TY - JOUR
T1 - Mono-objective function analysis using an optimization approach
AU - Clempner, J. B.
PY - 2014/3
Y1 - 2014/3
N2 - In this paper we propose an evolutionary technique based in a Lyapunov method (instead of Pareto) for mono-objective optimization, that associate to every Markov-ergodic process a Lyapunov-like mono-objective function. We show that for a class of controllable finite Markov Chains supplied by a given objective-function the system and the trajectory dynamics converge. For representing the trajectory-dynamics properties local-optimal policies are defined to minimize the one-step decrement of the cost-function. We propose a non-converging state-value function that increase and decrease between states of the decision process. Then, we show that a Lyapunov mono-objective function, which can only decrease (or remain the same) over time, can be built for this Markov decision processes. The Lyapunov mono-objective functions analyzed in this paper represent the most frequent type of behavior applied in practice in problems of evolutionary and real coded genetic algorithms considered within the Artificial Intelligence research area. They are naturally related with the, so-called, fixed-local-optimal actions or, in other words, with one-step ahead optimization algorithms widely used in the modern optimization theory. For illustration purposes, we present a simulated experiment that shows the trueness of the suggested method.
AB - In this paper we propose an evolutionary technique based in a Lyapunov method (instead of Pareto) for mono-objective optimization, that associate to every Markov-ergodic process a Lyapunov-like mono-objective function. We show that for a class of controllable finite Markov Chains supplied by a given objective-function the system and the trajectory dynamics converge. For representing the trajectory-dynamics properties local-optimal policies are defined to minimize the one-step decrement of the cost-function. We propose a non-converging state-value function that increase and decrease between states of the decision process. Then, we show that a Lyapunov mono-objective function, which can only decrease (or remain the same) over time, can be built for this Markov decision processes. The Lyapunov mono-objective functions analyzed in this paper represent the most frequent type of behavior applied in practice in problems of evolutionary and real coded genetic algorithms considered within the Artificial Intelligence research area. They are naturally related with the, so-called, fixed-local-optimal actions or, in other words, with one-step ahead optimization algorithms widely used in the modern optimization theory. For illustration purposes, we present a simulated experiment that shows the trueness of the suggested method.
KW - Lyapunov
KW - artificial intelligence
KW - genetic algorithms
KW - optimization
KW - problem solving control methods
KW - search heuristic methods
KW - vector optimization
UR - http://www.scopus.com/inward/record.url?scp=84900659782&partnerID=8YFLogxK
U2 - 10.1109/TLA.2014.6749552
DO - 10.1109/TLA.2014.6749552
M3 - Artículo
SN - 1548-0992
VL - 12
SP - 300
EP - 305
JO - IEEE Latin America Transactions
JF - IEEE Latin America Transactions
IS - 2
M1 - 6749552
ER -