Augmented Lagrangian and Tchebycheff Approaches in Multiple Objective Programming

Information technology (IT) is defined as the obtainment, procedure, storage and propagation of sounding, drawing, and textual information by combining microelectronics-based computing and telecommunications. Nowadays, IT is starting to spread further from the conventional personal computer and network technologies to integrations of other fields of technology such as the use of cell phones, televisions, automobiles, etc. In other words, IT has penetrated in daily life of human beings and become one part of the whole society. The importance of IT has become momentous. Therefore, to understand the performance of efficiency and productivity of the IT firms is critical for managers as well as for personal investors. Until now, there are very few researches tried to analyze final performance of the IT firms. As a result, this research intends to use traditional Data Envelopment Analysis (DEA) CCR or BCC models to evaluate the performance of IT firms. The Decision Making Units (DMUs) on this research are chosen from IT firms in S&P 500. However, the traditional DEA models are not fair models from the aspect of improper weight derivations. Thus, this paper intends to analyze the efficiency of IT firms in S&P 500 efficiencies by using multiple objective programming (MOP) based Data Envelopment Analysis (DEA). In a MOP based DEA approach, DMUs will be evaluated based on an equal standard and the results will be evaluated more fairly. The world’s leading IT firms in S&P 500 will be evaluated based on publicly available financial reports of the fiscal year 2010. In addition, the newly developed MOP can improve the traditional DEA’s unfair weights problems and benchmark the efficiency of IT firms in S&P 500 correctly. In the empirical study, the MOP based DEA demonstrated that F5 Networks should be the communications equipment companies of IT worthwhile to be invested. In the future, performance evaluation results can be served as foundations for investment strategies definition.KeywordsInformation Technology (IT)Standard and Poor’s 500 indexPerformance EvaluationData Envelopment Analysis (DEA)Multiple Objective Programming (MOP)

This study proposed a multiple objective programming method to solve assortment and packing problems. Instead of using a two-stage method, as proposed by Li & Tsai [7], this study integrated the two stages into a multiple objective program to address assortment problems in one application. Moreover, this method could be extended to solve packing problems containing fewer 0-1 variables, thus, compared with Li et al. [8] the performance time of the proposed method could be decreased. The numerical examples showed that the proposed method is more efficient than Li & Tsai's [7], and Li et al.'s approaches [8].

A multi-objective programming approach to feed ration balancing and nutrient management

Multiple-Objective (Goal) Programming Model for Feed Formulation: An Example for Reducing Nutrient Variation

At present, supply chain management has become not only a hot academic research, but also an important respect of the enterprise strategic management. A multi-product, multi-stage integrated supply chain management model was established by multiple-objective programming, which could describe the capability and profit of supply chain members and the coordination operation of supply chain. Then an example was given for testing the effectiveness and feasibility of the model, and the simulation result was compared with that of decentralization supply chain management model. The example shows that multiple objective programming can solve the problem of integrated supply chain management.

In this paper relationships between Pareto points and saddle points are studied in convex and nonconvex multiple objective programming. The analysis is based on partitioning the index sets of objectives and constraints and splitting the original problem into subproblems having a special structure. The results are based on scalarizations of multiple objective programs and related linear and augmented Lagrangian functions. In the nonconvex case, a saddle point characterization of Pareto points is possible under assumptions that guarantee existence of Pareto points and stability conditions of single objective problems. Essentially, these conditions are not stronger than those in analogous results for single objective programming.

Multiple objective management of public forests based on centralized regional planning is mandated by law in the United States and by development policy in developing countries. Multiple objective programming (MOP) methods have been applied to this problem, but public forests have multiple users whose relative preferences for forest products often cannot be determined, so preference-based goal programming and multiobjective linear programming solutions may be inaccurate or inflexible. The use of noninferior set generating algorithms to solve MOP's encourages more flexible planning by providing a range of possible solutions (the noninferior set), but requires or generates too much information. The NISE (noninferior set estimation) method is an MOP solution technique that uses repeated linear program (LP) solutions to generate an estimate of the true noninferior set, with a known error. The method provides explicit tradeoffs between objectives and requires little interaction with forest users. The NISE method is illustrated for a problem of forest management in Tanzania, and its applicability to centralized forest planning in the United States and developing countries is discussed in the light of legal, political, and institutional constraints. Forest Sci. 32:517-533.

In this paper, we investigate a non-elitist Evolution Strategy designed to handle black-box constraints by an adaptive Augmented Lagrangian penalty approach, AL-(μ/μw, λ)-CMA-ES, on problems with up to 28 constraints. Based on stability and performance observations, we propose an improved default parameter setting. We exhibit failure cases of the Augmented Lagrangian technique and show how surrogate modeling of the constraints can overcome some difficulties. Several variants of AL-CMA-ES are compared on a set of nonlinear constrained problems from the literature. Simple adaptive penalty techniques serve as a baseline for comparison.

In this paper, we propose a new interactive procedure for solving multiple objective programming problems. Based upon feed-forward artificial neural networks (FFANNs), the method is called the Interactive FFANN Procedure. In the procedure, the decision maker articulates preference information over representative samples from the nondominated set either by assigning preference “values” to the sample solutions or by making pairwise comparisons in a fashion similar to that in the Analytic Hierarchy Process. With this information, a FFANN is trained to represent the decision maker's preference structure. Then, using the FFANN, an optimization problem is solved to search for improved solutions. An example is given to illustrate the Interactive FFANN Procedure. Also, the procedure is compared computationally with the Tchebycheff Method (Steuer and Choo [Steuer, R. E., E.-U. Choo. 1983. An interactive weighted Tchebycheff procedure for multiple objective programming. Math. Programming 26(1) 326–344.]). The computational results indicate that the Interactive FFANN Procedure produces good solutions and is robust with regard to the neural network architecture.

Investment programing for multiple objectives rather than simply for the traditional water resource investment objective of increasing the national income has become an important new element in water resources planning in the United States. Reference is made to current multiple objective planning efforts, and the relevant theory is briefly explained. The benefit‐cost ratio appropriate to projects in multiple objective programs is presented, and it is shown how this ratio differs from the ratios required by current federal instructions, which do not allow agencies to reflect accurately the interaction of social preferences and investment opportunities. A change in the federal instructions is recommended.

Interdependence in fuzzy multiple objective programming

In this paper, we use the interval-valued fuzzy sets to derive linear programming in the fuzzy sense from crisp multiple objective programming. For many practical problems, if we just used the general fuzzy sets, it may not be quite well to describe the real situation. That is the reason why we use the interval-valued fuzzy sets and the method in Zimmerman to fuzzify the crisp linear programming.

In this paper, we focus on approximating convex compact bodies. For a convex body described as the feasible set in objective space of a multiple objective programme, we show that finding it is equivalent to finding the non-dominated set of a multiple objective programme. This equivalence implies that convex bodies can be approximated using multiple objective optimization algorithms. Therefore, we propose a revised outer approximation algorithm for convex multiple objective programming problems to approximate convex bodies. Finally, we apply the algorithm to solve reachable sets of control systems and use numerical examples to show the effectiveness of the algorithm.

Traditional space-time adaptive processing algorithm can not well balance the demands between canceling jams and beam-forming. Aimed at this problem, A new algorithm based on convex optimization and multiple objectives programming is proposed for the designing of space-time filter. Two object functions are defined, and are combined via an object weight coefficient to form a single optimization goal. The relationship between the object weight coefficient and the optimization results is analyzed, and then proposed the criterion for judge the rationality of the object weight coefficient. The method for finding the optimal object weight coefficient is then developed. Results of computer simulation show that: the new method can form wide band main beam for useful signal direction under both strong and weak jams with a more low inserting loss compared with PI method; it overcomes the shortcomings of MSINR method that pass band of equivalent filter for useful signal direction will get narrower when the taps increase; especially when the signal and narrow-band jams come from the same direction the new method can still perform well.

Multiobjective programming with related bargaining games An application to utility coal conversions