ROBUST PERFORMANCE VARIATION FOR ROBUST DESIGN OPTIMAZITION WITH MULTIPLE OPTIMAL POINTS

A coevolutionary algorithm using Self-organizing map approach for multimodal multi-objective optimization

Many recommendation methods for cooking recipes are proposed in previous research. There are many studies on maximizing evaluation score on healthcare, but few studies on maximization under the limits on the cost of purchasing additional ingredients and food loss. In this research new recommendation and purchase methods are proposed. Dynamic programming is applied in the proposed methods. The basic proposed method maximizes the evaluation score on healthcare under the limits on the cost of purchasing additional ingredients and food loss. It is possible that there are multiple optimal solutions. To address this issue, two improvements of the basic proposed method are implemented. The two improved proposed methods minimize the additional purchase cost and the food loss in addition to the maximization of the healthcare score when there are multiple optimal solutions. The minimization of the additional purchase cost takes priority over the minimization of the food loss in the first improved proposed method. The minimization of the food loss takes priority over the minimization of the additional purchase cost in the second improved proposed method. The effectiveness of the proposed methods is shown by some computational examples.

Optimal load distribution (OLD) among generator units of a hydropower plant is a vital task for hydropower generation scheduling and management. Traditional optimization methods for solving this problem focus on finding a single optimal solution. However, many practical constraints on hydropower plant operation are very difficult, if not impossible, to be modeled, and the optimal solution found by those models might be of limited practical uses. This motivates us to find multiple optimal solutions to the OLD problem, which can provide more flexible choices for decision-making. Based on a special dynamic programming model, we use a modified shortest path algorithm to produce multiple solutions to the problem. It is shown that multiple optimal solutions exist for the case study of China’s Geheyan hydropower plant, and they are valuable for assessing the stability of generator units, showing the potential of reducing occurrence times of units across vibration areas.

Due to the fact that a nonlinear equation system (NES) may contain multiple optimal solutions, solving NESs is one of the most important challenges in numerical computation. When applying evolutionary algorithms to solve NESs, two issues should be considered: 1) how to transform an NES into a kind of optimization problem and 2) how to develop an optimization algorithm to solve the transformed optimization problem. In this paper, we tackle the first issue by transforming an NES into a weighted biobjective optimization problem. By the above transformation, not only do all the optimal solutions of an original NES become the Pareto optimal solutions of the transformed biobjective optimization problem, but also their images are different points on a linear Pareto front in the objective space. In addition, we suggest an adaptive multiobjective differential evolution, the goal of which is to effectively locate the Pareto optimal solutions of the transformed biobjective optimization problem. Once these solutions are found, the optimal solutions of the original NES can also be obtained correspondingly. By combining the weighted biobjective transformation technique with the adaptive multiobjective differential evolution, we propose a generic framework for the simultaneous locating of multiple optimal solutions of NESs. Comprehensive experiments on 38 NESs with various features have demonstrated that our framework provides very competitive overall performance compared with several state-of-the-art methods.

We present a method for estimating the parameter sensitivity of a design alternative for use in robust design optimization. The method is non-gradient based: it is applicable even when the objective function of an optimization problem is non-differentiable and/or discontinuous with respect to the parameters. Also, the method does not require a presumed probability distribution for parameters, and is still valid when parameter variations are large. The sensitivity estimate is developed based on the concept that associated with each design alternative there is a region in the parameter variation space whose properties can be used to predict that design’s sensitivity. Our method estimates such a region using a worst-case scenario analysis and uses that estimate in a bi-level robust optimization approach. We present a numerical and an engineering example to demonstrate the applications of our method.

Branch-and-bound methods for mixed-integer programming (MIP) are traditionally based on solving a linear programming (LP) relaxation and branching on a variable which takes a fractional value in the (single) computed relaxation optimum. In this paper we study branching strategies for mixed-integer programs that exploit the knowledge of multiple alternative optimal solutions (a cloud) of the current LP relaxation. These strategies naturally extend state-of-the-art methods like strong branching, pseudocost branching, and their hybrids.We show that by exploiting dual degeneracy, and thus multiple alternative optimal solutions, it is possible to enhance traditional methods. We present preliminary computational results, applying the newly proposed strategy to full strong branching, which is known to be the MIP branching rule leading to the fewest number of search nodes. It turns out that cloud branching can reduce the mean running time by up to 30% on standard test sets.

The noisy intermediate-scale quantum (NISQ) devices that have just emerged in recent years provide an opportunity for the physical realization of quantum circuits. As the first step of mapping quantum circuits to these devices, qubit allocation imposes a great impact on the number of additional quantum operations required throughout the mapping. The global optimization of qubit allocation is NP-hard, but since many current NISQ devices have very few qubits, it is possible to solve this problem exactly. In this paper, we propose an exact approach for qubit allocation, which takes advantage of the branch and bound algorithm as the basic framework. In order to further prune the considerably huge state space, three techniques have been proposed and integrated into the exact approach, including an optimized lower bound for quadratic assignment problem, prioritization of logical qubits, and branch pruning by structural symmetry of physical qubits. Moreover, based on the multiple optimal solutions obtained by the exact approach, we give an error-aware qubit allocation method. For problems that are too large to be solved by the exact approach, we also give a heuristic qubit allocation approach with polynomial time complexity. Experimental evaluations show that the exact approach proposed in this paper is feasible for the qubit allocation of current NISQ architectures. For all benchmarks considered, this exact approach can find multiple optimal solutions to the qubit allocation problem on IBM Melbourne, a 16-qubit NISQ architecture, in no more than 20 min. It can serve as a evaluation baseline of any heuristic approach. Experimental evaluations also show that the proposed heuristic approach is near-optimal in terms of routing cost. Both the exact approach and the heuristic approach can be integrated into existing quantum circuit mapping approaches.

In this paper an extension of the Lintner model [1] is considered: the problem of portfolio optimization is studied when short-selling is allowed through the mechanism of margin requirements. This induces a non-linear constraint on the wealth. When interest on deposited margin is present, Lintner ingeniously solved the problem by recovering the unique optimal solution of the linear model (no margin requirements). In this paper an alternative and more realistic approach is explored: the nonlinear constraint is maintained but no interest is perceived on the money deposited against short-selling. This leads to a fully non-linear problem which admits multiple and unstable solutions very different among themselves but corresponding to similar risk levels. Our analysis is built on a seminal idea by Galluccio, Bouchaud and Potters [3], who have re-stated the problem of finding solutions of the portfolio optimization problem in futures markets in terms of a spin glass problem. In order to get the best portfolio (i.e. the one lying on the efficiency frontier), we have to implement a two-step procedure. A worked example with real data is presented.

In concept-based summarization, sentence selection is modelled as a budgeted maximum coverage problem. As this problem is NP-hard, pruning low-weight concepts is required for the solver to find optimal solutions efficiently. This work shows that reducing the number of concepts in the model leads to lower Rouge scores, and more importantly to the presence of multiple optimal solutions. We address these issues by extending the model to provide a single optimal solution, and eliminate the need for concept pruning using an approximation algorithm that achieves comparable performance to exact inference.

Multiobjective short‐term hydrothermal scheduling problems solved by the linear weighted sum method (LWSM) have multiple solutions with different weight coefficients. To compare the solutions of the formulated multiobjective hydrothermal model, we use the Charnes–Cooper–Rhodes (CCR) model of data envelopment analysis (DEA) to evaluate all solutions. A set of preference weight vectors is regarded as a decision‐making unit (DMU), and the CCR model is employed with the minimal objective values as the inputs of DMU and the maximal objective values as outputs. Multiple reasonable solutions are obtained through the DEA efficiency of DMUs. Results of simulations imply that the method is feasible to get reasonable solutions in solving multiobjective hydrothermal scheduling problem with LWSM. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

This study presents optimal placement of voltage sag monitors based on new Sag Occurrence Index (SOI) which ensures observability even in case of monitor failure or line outages. Multiple solutions for optimal placement of voltage sag monitors for voltage sag detection have been obtained by genetic algorithm approach such that observability of the whole system is guaranteed. A new Sag Occurrence Index (SOI) is proposed to obtain the severity of voltage sag at all the buses in the system. To obtain the best monitor arrangement in the system, the sum of SOI for each optimal combination is determined. IEEE 24-bus Reliability Test System (RTS) and IEEE 57-bus system were used to demonstrate the effectiveness of the proposed method. The details of implementation and simulation results are also presented.

The solutions for large-scale taixxxeyy and drexx instances solved by Hyper-heuristics. There are 20 instances for tai125eyy, tai175eyy and tai343eyy, 10 instances for tai729eyy, 12 instances for drexx. drexx instances might have multiple optimal solutions with the same objective function values

We consider a class of problems where a given number p of facility locations must be selected from a set of s potential locations so as to optimize a pre-determined fitness function. There exist outstanding location problems in this class, such as the p-median, max-covering, MAXCAP, and MAXPROFIT problems. These location problems may contain more than a single global optimal solution. Obtaining multiple global optimal solutions allows us to consider other characteristics in the process of selecting the preferred solution. In [B. Pelegrín, J. Redondo, P. Fernández, I. García, and P. Ortigosa, GASUB: Finding global optima to discrete location problems by a genetic-like algorithm, J. Glob. Optim. 38 (2007), pp. 249–264], a new ‘multimodal’ algorithm (gasub) was presented for solving the previously mentioned location problems. In the paper, the algorithm was fine-tuned to obtain a single global optimum (with 100% success) as fast as possible, and it was compared with two widely used techniques, that is, the standard optimizer Xpress-MP [Xpress-MP, Dashoptimization, 2004.] and the Multi Start Heuristic. In this paper, we propose a new set of parameter values so that gasub can explore the space more deeply and consequently find several alternative global optimal solutions. Moreover, two coarse-grain parallelizations of gasub are presented, cggasub and cggasub_mo. cggasub is able to reduce the computational time of gasub where solutions of the same quality are generated, while cggasub_mo finds more alternative global optima than the sequential version and spending similar computational time in the process. gasub, with the new parameter setting and also the parallel algorithms, will be evaluated using a comprehensive computational set of experiments. Additionally, some criteria can also be used to select one of the known global optimal solutions when several alternatives optimize the corresponding objective function.

This paper presents a dynamic programming algorithm to draw optimal intermodal freight routing with regard to international logistics of container cargo for export and import. This study looks into the characteristics of intermodal transport using multi-modes, and presents a Weighted Constrained Shortest Path Problem (WCSPP) model. This study draws Pareto optimal solutions that can simultaneously meet two objective functions by applying the Label Setting algorithm, a type of Dynamic Programming algorithms, after setting the feasible area. To improve the algorithm performance, pruning rules have also been presented. The algorithm is applied to real transport paths from Busan to Rotterdam, as well as to large-scale cases. This study quantitatively measures the savings in both transport cost and time by comparing single transport modes with intermodal transport paths. Last, this study applies a mathematical model and MADM model to the multiple Pareto optimal solutions to estimate the solutions.

The search for multiple optimal solutions in the traveling salesman problem (TSP), as a challenging multimodal optimization problem in the combinatorial domain, has received increasing attention in recent years. Nevertheless, the multisolution TSP (MSTSP) still remains extremely difficult for larger-scale TSP instances. In this article, we propose a niching Lin-Kernighan–Helsgaun (LKH)-based ant colony system (ACS), named nLKH-ACS, taking advantage of LKH’s ability to solve large-scale TSPs, ACS’s search efficiency, and the niching technique for diversity preservation. Specifically, first, to address multisolution problems, we design a niching LKH (nLKH) strategy to generate diverse cost-efficient spanning trees, and adopt the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-nearness on each tree to obtain a diverse candidate edge set. The nLKH strategy enhances the ACS by improving pheromone initialization, solution construction, and local search operation using spanning trees and candidate edge sets, thereby strengthening the search capability and diversity. Then, to balance convergence and diversity, an adaptive Gaussian strategy is utilized to update the pheromone matrix. Furthermore, we design an indicator to measure the geometric diversity between pairs of solutions in the MSTSP solution set. The comprehensive experiments on MSTSPs and TSPLIB are conducted to validate the performance of the proposed nLKH-ACS. The experimental results demonstrate the powerful solving capability and excellent diversity of the proposed nLKH-ACS, particularly in finding various optimal solutions in larger-scale TSP instances.