Large-Scale Multi-Objective Optimization Algorithm Based on Weighted Overlapping Grouping of Decision Variables

The large-scale multi-objective optimization algorithm(LSMOA),based on the grouping of decision variables,is an advanced method for handling high-dimensional decision variables.However,in practical problems,the interaction among decision variables is intricate,leading to large group sizes and suboptimal optimization effects;hence a large-scale multi-objective optimization algorithm based on weighted overlapping grouping of decision variables(MOEAWOD)is proposed in this paper.Initially,the decision variables are perturbed and categorized into convergence and diversity variables;subsequently,the convergence variables are subdivided into groups based on the interactions among different decision variables.If the size of a group surpasses the set threshold,that group undergoes a process of weighting and overlapping grouping.Specifically,the interaction strength is evaluated based on the interaction frequency and number of objectives among various decision variables.The decision variable with the highest interaction in the group is identified and disregarded,and the remaining variables are then reclassified into subgroups.Finally,the decision variable with the strongest interaction is added to each subgroup.MOEAWOD minimizes the interactivity between different groups and maximizes the interactivity of decision variables within groups,which contributed to the optimized direction of convergence and diversity exploration with different groups.MOEAWOD was subjected to testing on 18 benchmark large-scale optimization problems,and the experimental results demonstrate the effectiveness of our methods.Compared with the other algorithms,our method is still at an advantage.

Complete Convergenceand Complete Moment Convergence for Weighted Sums of ANA Random Variables

In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distribution.The obtained results not only extend those of An and Yuan[1]and Shen et al.[2]to the case of ANA random variables,but also partially improve them.

Multi-objective integrated optimization based on evolutionary strategy with a dynamic weighting schedule

The evolutionary strategy with a dynamic weighting schedule is proposed to find all the compromised solutions of the multi-objective integrated structure and control optimization problem, where the optimal system performance and control cost are defined by H2 or H∞ norms. During this optimization process, the weights are varying with the increasing generation instead of fixed values. The proposed strategy together with the linear matrix inequality （LMI） or the Riccati controller design method can find a series of uniformly distributed nondominated solutions in a single run. Therefore, this method can greatly reduce the computation intensity of the integrated optimization problem compared with the weight-based single objective genetic algorithm. Active automotive suspension is adopted as an example to illustrate the effectiveness of the proposed method.

Multi-objective reservoir operation using particle swarm optimization with adaptive random inertia weights

Based on conventional particle swarm optimization(PSO),this paper presents an efficient and reliable heuristic approach using PSO with an adaptive random inertia weight(ARIW)strategy,referred to as the ARIW-PSO algorithm,to build a multi-objective optimization model for reservoir operation.Using the triangular probability density function,the inertia weight is randomly generated,and the probability density function is automatically adjusted to make the inertia weight generally greater in the initial stage of evolution,which is suitable for global searches.In the evolution process,the inertia weight gradually decreases,which is beneficial to local searches.The performance of the ARIWPSO algorithm was investigated with some classical test functions,and the results were compared with those of the genetic algorithm(GA),the conventional PSO,and other improved PSO methods.Then,the ARIW-PSO algorithm was applied to multi-objective optimal dispatch of the Panjiakou Reservoir and multi-objective flood control operation of a reservoir group on the Luanhe River in China,including the Panjiakou Reservoir,Daheiting Reservoir,and Taolinkou Reservoir.The validity of the multi-objective optimization model for multi-reservoir systems based on the ARIW-PSO algorithm was verified.

On the Strong Laws for Weighted Sums of m-negatively Asso ciated Random Variables

In this article, the author establishes the strong laws for linear statistics that are weighted sums of a m-negatively associated(m-NA) random sample. The obtained results extend and improve the result of Qiu and Yang in [1] to m-NA random variables.

SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES

In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].

Strong Laws of Large Numbers for Weighted Sums of Ч-mixing Sequence

In this paper, strong laws of large numbers for weighted sums of ■-mixing sequence are investigated. Our results extend the corresponding results for negatively associated sequence to the case of ■-mixing sequence.

On complete convergence for Stout's type weighted sums of NOD sequence

In this paper, the complete convergence for the weighted sums of independent and identically distributed random variables in Stout [9] is improved and extended under NOD setup.The more optimal moment condition is given. The main results also hold for END sequence.

Almost Sure Convergence and Complete Convergence for the Weighted Sums of Martingale Differences

Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.

Equivalent Conditions of Complete Convergence for Weighted Sums of Sequences of Extended Negatively Dependent Random Variables

By using Rosenthal type moment inequality for extended negatively de- pendent random variables, we establish the equivalent conditions of complete convergence for weighted sums of sequences of extended negatively dependent random variables under more general conditions. These results complement and improve the corresponding results obtained by Li et al. （Li D L, RAO M B, Jiang T F, Wang X C. Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab., 1995, 8： 49-76） and Liang （Liang H Y. Complete convergence for weighted sums of negatively associated random variables. Statist. Probab. Lett., 2000, 48： 317-325）.

Almost Sure Convergence of Weighted Sums of NA Sequences

For double arrays of constants {a ni, 1≤i≤k n, n≥1} and NA r.v. 's {X n, n≥1}, conditions for almost sure convergence of are given. Both casesk n ↑ ∞ andk n=∞ are treated. A Marcinkiewicz-type theorem for i. d. NA sequences is obtained as a special case.

Complete Convergence of Weighted Sums for Asymptotically Almost Negatively Associated Sequences

For weighted sums of asymptotically almost negatively associated (AANA) random variables sequences, we use the Rosenthal type moment inequalities and prove the Marcinkiewicz-Zygmund type complete convergence and obtain the complete convergence rates. Our results extend some known ones.

On the Limiting Behavior of Weighted Partial Sums for B Valued Martingale Difference Sequences

Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are obtained.

ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES

We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.

Complete Convergence of Weighted Sums for Arrays of Rowwise m-negatively Associated Random Variables

In this paper, we discuss the complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables. By applying moment inequality and truncation methods, the sufficient conditions of complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables are established. These results generalize and complement some known conclusions.

A Precise Asymptotic Behaviour of the Large Deviation Probabilities for Weighted Sums

Let {Xn, n ≥ 1} be a sequence of independent and identically distributed positive valued random variables with a common distribution function F. When F belongs to the domain of partial attraction of a semi stable law with index α, 0 < α < 1, an asymptotic behavior of the large deviation probabilities with respect to properly normalized weighted sums have been studied and in support of this we obtained Chover’s form of law of iterated logarithm.

An Almost Sure Central Limit Theorem for Weighted Sums of Mixing Sequences

In this paper, we prove an almost sure central limit theorem for weighted sums of mixing sequences of random variables without stationary assumptions. We no longer restrict to logarithmic averages, but allow rather arbitrary weight sequences. This extends the earlier work on mixing random variables

Complete Convergence for Weighted Sums of WOD Random Variables

In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent random variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables.

Complete Convergence for Weighted Sums of φ-mixing Sequence

In this paper, the complete convergence and strong law of large numbers for weighted sums of φ-mixing sequence with different distribution are investigated under some weaker moment conditions. Our results extend ones of independent sequence with identical distribution to the case of φ-mixing sequence with different distribution.

Alienor Method for Nonlinear Multi-Objective Optimization

This paper deals with the Alienor method to tackle multiobjective nonlinear optimization problems. In this approach, the multiple criteria of the optimization problem are aggregated into a single one using weighted sums. Then, the resulting single objective nonlinear optimization problem is solved using the Alienor method associated with the Optimization Preserving Operators technique which has proved to be suitable for (nonlinear) optimization problems with a large number of variables (see [1]). The proposed approach is evaluated through test problems. The results show that the approach provides good approximations of the Pareto front while requiring small computational time, even for large instances.