A Novel Adaptive Multi-Objective Particle Swarm Optimization Based on Decomposition and Dominance for Long-term Generation Scheduling of Cascade Hydropower System

Abstract

Multi-objective long-term generation scheduling (MLGS) considering ecological flow demands is important for comprehensive utilization of water resources in cascade hydropower system (CHS). A novel adaptive multi-objective particle swarm optimization based on decomposition and dominance (D 2 AMOPSO) is developed in this paper to solve the MLGS problem. In D 2 AMOPSO, a constraint handling method based on repair strategy and individualconstraints and group constraints (ICGC) technique is embedded to address various constraints. An improved logistic map is adopted to initialize the population. During the evolutionary process, an improved Tchebycheff decomposition is introduced to select personal best and global best for each particle, and the non-dominated solutions found so far are stored in an external archive where crowding distance and elitist learning strategy are performed to improve its diversity. Meanwhile, an adaptive flight parameter adjustment mechanism based on Pareto entropy is adopted to balance the global exploration and local exploitation abilities of the population. A normal cloud mutation operator is used to keep the population diversity and escape local minima. In the case study of the Three Gorges Cascade hydropower system (TGC) under three typical years, the results of the proposed method and other four competitors show that D 2 AMOPSO can obtain better diversity and faster convergence solutions for the MLGS problem in less time.

Multiobjective Long-Term Generation Scheduling of Cascade Hydroelectricity System Using a Quantum-Behaved Particle Swarm Optimization Based on Decomposition

“…The feasible ranges of variables are delimited by the following rigid constraints, and between these constraints, tight coupling makes it possible to cast each feasible range into the decision space to find a feasible decision space without violating any of the constraints [30]. The variables mentioned here are average values in all scheduling intervals except forebay level and storage.…”

“…The improved Tchebycheff decomposition in Eq. (18) assigns uniform improvement regions for subproblems, leading to desirable diversity in the search results [30], [32]. However, the original generator of direction vectors is not suitable for the MOLTGS problem because the true Pareto front cannot be obtained in advance.…”

“…MOQPSO/D defines the personal best as the previous best position to the corresponding subproblem for each individual in the swarm with regard to the aggregation function of the improved Tchebycheff decomposition. The previous best is initialized at the same position as the particle (i.e., pb 0 n = x 0 n ) since there is no previous movement in the initial population, and updating occurs by comparing the current previous best with the new offspring generated by the particle [30]. The global best of particles should be defined carefully in MOQPSO/D since different particles are associated with different direction vectors and different subproblems.…”

“…In such MOHAs, a uniform distribution of weight vectors aggregates the objectives of an MOP into a set of interoperable mono-objectives, and then these mono-objectives are optimized simultaneously by single-objective HA with neighborhood information [24]. Many MOPs have been solved by decomposition-based MOHAs because of their simplicity and effectiveness [23], [29], [30]. Conventional Tchebycheff decomposition and simulated binary crossover (SBX) are widely used decomposition and evolution approaches [31], which bring decomposition-based MOHAs two shortcomings: uniformly distributed solutions cannot always be obtained by conventional Tchebycheff decomposition [32], and the new solutions generated by SBX are often poor in quality [33], [34].…”

“…Conventional Tchebycheff decomposition and simulated binary crossover (SBX) are widely used decomposition and evolution approaches [31], which bring decomposition-based MOHAs two shortcomings: uniformly distributed solutions cannot always be obtained by conventional Tchebycheff decomposition [32], and the new solutions generated by SBX are often poor in quality [33], [34]. Under such circumstances, this paper proposes a new variation of multiobjective QPSO (MOQPSO), called MOQPSO based on decomposition (MOQPSO/D), in which uniformization of subproblem improvement regions and nondimensionalization of objective functions are addressed by an improved Tchebycheff decomposition with a modified generator of direction vectors [30]; the possibility of generating an excellent solution is greatly enhanced by a modified QPSO operator, and the ability to avoid local optima is improved with the use of normal cloud mutation [35]. This paper is the first to integrate the above techniques to address MOPs.…”