Pareto Optimal Regions Research Articles

Two-stage evolutionary algorithm with fuzzy preference indicator for multimodal multi-objective optimization

Multimodal multi-objective optimization problems (MMOPs) are multi-objective optimization problems (MOPs) involving multiple equivalent global or local Pareto optimal solution sets (PSs). For decision-makers, not only the global optimal solution sets need to be found, but also the value of local optimal solution sets cannot be ignored. However, most multimodal multi-objective evolutionary algorithms (MMOEAs) tend to select solutions with better convergence, and it is difficult to obtain the global PSs and local PSs at the same time. Therefore, we propose a fuzzy preference indicator-based two-stage evolutionary algorithm (FPITSEA) in this paper. To evaluate more comprehensively the potential of each solution in the population for locating the global and local PS during the evolutionary process, a fuzzy preference indicator is designed in FPITSEA. The fuzzy preference indicator is used to guide the evolution of the population in the first stage to find the global and local Pareto optimal regions. Subsequently, an independent evolution strategy is implemented in the second stage to distinguish different PSs as accurately as possible while also ensuring the convergence quality of the solution set. In addition, an improved distance-based subset selection method is proposed, aiming to simultaneously improve the distribution of the solution set in the decision space and objective space. Experimental results on several test sets of MMOPs show the advantages of FPITSEA over several state-of-the-art MMOEAs.

Influences of information sharing and online recommendations in a supply chain: reselling versus agency selling

This paper investigates the effects of reselling and agency contracts on the platform’s incentive to share information under two scenarios, i.e., the recommendation scenario and non-recommendation scenario. Through analyzing the equilibrium solutions, we derive the following results. First, comparing the recommendation and non-recommendation scenarios, the platform prefers the recommendation scenario under the reselling contract. However, contrary to traditional wisdom, when the recommendation efficiency is relatively more efficient, the platform chooses the non-recommendation scenario in the agency contract; as the recommendation efficiency becomes less efficient, the recommendation scenario is preferred in the agency contract. Second, for the reselling contract, the platform prefers to withhold demand information in the recommendation and non-recommendation scenarios. However, the platform voluntarily shares this information under the agency contract for the two scenarios. Third, the platform’s optimal strategy depends on the commission rate, the platform’s recommendation efficiency, and the level of information accuracy. Intuitively, a lower commission rate induces the platform to prefer the reselling contract in the recommendation and non-recommendation scenarios. However, a higher commission rate does not always make the platform choose the agency contract. The recommendation efficiency and the level of information accuracy affect the platform’s optimal strategy. Furthermore, given the platform’s optimal strategy, there are Pareto optimal regions that make the manufacturer better off. That is, the platform and the manufacturer achieve a win–win situation. Finally, in an extension of the model, this paper shows the platform’s optimal strategy when a hybrid contract is used, which also demonstrates the robustness of the results.

Explicit Control of Implicit Parallelism in Decomposition-Based Evolutionary Many-Objective Optimization Algorithms [Research Frontier

Over the past two decades, Evolutionary Multi-objective Optimization (EMO) algorithms have demonstrated their ability to find and maintain multiple trade-off solutions in two and three-objective problems, making EMO as one of the most emergent and exciting fields of research and application within Computational Intelligence (CI) area. The main reason for EMO's success is that the population-based EMO operators are able to establish an implicit parallel search within an evolving population to find multiple Pareto-optimal regions of the search space parallelly. For many-objective optimization problems involving a largedimensional objective space, the extent of implicit parallelism is argued here to be too generic, compared to the same in a lower-dimensional objective space. Decomposition-based EMO algorithms - a recent trend in EMO literature - which divide the overall computing task into a number of sub-tasks of focusing within a region of the search space have found to be successful in solving many-objective problems. In this paper, we study the effect of explicit control of an algorithm's implicit parallelism mechanism for achieving an enhanced performance of decomposition-based EMO algorithms. We consider three decomposition-based many-objective evolutionary algorithms (EAs) - MOEA/D, MOEA/D-M2M, and NSGA-III - for this purpose. We also investigate another explicit control strategy of suitably choosing a normalization method of objectives for improving the performance of MOEA/D and MOEA/ D-M2M methods, and report much improved performance than their original counterparts. The principles of this study are valid for any population-based search and optimization algorithms and can be extended to improve the performance other single-objective EA, EMO, and other relevant CI methods.

Clear and smooth path planning

One of the challenging problems in motion planning is finding an efficient path for a robot in different aspects such as length, clearance and smoothness. We formulate this problem as two multi-objective path planning models with the focus on robot's energy consumption and path's safety. These models address two five- and three-objectives optimization problems. We propose an evolutionary algorithm for solving the problems. For efficient searching and achieving Pareto-optimal regions, in addition to the standard genetic operators, a family of path refiner operators is introduced. The new operators play a local search role and intensify power of the algorithm in both explorative and exploitative terms. Finally, we verify the models and compare efficiency of the algorithm and the refiner operators by other multi-objective algorithms such as strength Pareto evolutionary algorithm 2 and multi-objective particle swarm optimization on several complicated path planning test problems.

Large-scale parallelization of the Borg multiobjective evolutionary algorithm to enhance the management of complex environmental systems

The Borg MOEA is a self-adaptive multiobjective evolutionary algorithm capable of solving complex, many-objective environmental systems problems efficiently and reliably. Water and environmental resources problems pose significant computational challenges due to their potential for large Pareto optimal sets, the presence of disjoint Pareto-optimal regions that arise from discrete choices, multi-modal suboptimal regions, and expensive objective function calculations. This work develops two large-scale parallel implementations of the Borg MOEA, the master–slave and multi-master Borg MOEA, and applies them to a highly challenging risk-based water supply portfolio planning problem. The performance and scalability of both implementations are compared on up to 16384 processors. The multi-master Borg MOEA is shown to scale efficiently on tens of thousands of cores while dramatically improving the reliability of attaining high-quality solutions. Our results dramatically expand the scale and scope of complex environmental systems that can be addressed using many-objective evolutionary optimization.

Network and Economic Trade-Off Performance Regions of Cognitive Radio Systems with Power Control

Cognitive radio will enable terminals with access to licensed and unlicensed portions of the spectrum. This feature is expected to solve bandwidth scarcity problems in future wireless networks. However, different parts of the spectrum will be subject not only to different propagation conditions, but also to different licensing a nd billing agreements. Therefore, in order to obtain the major profit and spectrum efficiency, resource allocation algorithms must no w target both network and economic performance metrics. This problem can be conveniently expressed as a multi-objective portfolio optimization problem, which has been studied in detail in the field of economics. This paper addresses the study of network and eco nomic Pareto optimal trade-off performance regions of cognitive radio systems under average transmit power control policies. Each packet transmission in primary and secondary mode is regarded as a financial asset whose average transmit power is optimized so as to simu ltaneously maximize return and minimize risk, where risk is the variance of the return. This paper studies three types of Pareto optima l trade-off regions: primary vs. secondary throughput, return vs. risk, and sum-throughput vs. fairness, where fairness is evalu ated by means of the Gini index. The boundaries of these trade-off regions are derived in parametric closed-form expressions. A power control policy is further proposed that maximizes return while simultaneously controlling risk and ensuring a level of quality of service fo r primary and secondary users. This means that operators can maximize revenue and network efficiency, while simultaneously minimiz ing risk and also ensuring fairness between primary and secondary users.

Comparison between Multiobjective Population-Based Algorithms in Mechanical Problem

The objective of this paper was to perform a comparative study among multiobjective optimization methods on practical problem by using modeFRONTIER optimization software, to determine the efficiency of each method. In order to measure the effectiveness and competence of each method, the lifting arm problem was chosen from the literature [1]. Two numerical performance metrics and one visual criterion were chosen for qualitative and quantitative comparisons:(1) the variance of solution distribution in the Pareto optimal regions, (2) the ratio between the number of resulting Pareto front members to total numbers fitness function calculations which is denoted by hit rate [2], and lastly (3) graphical representation of the Pareto fronts for discussion. These metrics were chosen to represent the quality, as well as speed of the algorithms by ensuring well extends solutions. The definition of the variance as the sum of the square difference between the distance of each Pareto solutions and the average distance between Pareto solutions, over the total number of Pareto solutions. Comparisons among the results obtained using different algorithms have been performed to verify their performance. The experiments carried out indicate that FMOGA-II obtains remarkable results regarding all metrics used.

Searching for knee regions of the Pareto front using mobile reference points

Evolutionary Algorithms (EAs) have been recognized to be well suited to approximate the Pareto front of Multi-objective Optimization Problems (MOPs). In reality, the Decision Maker (DM) is not interested in discovering the whole Pareto front rather than finding only the portion(s) of the front that matches at most his/her preferences. Recently, several studies have addressed the decision-making task to assist the DM in choosing the final alternative. Knee regions are potential parts of the Pareto front presenting the maximal trade-offs between objectives. Solutions residing in knee regions are characterized by the fact that a small improvement in either objective will cause a large deterioration in at least another one which makes moving in either direction not attractive. Thus, in the absence of explicit DM’s preferences, we suppose that knee regions represent the DM’s preferences themselves. Recently, few works were proposed to find knee regions. This paper represents a further study in this direction. Hence, we propose a new evolutionary method, denoted TKR-NSGA-II, to discover knee regions of the Pareto front. In this method, the population is guided gradually by means of a set of mobile reference points. Since the reference points are updated based on trade-off information, the population converges towards knee region centers which allows the construction of a neighborhood of solutions in each knee. The performance assessment of the proposed algorithm is done on two- and three-objective knee-based test problems. The obtained results show the ability of the algorithm to: (1) find the Pareto optimal knee regions, (2) control the extent (We mean by extent the breadth/spread of the obtained knee region.) of the obtained regions independently of the geometry of the front and (3) provide competitive and better results when compared to other recently proposed methods. Moreover, we propose an interactive version of TKR-NSGA-II which is useful when the DM has no a priori information about the number of existing knees in the Pareto optimal front.

A computationally efficient metamodeling approach for expensive multiobjective optimization

This paper explores a new metamodeling framework that may collapse the computational explosion that characterizes the modeling of complex systems under a multiobjective and/or multidisciplinary setting. Under the new framework, a pseudo response surface is constructed for each design objective for each discipline. This pseudo response surface has the unique property of being highly accurate in Pareto optimal regions, while it is intentionally allowed to be inaccurate in other regions. In short, the response surface for each design objective is accurate only where it matters. Because the pseudo response surface is allowed to be inaccurate in other regions of the design space, the computational cost of constructing it is dramatically reduced. An important distinguishing feature of the new framework is that the response surfaces for all the design objectives are constructed simultaneously in a mutually dependent fashion, in a way that identifies Pareto regions for the multiobjective problem. The new framework supports the puzzling notion that it is possible to obtain more accuracy and radically more design space exploration capability, while actually reducing the computation effort. This counterintuitive metamodeling paradigm shift holds the potential for identifying highly competitive products and systems that are well beyond today’s state of the art.

The Topology of Pareto-Optimal Regions with Public Goods

The Topology of Pareto-Optimal Regions with Public Goods