Anupam Trivedi

A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition

Decomposition is a well-known strategy in traditional multiobjective optimization. However, the decomposition strategy was not widely employed in evolutionary multiobjective optimization until Zhang and Li proposed multiobjective evolutionary algorithm based on decomposition (MOEA/D) in 2007. MOEA/D proposed by Zhang and Li decomposes a multiobjective optimization problem into a number of scalar optimization subproblems and optimizes them in a collaborative manner using an evolutionary algorithm (EA). Each subproblem is optimized by utilizing the information mainly from its several neighboring subproblems. Since the proposition of MOEA/D in 2007, decomposition-based MOEAs have attracted significant attention from the researchers. Investigations have been undertaken in several directions, including development of novel weight vector generation methods, use of new decomposition approaches, efficient allocation of computational resources, modifications in the reproduction operation, mating selection and replacement mechanism, hybridizing decomposition- and dominance-based approaches, etc. Furthermore, several attempts have been made at extending the decomposition-based framework to constrained multiobjective optimization, many-objective optimization, and incorporate the preference of decision makers. Additionally, there have been many attempts at application of decomposition-based MOEAs to solve complex real-world optimization problems. This paper presents a comprehensive survey of the decomposition-based MOEAs proposed in the last decade.

Hybridizing genetic algorithm with differential evolution for solving the unit commitment scheduling problem

Abstract This paper proposes a hybrid of genetic algorithm (GA) and differential evolution (DE), termed hGADE, to solve one of the most important power system optimization problems known as the unit commitment (UC) scheduling. The UC problem is a nonlinear mixed-integer combinatorial high-dimensional and highly constrained optimization problem consisting of both binary UC variables and continuous power dispatch variables. Although GA is more capable of efficiently handling binary variables, the performance of DE is more remarkable in real parameter optimization. Thus, in the proposed algorithm hGADE, the binary UC variables are evolved using GA while the continuous power dispatch variables are evolved using DE. Two different variants of hGADE are presented by hybridizing GA with two classical variants of DE algorithm. Additionally, in this paper a problem specific heuristic initial population generation method and a replacement strategy based on preservation of infeasible solutions in the population are incorporated to enhance the search capability of the hybridized variants on the UC problem. The scalability of the proposed algorithm hGADE is demonstrated by testing on systems with generating units in the range of 10 up to 100 in one-day scheduling period and the simulation results demonstrate that hGADE algorithm can provide a system operator with remarkable cost savings as compared to the best approaches in the literature. Finally, an ensemble optimizer based on combination of hGADE variants is implemented to further amplify the performance of the presented algorithm.

A genetic algorithm - differential evolution based hybrid framework

This research article proposes a hybrid evolutionary framework based on hybridization of genetic algorithm (GA) and differential evolution (DE) for solving a nonlinear, high-dimensional, highly constrained, mixed-integer optimization problem called the unit commitment (UC) problem. Although GA is more capable of efficiently handling binary variables, the performance of DE is better in real parameter optimization. Thus, in the proposed hybrid framework, termed hGADE, the binary variables are evolved using GA while the continuous variables are evolved using DE. To test the efficiency of the presented framework, GA is hybridized with 4 classical and 2 state-of-the-art self-adaptive DE variants. We also incorporate a heuristic initial population generation method and a replacement scheme based on preserving infeasible solutions in the population to enhance the performance of the hGADE variants. A systematic classification of the proposed hybrid optimizer is presented in accordance with a recently proposed taxonomy in the literature. Extensive case studies are presented on different test systems and the effectiveness of the heuristic initialization, the replacement scheme, and the hybrid strategy is verified through stringent simulated results. We perform exhaustive benchmarking against some of the best algorithms proposed in the literature for UC problem to demonstrate the efficiency of the hGADE variants. Furthermore, the proposed hGADE variants are statistically compared among themselves to determine the best hGADE variants. Additionally, GA and DE are hybridized within multi-objective evolutionary algorithm based on decomposition (MOEA/D) framework and the effectiveness of hybridization is demonstrated on multi-objective UC problem as well. The proposed hybrid framework is generic and other discrete and/or real parameter operators can be easily incorporated within the framework for solving different mixed-integer optimization problems.

Evolutionary Multi-Objective Day-Ahead Thermal Generation Scheduling in Uncertain Environment

This paper addresses day-ahead thermal generation scheduling as a realistic multi-objective optimization problem in an uncertain environment considering system operation cost, emission cost and reliability as the multiple objectives. The uncertainties occurring due to unit outage and load forecast error are incorporated using loss of load probability (LOLP) and expected unserved energy (EUE) reliability indices. For solving the above-mentioned scheduling problem, a multi-objective generation scheduling algorithm (MOGSA) is proposed in this paper. Three case studies are performed on large scale test systems considering two different bi-objective optimization models and a three-objective optimization model that may be chosen by the system operator according to his/her own preference. The simulation results demonstrate the advantages of solving the thermal generation scheduling problem as a realistic multi-objective optimization problem in an uncertain environment. Finally the authors suggest a systematic procedure for the system operators to choose a single solution for the thermal generation scheduling problem.

A Decentralized Multiagent System Approach for Service Restoration Using DG Islanding

This paper proposes a decentralized multiagent system (MAS) approach for service restoration using controlled distributed generator (DG) islanding. Furthermore, it investigates the impacts of vehicle-to-grid (V2G) facility of the electric vehicles (EVs) for service restoration. Service restoration is formulated as a multiobjective optimization problem considering maximization of priority load restored and minimization of switching operations as the multiple objectives and solved using the proposed decentralized MAS approach. Extensive case studies are conducted on 38, 69, and 119 bus distribution systems, and the following advantages of the proposed MAS approach are observed: 1) flexibility-to perform under different DG and EV penetration levels; 2) scalability-to restore service for different size test systems, small as well as large; and 3) robustness-ability to perform efficiently for both single as well as multiple-fault situations. The simulation results also highlight the benefits of V2G feature of EVs for service restoration.

Enhanced Multiobjective Evolutionary Algorithm Based on Decomposition for Solving the Unit Commitment Problem

In this paper, a multiobjective evolutionary algorithm based on decomposition (MOEA/D) is proposed to solve the unit commitment (UC) problem as a multiobjective optimization problem (MOP) considering minimizing cost and emission as the multiple objectives. Since UC problem is a mixed-integer optimization problem, a hybrid strategy is integrated within the framework of MOEA/D such that genetic algorithm (GA) evolves the binary variables, while differential evolution (DE) evolves the continuous variables. Further, a novel nonuniform weight-vector distribution (NUWD) strategy is proposed and an ensemble algorithm based on combination of MOEA/D with uniform weight-vector distribution (UWD) and NUWD strategy is implemented to enhance the performance of the presented algorithm. Extensive case studies are presented on different test systems and the effectiveness of the hybrid strategy, the NUWD strategy, and the ensemble algorithm is verified through stringent simulated results. Further, exhaustive benchmarking against the algorithm proposed in the literature is presented to demonstrate the superiority of the proposed algorithm.

Improved multi-objective evolutionary algorithm for day-ahead thermal generation scheduling

This paper presents a multi-objective evolutionary algorithm to solve the day-ahead thermal generation scheduling problem. The objective functions considered to model the scheduling problem are: 1) minimizing the system operation cost and 2) minimizing the emission cost. In the proposed algorithm, the chromosome is formulated as a binary unit commitment matrix (UCM) which stores the generator on/off states and a real power matrix (RPM) which stores the corresponding power dispatch. Problem specific binary genetic operators act on the binary UCM and real genetic operators act on the RPM to effectively explore the large binary and real search spaces separately. Heuristics are used in the initial population by seeding the random population with two Priority list (PL) based solutions for faster convergence. Intelligent repair operator based on PL is designed to repair the solutions for load demand equality constraint violation. The ranking, selection and elitism methods are borrowed from NSGA-II. The proposed algorithm is applied to a large scale 60 generating unit power system and the simulation results are presented and compared with our earlier algorithm [26]. The presented algorithm is found to outperform our earlier algorithm in terms of both convergence and spread in the final Pareto-optimal front.

Multi-agent modeling for solving profit based unit commitment problem

a b s t r a c t Profit based unit commitment problem (PBUC) from power system domain is a high-dimensional, mixed variables and complex problem due to its combinatorial nature. Many optimization techniques for solving PBUC exist in the literature. However, they are either parameter sensitive or computationally expensive. The quality of PBUC solution is important for a power generating company (GENCO) because this solu- tion would be the basis for a good bidding strategy in the competitive deregulated power market. In this paper, the thermal generators of a GENCO is modeled as a system of intelligent agents in order to generate the best profit solution. A modeling for multi-agents is done by decomposing PBUC problem so that the profit maximization can be distributed among the agents. Six communication and negotiation stages are developed for agents that can explore the possibilities of profit maximization while respecting PBUC problem constraints. The proposed multi-agent modeling is tested for different systems having 10-100 thermal generators considering a day ahead scheduling. The results demonstrate the superiority of proposed multi-agent modeling for PBUC over the benchmark optimization techniques for generating the best profit solutions in substantially smaller computation time.

Smart Charging Strategies for Optimal Integration of Plug-In Electric Vehicles Within Existing Distribution System Infrastructure

In this paper, smart charging strategies incorporating a unified grid-to-vehicle and vehicle-to-grid charging framework are proposed for optimal integration of plug-in electric vehicles (PEVs) within the existing distribution system infrastructure. Two smart strategies with objective functions considering minimization of total daily cost and peak-to-average ratio, respectively, are developed to study the impact on PEV charging from an economic and technical perspective. The proposed strategies are implemented for PEV charging at workplace car parks located in a 37-bus distribution system and an analytical study is presented to evaluate the maximum possible PEV penetration that the existing distribution infrastructure can accommodate corresponding to the two strategies. A comparative analysis of the two strategies is performed in terms of various economic and technical benefits that are derived. Moreover, a performance comparison of the two strategies in presence of slow and fast charging of PEVs is also presented. Finally, an investigative study is conducted for both the strategies to evaluate the maximum PEV penetration that can be integrated in the upcoming years without infrastructure reinforcement. The simulation results present a comprehensive evaluation of the two proposed strategies.

Modified NSGA-II for day-ahead multi-objective thermal generation scheduling

In this paper, a novel approach is proposed to solve the day-ahead multi-objective thermal generation scheduling problem. The proposed method combines the principles of Non-dominated Sorting Genetic Algorithm-II (NSGA-II) with problem specific crossover and mutation operators. Heuristics are used in the initial population by seeding the random population with a Priority list based solution for better convergence. The penalty-parameter-less constrained binary tournament method is used as the selection operator to efficiently handle the constraints. Constrain-domination relation is used as the non-dominated classification procedure to classify the population into non-dominated fronts in presence of constraints. Lambda-iteration method is probabilistically used for assigning the economic/environmental real power dispatch to solve the problem. The proposed method is effectively applied to a large scale 60 generating unit power system for short-term generation scheduling problem. It is found that the presented approach gives good convergence to obtain the Pareto-optimal solutions.