Introduction to linear and nonlinear programming

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

Economic environmental dispatch (EED) is an important optimization task in fossil fuel fired power plant operation for allocating generation among the committed units such that fuel cost and emission level are optimized simultaneously while satisfying all operational constraints. It is a highly constrained multiobjective optimization problem involving conflicting objectives with both equality and inequality constraints. In this paper, multi-objective differential evolution has been proposed to solve EED problem. Numerical results of three test systems demonstrate the capabilities of the proposed approach. Results obtained from the proposed approach have been compared to those obtained from pareto differential evolution, nondominated sorting genetic algorithm-II and strength pareto evolutionary algorithm 2.

Economic environmental dispatch using multi-objective differential evolution

Dynamic economic emission dispatch using nondominated sorting genetic algorithm-II

Stochastic economic emission load dispatch

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

Multiobjective optimal thermal power dispatch

Fuzzy decision making in multiobjective long-term scheduling of hydrothermal system

Recently, multiple objective decision making has been well established as a practical approach to seek satisfactory solutions to decision making problems in limited resources, information and cognitive ability of the Decision Maker (DM). In the past, it was normal to assume well behaved and deterministic system data. Now the trend is to assume them variable and uncertain for more realistic approach. This paper deals with decision making methodology based on fuzzy set theory in order to determine the optimal generation dispatch with due consideration of uncertainties in system production cost and randomness of load demand. The classical economic dispatch problem is formulated as stochastic multiobjective optimisation problem where operating cost and variance of generation mismatch are two non-commensurable objectives. Such problems are solved to generate non-inferior solutions. Weighted sum technique is used to simulate trade_off relation among the conflicting objectives in the non-inferior domain...

S.C. Parti

Papers

Stochastic economic emission load dispatch

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

Multiobjective optimal thermal power dispatch

Fuzzy decision making in multiobjective long-term scheduling of hydrothermal system

Multiobjective decision making in stochastic economic dispatch