In this paper,we consider a multi-objective optimal control problem with endpoints satisfying equality and inequality type *** obtain the first and second-order necessary optimality conditions for weak Pareto optimal ...
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ISBN:
(数字)9789887581536
ISBN:
(纸本)9781665482561
In this paper,we consider a multi-objective optimal control problem with endpoints satisfying equality and inequality type *** obtain the first and second-order necessary optimality conditions for weak Pareto optimal pairs,by means of applying the separation technique of convex sets to the sets obtained by the first and second-order variation of the controlproblem.
BACKGROUND: This study explores the dynamics of a mathematical model, utilizing ordinary differential equations (ODE), to depict the interplay between cancer cells and effector cells under chemotherapy. The stability ...
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BACKGROUND: This study explores the dynamics of a mathematical model, utilizing ordinary differential equations (ODE), to depict the interplay between cancer cells and effector cells under chemotherapy. The stability of the equilibrium points in the model is analysed using the Jacobian matrix and eigenvalues. Additionally, bifurcation analysis is conducted to determine the optimal values for the control parameters. objective: To evaluate the performance of the model and control strategies, benchmarking simulations are performed using the PlatEMO platform. METHODS: The Pure multi-objective optimal control problem (PMOCP) and the Hybrid multi-objective optimal control problem (HMOCP) are two different forms of optimalcontrolproblems that are solved using revolutionary metaheuristic optimisation algorithms. The utilization of the Hypervolume (HV) performance indicator allows for the comparison of various metaheuristic optimization algorithms in their efficacy for solving the PMOCP and HMOCP. RESULTS: Results indicate that the MOPSO algorithm excels in solving the HMOCP, with M-MOPSO outperforming for PMOCP in HV analysis. CONCLUSION: Despite not directly addressing immediate clinical concerns, these findings indicates that the stability shifts at critical thresholds may impact treatment efficacy.
This study aimed to minimize the tumor cell population using minimal medicine for chemotherapy treatment, while maintaining the effector-immune cell population at a healthy threshold. Therefore, a mathematical model w...
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This study aimed to minimize the tumor cell population using minimal medicine for chemotherapy treatment, while maintaining the effector-immune cell population at a healthy threshold. Therefore, a mathematical model was developed in the form of ordinary differential equations (ODE), and the solution to the multi-objective optimal control problem (MOOCP) was obtained using multi-objective Optimization algorithms. In this study, the interaction of the tumor cell and effector cell populations with chemotherapy was investigated using Pure MOOCP and Hybrid MOOCP methods. The handling of constraints and the Pontryagin Maximum Principle (PMP) differ among these methods. Swarm Intelligence (SI) and Evolutionary Algorithms (EA) were used to process the results of these methods. The numerical outcomes of SI and EA are displayed via the Pareto optimal Front. In addition, the solutions from these algorithms were further analyzed using the Hypervolume Indicator. The findings of this study demonstrate that the Hybrid Method outperforms Pure MOOCP via multi-objective Differential Evolution (MODE). MODE produces a point on the Pareto optimal Front with a minimal distance to the origin, where the distance represents the best solution.
In this paper, two approaches based on evolutionary algorithms are applied to solve a multi-objective optimal control problem governed by semilinear parabolic partial differential equations. In this approach, first, w...
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In this paper, two approaches based on evolutionary algorithms are applied to solve a multi-objective optimal control problem governed by semilinear parabolic partial differential equations. In this approach, first, we change the problem into a measure-theoretical one, replace this with an equivalent infinite dimensional multi-objective nonlinear programming problem and apply approximating schemes. Finally, non-dominated sorting genetic algorithm and multi-objective particle swarm optimization are employed to obtain Pareto optimal solutions of the problem. Numerical examples are presented to show the efficiency of the given approach.
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