1. Thesis topic
2. Common and unfamiliar terms
3. Multi-objective solution
4. Multi-objective optimization algorithm
5. Multi-objective evolutionary algorithm (MOEA)
First, the thesis topic
1.Preference-inspired co-evolutionary algorithms using weight vectors
preference enlightenment weight vector co-evolutionary algorithm
2.Differential evolution with multi-population based ensemble of mutation strategies
based on mutation strategy integrated differential populations evolution
11.Multi -objective optimal design of hybrid renewable energy systems using preference-inspired coevolutionary approach
multiobjective heuristic mixing method Coevolutionary preference renewable energy systems with optimized design
16.The iPICEA-g: a new hybrid evolutionary multi-criteria decision making approach using brushing technique the
of the iPICEA-G: a new hybrid based brushing technique (??) evolution MCDM method
22.Recon of satellite orbit for cooperative observation using variable-size multi-objective differential evolution fi guration
multiobjective with variable size Differential Evolution Algorithm for Reconstruction of Satellite Orbital Cooperative Observation
23.Two phased hybrid local search for the periodic capacitated arcrouting problem
two stage arc path planning problem with periodic mixing capacitance limits the local search
28.Multi-objective optimization for a closed- loop network design problem using an improved genetic algorithm
based on improved closed-loop multi-objective network design problem genetic algorithm
32.Learning-driven many-objective evolutionary algorithms for satellite-ground time synchronization task planning problem
multi-objective learning to drive a satellite mission planning time synchronization problem of evolutionary algorithm
2. Common and unfamiliar terms
Evolutionary algorithms
Multi-objective optimisation Multi-objective optimisation
Many-objective High-dimensional targets
Co-evolution Co-evolution
Weights
Decomposition based algorithms
Pareto optimal front Pareto optimal front
Pareto Dominate Pareto
Optimal Pareto Optimal
Pareto Optimal Set Pareto Optimal Set Pareto Optimal Set
evenly distributed uniformly distributed
adaptive weights adaptive weights
problem geometries problem geometries
Intelligent Computation Intelligent Algorithm
Vector-Evaluated Genetic Algorithm Vector-Evaluated Genetic Algorithm
Multi -Objective Simulated Annealing
Ant Colony Algorithm
Multi-Objecttive Genetic Algorithm
Particle Swarm Optimization Particle Swarm Optimization
Non-dominated Sorting Genetic Algorithm
Efficient Solution
Niched Pareto Genetic Algorithm Niched Pareto Genetic Algorithm
Strength Pareto Evolutionary Algorithm Strength Pareto Evolutionary Algorithm
Pareto Archived Evolution Strategy Pareto Archived Evolution Strategy
Comparison Algorithm Comparison Algorithm
posteriori decision-making
a proximal and diverse representation
weights based decomposition based MOEAs weights based decomposition based MOEAs weights based decomposition based multi-objective evolutionary algorithm
convergence convergence
real-parameter function optimisation problems real-parameter function optimization problems
multi-objective combinatorial problems Objective combination problem
scalarising function
genetic operators genetic operators
Numerical optimization
fitness improvement fitness improvement
mutation strategies
dynamically partitioned
particle swarm optimization (PSO)
Biogeography-based optimization (BBO) biogeography optimization algorithm
fitness assignment method
annualized cost of system (ACS)
the loss of power supply probability (LPSP) the probability of power loss
the fuel emissions fuel emissions
PV panels photovoltaic panels
wind turbines wind turbines
diesel generators diesel generators
non-dominated solutions non-dominated solutions
battery storage battery storage battery energy storage
best-in-class first-class
storage devices storage equipment
followed by followed by
Preference articulation
utility function
aspiration levels
in some sense
an interactive decision-making an interactive decision-making
posteriori decision making
group decisionmaking process group decision making process
fuzzy preferences fuzzy preference
foster improvement promote improvement
user friendly interface
satellite orbit reconfiguration satellite orbit reconfiguration
variable-size optimization variable-size optimization
estimation of distribution algorithm distribution estimation algorithm
on- orbit satellites
coverage metrics
fixed-length chromosome encoding scheme fixed-length chromosome encoding scheme
expression vector
modified initialization, mutation, crossover and selection operators modify initialization, mutation, crossover and selection operators
minimizing fuel consumption
maneuver time
the average revisit time (ART) for single target
the total coverage time (TCT) for multi-targets the total coverage time (TCT) for multi-targets
the coverage statistics based on task scheduling (CSTS)
maneuver variables
component values component values
Arc Routing Problem Arc Routing Problem
Capacitated Arc Routing Problem (CARP) Arc Routing Problem with Capacitance Limit
Heuristics Heuristic
Capacitated arc routing Arc path planning with capacitance
Bi-level optimization
Constrained combinatorial search Constrained combinatorial search
primary objective primary objective
secondary objective secondary objective
upper bound upper limit
prune the search space deletion search space
local search heuristics local search heuristics
benchmark instances benchmark instance
aggregated weight function aggregated weight function
irrelevant solutions irrelevant solutions
dedicated search operators dedicated search operators
heuristics heuristics
tabu search procedure tabu search procedure
ameliorate Improve
complementary complementary
perturbation procedure
Closed loop supply chain
Carbon emission Carbon emission
Multi-objective programming Multi-objective programming
Facility location Facility location
Evaluation algorithm Evaluation algorithm
Mixed Integer Programming model
responsiveness of the network Responsiveness
distribution center distribution center
allocation policy/reallocation policy allocation strategy/redistribution strategy
explicitly considered
carbon market trading carbon market trading
carbon market trading ozone depletion
market share market share
company image company image
monetize monetization
Nondominated Sorting Genetic Algorithm II (NSGA II)
Elitist Non-Dominated Sorting Genetic Algorithm, NSGA-II Non-Dominated Sorting Genetic Algorithm with Elite Strategy
logistic network logistics network
automobile parts auto parts
Heuristic algorithms based on improved spanning tree approach
epsilon constraint methods epsilon constraint methods
the quantities of demand and return
remanufacturing option remanufacturing option Select
refurbishing renovation
cannibalization parts disassembly
ground station scheduling problem ground station scheduling problem
navigation systems
time-consuming time-consuming and time-consuming
dynamic learning-based roll planning algorithm dynamic learning-based roll planning algorithm
Chinese Compass navigation system Chinese Compass navigation system
3. Three methods of multi-objective solution:
(1) The generation method of seeking non-inferior solutions, that is, first find a large number of non-inferior solutions to form a subset of non-inferior solutions, and then find the final solution according to the intention of the decision maker ; (Generation methods mainly include weighting method, constraint method, hybrid method combining weighting method and constraint method, and multi-objective genetic algorithm)
(2) Interactive method, which does not first seek out many non-inferior solutions, but through analysts and decision-making The final solution is gradually obtained in the way of dialogue
between the makers. (3) The decision makers are required to provide the relative importance of the goals in advance. Based on this, the algorithm converts the multi-objective problem into a single-objective problem for solution.
4. Multi-objective optimization algorithm (MOPT)
Multi-objective optimization algorithm can be summed up into two categories: traditional optimization algorithm and intelligent optimization algorithm:
(1) Traditional optimization algorithm includes weighting method, constraint method and linear programming method. The objective function is transformed into a single objective function, and the multi-objective function is solved by adopting a single objective optimization method.
Linear weighted summation method-N objectives in the multi-objective optimization problem are assigned appropriate weight coefficients according to their importance, and the product sum is used as a new objective function, and then the optimal solution is found.
(2) Intelligent optimization algorithms include Evolutionary Algorithm (EA), Particle Swarm Optimization (PSO), etc.
5. Multi-objective evolutionary algorithm (MOEA)
(1) MOEA generates the next-generation population X (t + 1) by performing selection, crossover, and mutation operations on the population X (t);
(2) In each generation of evolution, first Copy all the non-inferior solution individuals in the population X (t) to the outer set A (t);
(3) Then use the niche truncation operator to eliminate the inferior solutions in A (t) and some closer non-inferior solutions. Solve the inferior individuals to obtain the next generation outer set A (t + 1) with a more even distribution of individuals;
(4) According to the probability pe, select a certain number of excellent individuals from A (t + 1) to enter the next generation population;
( 5) At the end of evolution, the externally concentrated non-inferior solution individuals are output as the optimal solution.
(1)
Common terminology of NSGA (Non-dominant Sorting Genetic Algorithm) :
Niche technology —divide each generation of individuals into several categories, and select a number of individuals with greater fitness from each category as outstanding representatives of a category to form a group , And then in the population, as well as between different populations, cross and mutate to produce a new generation of individual groups. At the same time, the pre-selection mechanism and the crowding mechanism or sharing mechanism are used to complete the task.
Niche realization method based on sharing mechanism ——Adjust the fitness of each individual in the group through the sharing function reflecting the degree of similarity between individuals, so that in the subsequent evolution of the group, the algorithm can be based on this adjusted new adaptation To maintain the diversity of the population and create a niche evolutionary environment.
Sharing function -a function that indicates the degree of close relationship between two individuals in a group
(2) NSGAII (genetic algorithm for non-dominant sorting with elite strategy)
The basic idea of NSGA-II algorithm:
(1) First, randomly generate an initial population of size N, and after non-dominant sorting, the selection, crossover, The three basic operations of mutation get the first-generation offspring population;
(2) Secondly, starting from the second generation, merge the parent population with the offspring population to perform rapid non-dominated sorting, and at the same time, the individual in each non-dominated layer Calculate the crowding degree, and select suitable individuals to form a new parent population according to the non-dominated relationship and the crowdedness of the individual;
(3) Finally, a new offspring population is generated through the basic operation of the genetic algorithm: and so on, until the program is satisfied Conditions for the end.
(3) Multi-objective particle swarm optimization (PSO)
basic particle swarm algorithm: the
particle swarm consists of n particles, and the position xi of each particle represents the potential solution of the optimization problem in the D-dimensional search space; the
particles in the search space are determined The speed of flight is based on its own flight experience and companion’s flight experience to dynamically adjust the next flight direction and distance;
all particles have an fitness value determined by the objective function (which can be understood as distance "corn field ”Distance), and know the best position (individual extreme value pi) and current position (xi) that you have found so far.
The basic idea of particle swarm algorithm:
(1) After initializing the population, the size of the population is recorded as N. Based on the idea of fitness dominance, the population is divided into two subgroups, one is called the non-dominated subset A, the other is called the dominated subset B, and the bases of the two subsets are n1 and n2 respectively.
(2) The external elite set is used to store the non-inferior solution subset A generated in each generation, and each iteration process only updates the speed and position of the particles in B;
(3) Based on the updated particles in B The fitness dominance idea is compared with the particles in A. If xi ∈ B, ϖ xj ∈ A, so that xi dominates xj, delete xj and add xi to A to update the external elite set; and the size of the elite set should be maintained by some technology Within an upper limit, such as density evaluation technology, dispersion technology, etc.
(4) Finally, the criterion for the termination of the algorithm can be the maximum number of iterations Tmax, the calculation accuracy ε, or the maximum number of stagnation steps Δt of the optimal solution.
Reference: https://blog.csdn.net/weixin_43202635/article/details/82700342