Feasibility-Guided Constraint-Handling Techniques for Engineering Optimization Problems

The particle swarm optimization(PSO)algorithm is an established nature-inspired population-based meta-heuristic that replicates the synchronizing movements of birds and sh.PSO is essentially an unconstrained algorithm and requires constraint handling techniques(CHTs)to solve constrained optimization problems(COPs).For this purpose,we integrate two CHTs,the superiority of feasibility(SF)and the violation constraint-handling(VCH),with a PSO.These CHTs distinguish feasible solutions from infeasible ones.Moreover,in SF,the selection of infeasible solutions is based on their degree of constraint violations,whereas in VCH,the number of constraint violations by an infeasible solution is of more importance.Therefore,a PSO is adapted for constrained optimization,yielding two constrained variants,denoted SF-PSO and VCH-PSO.Both SF-PSO and VCH-PSO are evaluated with respect to ve engineering problems:the Himmelblau’s nonlinear optimization,the welded beam design,the spring design,the pressure vessel design,and the three-bar truss design.The simulation results show that both algorithms are consistent in terms of their solutions to these problems,including their different available versions.Comparison of the SF-PSO and the VCHPSO with other existing algorithms on the tested problems shows that the proposed algorithms have lower computational cost in terms of the number of function evaluations used.We also report our disagreement with some unjust comparisons made by other researchers regarding the tested problems and their different variants.

Improved genetic algorithm for nonlinear programming problems

An improved genetic algorithm（IGA） based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector which is composed of objective function value,the degree of constraints violations and the number of constraints violations.It is easy to distinguish excellent individuals from general individuals by using an individuals＇ feature vector.Additionally,a local search（LS） process is incorporated into selection operation so as to find feasible solutions located in the neighboring areas of some infeasible solutions.The combination of IGA and LS should offer the advantage of both the quality of solutions and diversity of solutions.Experimental results over a set of benchmark problems demonstrate that IGA has better performance than other algorithms.

Hybrid optimization of dynamic deployment for networked fire control system

With applying the information technology to the military field, the advantages and importance of the networked combat are more and more obvious. In order to make full use of limited battlefield resources and maximally destroy enemy targets from arbitrary angle in a limited time, the research on firepower nodes dynamic deployment becomes a key problem of command and control. Considering a variety of tactical indexes and actual constraints in air defense, a mathematical model is formulated to minimize the enemy target penetration probability. Based on characteristics of the mathematical model and demands of the deployment problems, an assistance-based algorithm is put forward which combines the artificial potential field （APF） method with a memetic algorithm. The APF method is employed to solve the constraint handling problem and generate feasible solutions. The constrained optimization problem transforms into an optimization problem of APF parameters adjustment, and the dimension of the problem is reduced greatly. The dynamic deployment is accomplished by generation and refinement of feasible solutions. The simulation results show that the proposed algorithm is effective and feasible in dynamic situation.

Evolutionary Multi-objective Portfolio Optimization in Practical Context

This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search process. The former is essential to enhance the realism of the classical mean-variance model proposed by Harry Markowitz, since portfolio managers often face a number of realistic constraints arising from business and industry regulations, while the latter reflects the fact that portfolio managers are ultimately interested in specific regions or points along the efficient frontier during the actual execution of their investment orders. For the former, this paper proposes an order-based representation that can be easily extended to handle various realistic constraints like floor and ceiling constraints and cardinality constraint. An experimental study, based on benchmark problems obtained from the OR-library, demonstrates its capability to attain a better approximation of the efficient frontier in terms of proximity and diversity with respect to other conventional representations. The experimental results also illustrated its viability and practicality in handling the various realistic constraints. A simple strategy to incorporate preferences into the multi-objective optimization process is highlighted and the experimental study demonstrates its capability in driving the evolutionary search towards specific regions of the efficient frontier.

Shuffled complex evolution coupled with stochastic ranking for reservoir scheduling problems

This paper introduces an optimization method(SCE-SR)that combines shuffled complex evolution(SCE)and stochastic ranking(SR)to solve constrained reservoir scheduling problems,ranking individuals with both objectives and constrains considered.A specialized strategy is used in the evolution process to ensure that the optimal results are feasible individuals.This method is suitable for handling multiple conflicting constraints,and is easy to implement,requiring little parameter tuning.The search properties of the method are ensured through the combination of deterministic and probabilistic approaches.The proposed SCE-SR was tested against hydropower scheduling problems of a single reservoir and a multi-reservoir system,and its performance is compared with that of two classical methods(the dynamic programming and genetic algorithm).The results show that the SCE-SR method is an effective and efficient method for optimizing hydropower generation and locating feasible regions quickly,with sufficient global convergence properties and robustness.The operation schedules obtained satisfy the basic scheduling requirements of reservoirs.

Coordinate scheduling approach for EDS observation tasks and data transmission jobs

Electromagnetic detection satellite（EDS） is a type of Earth observation satellite（EOS）. Satellites observation and data down-link scheduling plays a significant role in improving the efficiency of satellite observation systems. However, the current works mainly focus on the scheduling of imaging satellites, little work focuses on the scheduling of EDSes for its specific requirements.And current works mainly schedule satellite resources and data down-link resources separately, not considering them in a globally optimal perspective. The EDSes and data down-link resources are scheduled in an integrated process and the scheduling result is searched globally. Considering the specific constraints of EDS, a coordinate scheduling model for EDS observation tasks and data transmission jobs is established and an algorithm based on the genetic algorithm is proposed. Furthermore, the convergence of our algorithm is proved. To deal with some specific constraints, a solution repairing algorithm of polynomial computing time is designed. Finally, some experiments are conducted to validate the correctness and practicability of our scheduling algorithms.

Method for electromagnetic detection satellites scheduling based on genetic algorithm with alterable penalty coefficient

The electromagnetic detection satellite （EDS） is a type of earth observation satellites （EOSs）. The Information collected by EDSs plays an important role in some fields, such as industry, science and military. The scheduling of EDSs is a complex combinatorial optimization problem. Current research mainly focuses on the scheduling of imaging satellites and SAR satellites, but little work has been done on the scheduling of EDSs for its specific characteristics. A multi-satellite scheduling model is established, in which the specific constrains of EDSs are considered, then a scheduling algorithm based on the genetic algorithm （GA） is proposed. To deal with the specific constrains of EDSs, a penalty function method is introduced. However, it is hard to determine the appropriate penalty coefficient in the penalty function. Therefore, an adaptive adjustment mechanism of the penalty coefficient is designed to solve the problem, as well as improve the scheduling results. Experimental results are used to demonstrate the correctness and practicability of the proposed scheduling algorithm.

Discrete differential evolution algorithm for integer linear bilevel programming problems

A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods.

Model Predictive Controller Design for the Dynamic Positioning System of a Semi-submersible Platform

This paper researches how to apply the advanced control technology of model predictive control （MPC） to the design of the dynamic positioning system （DPS） of a semi-submersible platform. First, a linear low-frequency motion model with three degrees of freedom was established in the context of a semi-submersible platform. Second, a model predictive controller was designed based on a model which took the constraints of the system into account. Third, simulation was carried out to demonstrate the feasibility of the controller. The results show that the model predictive controller has good performance and good at dealing with the constraints or the system.

Adaptive leader–follower formation control for swarms of unmanned aerial vehicles with motion constraints and unknown disturbances

In this paper,the 3D leader–follower formation control problem,which focuses on swarms of fixed-wing Unmanned Aerial Vehicles(UAVs)with motion constraints and disturbances,has been investigated.Original formation errors of the follower UAVs have been transformed into the Frenet-Serret frame.Formation control laws satisfying five motion constraints(i.e.,linear velocity,linear acceleration,heading rate,climb rate and climb angle)have been designed.The convergence of the control laws has been discussed via the Lyapunov stability tool.In addition,to address the unknown disturbances,an adaptive disturbance observer is exploited.Furthermore,formation control laws involving estimated disturbances are presented as well.The collision avoidance between UAVs is achieved with the artificial potential method.Simulation results obtained using four scenarios verify the effectiveness of the proposed method in situations with constant disturbances and varying disturbances,as well as without disturbances.

An improved chaotic hybrid differential evolution for the short-term hydrothermal scheduling problem considering practical constraints

Short-term hydrothermal scheduling(STHTS) is a non-linear and complex optimization problem with a set of operational hydraulic and thermal constraints. Earlier, this problem has been addressed by several classical techniques; however, due to limitations such as non-linearity and non-convexity in cost curves, artificial intelligence tools based techniques are being used to solve the STHTS problem. In this paper an improved chaotic hybrid differential evolution(ICHDE) algorithm is proposed to find an optimal solution to this problem taking into account practical constraints. A self-adjusted parameter setting is obtained in differential evolution(DE) with the application of chaos theory, and a chaotic hybridized local search mechanism is embedded in DE to effectively prevent it from premature convergence. Furthermore, heuristic constraint handling techniques without any penalty factor setting are adopted to handle the complex hydraulic and thermal constraints. The superiority and effectiveness of the developed methodology are evaluated by its application in two illustrated hydrothermal test systems taken from the literature. The transmission line losses, prohibited discharge zones of hydel plants, and ramp rate limits of thermal plants are also taken into account. The simulation results reveal that the proposed technique is competent to produce an encouraging solution as compared with other recently established evolutionary approaches.

Input shaping for PFC:how and why?

Predictive functional control(PFC)is a highly successful strategy within industry,but for cases with challenging dynamics the most effective tuning approaches are still an active research area.This paper shows how one can deploy some insights from the more traditional model predictive control literature in order to enable systematic tuning and in particular,to ensure that the key PFC tuning parameter,that is the desired closed-loop time constant,is effective.In addition to enabling easier and more effective tuning,the proposed approach has the advantage of being simple to code and thus retaining the simplicity of implementation and tuning that is a key selling point of PFC.This paper focuses on design for open-loop unstable and also processes with significant under-damping in their open-loop behaviour.

Evolutionary decision-makings for the dynamic weapon-target assignment problem

The dynamic weapon-target assignment （DWTA） problem is an important issue in the field of military command and control. An asset-based DWTA optimization model was proposed with four kinds of constraints considered, including capability constraints, strategy constraints, resource constraints and engagement feasibility constraints. A general ＂virtual＂ representation of decisions was presented to facilitate the generation of feasible decisions. The representation is in essence the permutation of all assignment pairs. A construction procedure converts the permutations into real feasible decisions. In order to solve this problem, three evolutionary decision-making algorithms, including a genetic algorithm and two memetic algorithms, were developed. Experimental results show that the memetic algorithm based on greedy local search can generate obviously better DWTA decisions, especially for large-scale problems, than the genetic algorithm and the memetic algorithm based on steepest local search.