Bounded Variables nonlinear Multiple Criteria Optimization using Scatter search

This paper introduces an adaptation of multiple criteria scatter search to deal with nonlinear continuous vector optimization problems on bounded variables, applying Tabu Search approach as diversification generator method. Frequency memory and another escape mechanism are used to diversify the search. A relation Pareto is apply in order to designate a subset of the best generated solutions to be reference solutions. A choice function called Kramer Selection is used to divide the reference solution in two subsets. The Euclidean distance is used as a measure of dissimilarity in order to find diverse solutions to complement the subsets of high quality current Pareto solutions to be combined. Convex combination is used as a combined method. The performance of this approach is evaluated on several test problems taken from the literature.El artículo presenta una adaptación del algoritmo de Búsqueda Dispersa Multiobjetivo para la solucionar problemas de optimización vectorial no lineales continuos, empleando un enfoque de Búsqueda Tabú como un método generador de soluciones diversas. Memoria de Frequencias y otros mecanismos de escapes son utilizados para diversificar la búsqueda. La relación Pareto es aplicada para designar un subconjunto de las mejores soluciones generadas a ser soluciones de referencias. Una función de selección denominada selección de Kramer se utiliza para dividir al conjunto de referencia en dos subconjuntos. La distancia Euclideana es usada como una medida de disimilaridad a modo de hallar soluciones diversas que complementen los subconjuntos de soluciones potencialmente Pareto de alta calidad a ser combinadas. Como método de conbinación usamos la combinación convexa. El desempeño de este enfoque es evaluado con diferentes problemas de pruebas tomados de la literatura

A Tabu search Approach for the Weighted Tardiness with Sequence-Dependent Setups in one-machine Problem

In this paper, a Tabu Search Approach for the weighted tardiness single machine problem with sequence-dependent setups is proposed. The main contribution is the balance obtained between intensification and diversification strategies. The strategy of combine large step optimization, frequency-based memory, intensification by decomposition supplementing this with an additional intensification using path relinking produce good solutions with a low computational cost. Our Tabu Search approach is compared with a re-start method that employs the all-pairs neighborhood. Results of computational experiments are reported for a set of randomly generated test problems.En este artículo, se propone un enfoque basado en Búsqueda Tabú para el problema de una sola máquina, con retardo ponderado, con puestas a punto que dependen de la sucesión. La principal contribución es el balance obtenido entre las estrategias de intensificación y diversificación. La estrategia de combinar amplios pasos de optimización, memoria basada en la frecuencia, intensificación por descomposición con una intensificación adicional que usa religamen de caminos, produce buenas soluciones con un costo computacional bajo. Nuestro enfoque de Búsqueda Tabú es comparado con el método de inicio múltiple que emplea el vecindario de todos los pares. Se reportan resultados de experimentos computacionales para un conjunto de problemas test generados aleatoriamente

New results with scatter search applied to multiobjective combinatorial and nonlinear optimization problems

This paper introduces two variants of a multiple criteria scatter search to deal withnonlinear continuous and combinatorial problems, applying a tabu search approach asa diversification generator method. Frequency memory and another escape mechanismare used to diversify the search. A Pareto relation is applied in order to designatea subset of the best generated solutions to be reference solutions. A choice functioncalled Kramer Choice is used to divide the reference solution in two subsets. Euclideanand Hamming distances are used as measures of dissimilarity in order to find diversesolutions to complement the subsets of high quality current Pareto solutions to becombined. Linear combination and path relinking are used as a combination methods.The performance of these approaches are evaluated on several test problems taken fromthe literature.Keywords: Multiple objectives, metaheuristics, tabu search, scatter search, nonlinearoptimization.Este art´?culo introduce dos variantes de b´usqueda dispersa multiobjetivo para problemascontinuos y combinatorios, aplicando un enfoque de b´usqueda tab´u como unm´etodo generador de diversificaci´on. Una memoria de frecuencia y otros mecanismosde escape para diversificar la b´usqueda son utilizados. La relaci´on Pareto es aplicadapara designar un subconjunto de las mejores soluciones como conjunto de solucionesde referencia. Una funci´on de selecci´on llamada selecci´on de Kramer es usada paradividir las soluciones de referencia en dos subconjuntos. Las distancias Euclidianas yHamming son utilizadas como medida de desemejanza para hallar soluciones diversas como complemento de las soluciones actualmente Pareto a ser combinadas. Combinacioneslineales y reencadenamiento de trayectorias son usadas como m´etodos decombinaciones. El desempe˜no de estos enfoques es evaluado sobre varios problemasde prueba tomados de la literatura.Palabras clave: Objetivos m´ultiples, metaheur´?sticas, b´usqueda tab´u, b´usqueda dispersa,optimizaci´on no lineal

BÚSQUEDA TABÚ/DISPERSA MULTIOBJETIVO INTERACTIVAS BASADAS EN PUNTO DE REFERENCIA

This paper presents multiobjective tabu/scatter search architecture with preference information based on reference points for problems of contin- uous nature. Features of this new version are: its interactive behavior, its deterministic approximation to Pareto-optimality solutions near the refer- ence point, and the possibility to change progressively the reference point to explore different preference regions. The approach does not impose any restrictions with respect to the location of the reference points in the objective space. On 2-objective to 10-objective optimization test problems the modified approach shows its efficacy and efficiency to find an adequate non-dominated set of solutions in the preferred region.  Este artículo presenta una arquitectura Tabú/Búsqueda Dispersa mul- tiobjetivo, con información de preferencia basada en punto de referencia para problemas de naturaleza continua. Los rasgos de esta nueva versión son los siguientes: funcionamiento interactivo, aproximación determinística a las soluciones Pareto cercanas al punto de referencia y la posibilidad de cambiar el punto de referencia para explorar deferentes regiones de preferencia. El enfoque no impone restricciones con relación a los puntos de referencia en el espacio de los objetivos, y muestra su habilidad en la solución de problemas desde 2 hasta más de 10 objetivos, hallando conjuntos de soluciones eficientes cercanas al punto de preferencia.

New results with scatter search applied to multiobjective combinatorial and nonlinear optimization problems

This paper introduces two variants of a multiple criteria scatter search to deal withnonlinear continuous and combinatorial problems, applying a tabu search approach asa diversification generator method. Frequency memory and another escape mechanismare used to diversify the search. A Pareto relation is applied in order to designatea subset of the best generated solutions to be reference solutions. A choice functioncalled Kramer Choice is used to divide the reference solution in two subsets. Euclideanand Hamming distances are used as measures of dissimilarity in order to find diversesolutions to complement the subsets of high quality current Pareto solutions to becombined. Linear combination and path relinking are used as a combination methods.The performance of these approaches are evaluated on several test problems taken fromthe literature.Keywords: Multiple objectives, metaheuristics, tabu search, scatter search, nonlinearoptimization.Este art´?culo introduce dos variantes de b´usqueda dispersa multiobjetivo para problemascontinuos y combinatorios, aplicando un enfoque de b´usqueda tab´u como unm´etodo generador de diversificaci´on. Una memoria de frecuencia y otros mecanismosde escape para diversificar la b´usqueda son utilizados. La relaci´on Pareto es aplicadapara designar un subconjunto de las mejores soluciones como conjunto de solucionesde referencia. Una funci´on de selecci´on llamada selecci´on de Kramer es usada paradividir las soluciones de referencia en dos subconjuntos. Las distancias Euclidianas yHamming son utilizadas como medida de desemejanza para hallar soluciones diversas como complemento de las soluciones actualmente Pareto a ser combinadas. Combinacioneslineales y reencadenamiento de trayectorias son usadas como m´etodos decombinaciones. El desempe˜no de estos enfoques es evaluado sobre varios problemasde prueba tomados de la literatura.Palabras clave: Objetivos m´ultiples, metaheur´?sticas, b´usqueda tab´u, b´usqueda dispersa,optimizaci´on no lineal

A Tabu search Approach for the Weighted Tardiness with Sequence-Dependent Setups in one-machine Problem

In this paper, a Tabu Search Approach for the weighted tardiness single machine problem with sequence-dependent setups is proposed. The main contribution is the balance obtained between intensification and diversification strategies. The strategy of combine large step optimization, frequency-based memory, intensification by decomposition supplementing this with an additional intensification using path relinking produce good solutions with a low computational cost. Our Tabu Search approach is compared with a re-start method that employs the all-pairs neighborhood. Results of computational experiments are reported for a set of randomly generated test problems

A Tabu search Approach for the Weighted Tardiness with Sequence-Dependent Setups in one-machine Problem

In this paper, a Tabu Search Approach for the weighted tardiness single machine problem with sequence-dependent setups is proposed. The main contribution is the balance obtained between intensification and diversification strategies. The strategy of combine large step optimization, frequency-based memory, intensification by decomposition supplementing this with an additional intensification using path relinking produce good solutions with a low computational cost. Our Tabu Search approach is compared with a re-start method that employs the all-pairs neighborhood. Results of computational experiments are reported for a set of randomly generated test problems.En este artículo, se propone un enfoque basado en Búsqueda Tabú para el problema de una sola máquina, con retardo ponderado, con puestas a punto que dependen de la sucesión. La principal contribución es el balance obtenido entre las estrategias de intensificación y diversificación. La estrategia de combinar amplios pasos de optimización, memoria basada en la frecuencia, intensificación por descomposición con una intensificación adicional que usa religamen de caminos, produce buenas soluciones con un costo computacional bajo. Nuestro enfoque de Búsqueda Tabú es comparado con el método de inicio múltiple que emplea el vecindario de todos los pares. Se reportan resultados de experimentos computacionales para un conjunto de problemas test generados aleatoriamente

MULTIOBJECTIVE TABU SEARCH WITH MIXED INTEGERS AND REFERENCE POINT

In this work we present a domain-independent Tabu Search approach for multiobjective optimization with mixed-integer variables. In this we investigate two aspects: domain-independence and applicability in optimization practice and focus our attention in problems that appear frequently in the real world, like logistic network (for example: multi-stage distribution networks problems, location-allocation problems, time-tabling problems); however, other classical problems were investigated, like: coverage set problem, partitioning set problem, multidimentional knapsack problem and shortest path problem. All these problems belong to the NP-hard class, with a great number of decision variables, containing a great number of heterogeneous constrains, presenting a challenge to find feasible solutions

SOLVING ENGINEERING OPTIMIZATION PROBLEMS WITH TABU/SCATTER SEARCH

This paper introduces an adaptation of a multiobjective tabu/scatter search to deal with nonlinear discrete, mixed-integer constrained engineering optimization problems. The problem is reduced to a bi-objective problem (the objective function and the constraint violation function). This approach eliminates the use of penalties for constraint handling. Its performance was proved with different standard engineering optimization problems, including mathematical function minimization and structural engineering. The results show that the proposed method performs well in terms of efficiency and robustness