Fuzzy decision-making in stochastic multiobjective short-term hydrothermal scheduling

Combined heat and power economic dispatch using integrated civilized swarm optimization and Powells pattern search method