As a common concept in multi-objective optimization, minimizing a weighted sum constitutes an independent method as well as a component of other methods. Consequently, insight into characteristics of the weighted sum method has far reaching implications. However, despite the many published applications for this method and the literature addressing its pitfalls with respect to depicting the Pareto optimal set, there is little comprehensive discussion concerning the conceptual significance of the weights and techniques for maximizing the effectiveness of the method with respect to a priori articulation of preferences. Thus, in this paper, we investigate the fundamental significance of the weights in terms of preferences, the Pareto optimal set, and objective-function values. We determine the factors that dictate which solution point results from a particular set of weights. Fundamental deficiencies are identified in terms of a priori articulation of preferences, and guidelines are provided to help avoid blind use of the method.

The weighted sum method for multi-objective optimization: new insights

In the current era of sustainable development, energy planning has become complex due to the involvement of multiple benchmarks like technical, social, economic and environmental. This in turn puts major constraints for decision makers to optimize energy alternatives independently and discretely especially in case of rural communities. In addition, topographical limitations concerning renewable energy systems which are mostly distributed in nature, the energy planning becomes more complicated. In such cases, decision analysis plays a vital role for designing such systems by considering various criteria and objectives even at disintegrated levels of electrification. Multiple criteria decision making (MCDM) is a branch of operational research dealing with finding optimal results in complex scenarios including various indicators, conflicting objectives and criteria. This tool is becoming popular in the field of energy planning due to the flexibility it provides to the decision makers to take decisions while considering all the criteria and objectives simultaneously. This article develops an insight into various MCDM techniques, progress made by considering renewable energy applications over MCDM methods and future prospects in this area. An extensive review in the sphere of sustainable energy has been performed by utilizing MCDM technique.

A review of multi criteria decision making (MCDM) towards sustainable renewable energy development

The rapid uptake of residential photovoltaic (PV) systems is causing serious power quality issues such as significant voltage fluctuation and unbalance that are restricting the ability of networks to accommodate further connections. Based on the latent reactive power capability and real power curtailment of single-phase inverters, this paper proposes a new comprehensive PV operational optimization strategy to improve the performance of significantly unbalanced three-phase four-wire low voltage (LV) distribution networks with high residential PV penetrations. A multiobjective optimal power flow (OPF) problem that can simultaneously improve voltage magnitude and balance profiles, while minimizing network losses and generation costs, is defined and then converted into an aggregated single-objective OPF problem using the weighted-sum method, which can be effectively solved by the global Sequential Quadratic Programming (SQP) approach with multiple starting points in MATLAB. Detailed simulations are performed and analyzed for various operating scenarios over 24 h on a real unbalanced four-wire LV distribution network in Perth Solar City trial, Australia. Finally, smart meter readings are used to justify the validity and accuracy of the proposed optimization model and considerations on the application of the proposed PV control strategy are also presented.

Optimal PV Inverter Reactive Power Control and Real Power Curtailment to Improve Performance of Unbalanced Four-Wire LV Distribution Networks

Role assignment is a critical task in role-based collaboration. It has three steps, i.e., agent evaluation, group role assignment, and role transfer, where group role assignment is a time-consuming process. This paper clarifies the group role assignment problem (GRAP), describes a general assignment problem (GAP), converts a GRAP to a GAP, proposes an efficient algorithm based on the Kuhn-Munkres (K-M) algorithm, conducts numerical experiments, and analyzes the solutions' performances. The results show that the proposed algorithm significantly improves the algorithm based on exhaustive search. The major contributions of this paper include formally defining the GRAPs, giving a general efficient solution for them, and expanding the application scope of the K-M algorithm. This paper offers an efficient enough solution based on the K-M algorithm that outperforms significantly the exhaustive search approach.

Group Role Assignment via a Kuhn–Munkres Algorithm-Based Solution

Decomposition via scalarization is a basic concept for multiobjective optimization. The weighted sum (WS) method, a frequently used scalarizing method in decomposition-based evolutionary multiobjective (EMO) algorithms, has good features such as computationally easy and high search efficiency, compared to other scalarizing methods. However, it is often criticized by the loss of effect on nonconvex problems. This paper seeks to utilize advantages of the WS method, without suffering from its disadvantage, to solve many-objective problems. A novel decomposition-based EMO algorithm called multiobjective evolutionary algorithm based on decomposition LWS (MOEA/D-LWS) is proposed in which the WS method is applied in a local manner. That is, for each search direction, the optimal solution is selected only amongst its neighboring solutions. The neighborhood is defined using a hypercone. The apex angle of a hypervcone is determined automatically in a priori . The effectiveness of MOEA/D-LWS is demonstrated by comparing it against three variants of MOEA/D, i.e., MOEA/D using Chebyshev method, MOEA/D with an adaptive use of WS and Chebyshev method, MOEA/D with a simultaneous use of WS and Chebyshev method, and four state-of-the-art many-objective EMO algorithms, i.e., preference-inspired co-evolutionary algorithm, hypervolume-based evolutionary, $\boldsymbol {\theta }$ -dominance-based algorithm, and SPEA2+SDE for the WFG benchmark problems with up to seven conflicting objectives. Experimental results show that MOEA/D-LWS outperforms the comparison algorithms for most of test problems, and is a competitive algorithm for many-objective optimization.

Localized Weighted Sum Method for Many-Objective Optimization

It is useful with multi-objective optimization (MOO) to transform the objective functions such that they all have similar units and orders of magnitude. This article evaluates various transformation methods using simple example problems. Viewing these methods as different means to restrict function values sheds light on how the methods perform. The weighted sum approach for MOO is used to study how well different methods aid in depicting the Pareto optimal set. Whereas using unrestricted weights is well suited for providing a single solution that reflects preferences, it is found that using a convex combination of functions is desirable when generating the Pareto set. In addition, it is shown that some transformation methods are detrimental to the process of generating a diverse spread of points, and criteria are proposed for determining when the methods fail to generate an accurate representation of the Pareto set. Advantages of using a simple normalization–modification are demonstrated.

Function-transformation methods for multi-objective optimization

*† ‡ § ** The demand for realistic autonomous virtual humans is increasing, with potential application to prototype design and analysis for a reduction in design cycle time and cost. In addition, virtual humans that function independently, without input from a user or a database of animations, provide a convenient tool for biomechanical studies. However, development of such avatars is limited. In this paper, we capitalize on the advantages of optimization-based posture prediction for virtual humans. We extend this approach by incorporating multi-objective optimization (MOO) in two capacities. First, the objective sum and lexicographic approaches for MOO are used to develop new human performance measures that govern how an avatar moves. Each measure is based on a different concept with different potential applications. Secondly, the objective sum, the min-max, and the global criterion methods are used as different means to combine these performance measures. It is found that although using MOO to combine the performance measures generally provides reasonable results especially with a target point located behind the avatar, there is no significant difference between the results obtained with different MOO methods.

Multi-objective Optimization for Upper Body Posture Prediction

Using multi-objective optimization, we develop a new human performance measure for direct optimizationbased posture prediction that incorporates three key factors associated with musculoskeletal discomfort: 1) the tendency to move different segments of the body sequentially, 2) the tendency to gravitate to a comfortable neutral position, and 3) the discomfort associated with moving while joints are near their respective limits. This performance measure operates in real-time and provides realistic postures. The results are viewed using Santos TM , an advanced virtual human, and they are validated using motion-capture. This research lays groundwork for studying how and why humans move as they do.

A New Discomfort Function for Optimization-Based Posture Prediction

Several digital human softwares have shown the capabilities of simulating simple reach motions. However, predicting the dynamic effects on human motion due to different task loads is still immature. This paper presents an optimisation-based algorithm for simulating the dynamic motion of a digital human. The hypothesis is that human performance measures such as the total energy consumption governs human motion; thus the process of human motion simulation can be formulated as an optimisation problem that minimises human performance measures given at different constraints and hand loads, corresponding to a number of tasks. General equations of motion using Lagrangian dynamics method are derived for the digital human, and human metabolic energy is formulated in terms of joint space. Joint actuator torques and metabolic energy expenditure during motion are formulated and calculated within the algorithm, and it is applied to Santos™, a kinematically realistic digital human, developed at the University of Iowa. Results show that different external loads and tasks lead to different human motions and actuator torque distributions.

R. Timothy Marler

Papers

The weighted sum method for multi-objective optimization: new insights

Function-transformation methods for multi-objective optimization

Multi-objective Optimization for Upper Body Posture Prediction

A New Discomfort Function for Optimization-Based Posture Prediction

Prediction and analysis of human motion dynamics performing various tasks