Hiroshi Tsuda

Random fuzzy multi-objective linear programming: Optimization of possibilistic value at risk (pVaR)

This paper considers multiobjective linear programming problems (MOLPP) where random fuzzy variables are contained in objective functions and constraints. A new decision making model optimizing possibilistic value at risk (pVaR) is proposed by incorporating the concept of value at risk (VaR) into possibility theory. It is shown that the original MOLPPs involving random fuzzy variables are transformed into deterministic problems. An interactive algorithm is presented to derive a satisficing solution for a decision maker (DM) from among a set of Pareto optimal solutions. Each Pareto optimal solution that is a candidate of the satisficing solution is exactly obtained by using convex programming techniques. A simple numerical example is provided to show the applicability of the proposed methodology to real-world problems with multiple objectives in uncertain environments.

Random fuzzy bilevel linear programming through possibility-based value at risk model

This article considers bilevel linear programming problems where random fuzzy variables are contained in objective functions and constraints. In order to construct a new optimization criterion under fuzziness and randomness, the concept of value at risk and possibility theory are incorporated. The purpose of the proposed decision making model is to optimize possibility-based values at risk. It is shown that the original bilevel programming problems involving random fuzzy variables are transformed into deterministic problems. The characteristic of the proposed model is that the corresponding Stackelberg problem is exactly solved by using nonlinear bilevel programming techniques under some convexity properties. A simple numerical example is provided to show the applicability of the proposed methodology to real-world hierarchical problems.

Production of negative lithium ions from the surface immersed in magnetic-field-free plasmas

Abstract A beam of negative lithium ions was produced from a 2.5 cm diameter Li metal-coated surface immersed in a magnetic-field-free plasma. The Li− current produced at the surface increased as the negative bias applied to the surface was increased, but did not increase in proportion to the ion current density irradiating the surface. Among He, Ne, Ar, Kr, and Xe plasmas, the Li− yield was higher for a plasma of heavier inert gas, and was also dependent upon the condition of the production surface. In particular, the Cs coverage and the oxygen adsorption on the surface seemed to play an important role to enhance the Li− sputtering yield.

Direct extraction of negative lithium ions from a lithium plasma

Negative lithium ions (Li−) were directly extracted from a lithium plasma in a multiline cusp plasma container. A pair of permanent magnets mounted near the extractor electrode created the filter magnetic field that separated the extraction region plasma from the main discharge plasma. The plasma electrode facing the extraction region plasma was biased with respect to the other parts of the chamber wall, which acted as discharge anodes. The larger filter magnetic field resulted larger Li− current. When the bias to the plasma electrode was several volts positive against the anode potential, extracted Li− current took the maximum for a fixed strength of the filter field. These dependences of Li− upon the filter magnetic field and the plasma electrode bias are similar to the ones of negative hydrogen ions.

Microwave ion source with linear antennaea)

A microwave ion source equipped with two linear antennae set parallel to the wall of the source chamber has been designed and built. A homogeneous plasma of Ar was produced in an aluminum chamber of 22 cm long, 9 cm wide, and 6 cm deep. Beam forming grids produced a rectangular beam of 17 cm by 3 cm. The current density of the extracted Ar+ beam was 0.16 mA/cm2 at the center of the extraction area when the input power to the magnetrons was 360 W. The energy distribution function of the extracted ions was measured with an electrostatic analyzer. The measured energy distribution showed a presence of high energy ions in the extracted beam.

Characteristics of a sheet plasma and its application to a large extraction area negative ion source

A sheet plasma with a thickness as thin as several millimeters was produced by the combination of a pair of dipole magnetic fields and a mirror magnetic field. The negative hydrogen ion produced in the peripheral region of the sheet plasma was measured with a movable Faraday cup. The maximum negative ion current was observed when the extraction electrode of the Faraday cup was biased slightly negative with respect to the plasma potential. The optimum position for the negative ion extraction appeared to be 2 to 3 cm from the center of the sheet plasma. A large concentration of high‐energy electrons was found inside of the sheet plasma. The measured negative ion current showed a dependence on the density of high‐energy electrons in the sheet plasma.

A Route Recommendation System for Sightseeing with Network Optimization and Conditional Probability

This paper proposes a route recommendation system for sightseeing based on a network optimization problem. Traveling and sightseeing times are randomly changed dependent on current traffic and congestion conditions, and hence, Time-Expanded Network (TEN) to contain a copy to the set of nodes in the underlying static network for each discrete time step is introduced. In addition, in order to select the next sightseeing site, conditional probabilities are introduced, which are calculated by current conditions, statistical and Web data. Our proposed model is formulated as a nonlinear and discrete optimization problem, and it is hard to solve it directly and efficiently. Therefore, an efficient algorithm is also developed based on dynamic programming and transformation of the main problem into the recursive equation.

Route planning problem with groups of sightseeing sites classified by tourist's sensitivity under Time-Expanded Network

This paper proposes a sightseeing route planning problem with time-dependent traveling times among sightseeing sites. Since traveling times are dependent on the time of day, Time-Expanded Network (TEN), which contains a copy to the set of nodes in the underlying static network for each discrete time step, is introduced. In addition, it is hard to set satisfaction values at sightseeing sites numerically due to tourists ambiguous sensitivity, but it is not difficult to classify sightseeing sites into several groups by the tourist. Therefore, the objective function of our proposed model is set to maximize the total visiting sightseeing sites in each group. The problem is a multiobjective programming problem, and hence, a principle of compromise is introduced to solve our proposed problem in network optimization. Furthermore, a strict algorithm is also developed to equivalently transform the main problem into the existing TEN-based problem.

A Flexible Tour Route Planning Problem with Time-Dependent Parameters Considering Rescheduling Based on Current Conditions

This paper proposes a tour route planning problem to flexibly reschedule the initial route plan with uncertain traveling times and satisfaction values of sightseeing places dependent on sightseeing. The objective of our proposed model is to maximize the total satisfaction value in all possible conditions after visiting a sightseeing place under such time-dependent parameters. Since traveling times are dependent on the time of day, it is hard to represent our proposed model using the general static network model. In this paper, Time-Expanded Network (TEN), which contains a copy to the set of nodes in the underlying static network for each discrete time step, is introduced. Using the proposed TEN-based model, it is possible to construct various types of tour route planning problems in a single static network. Furthermore, a 0-1 mixed integer programming problem is formulated to the above-mentioned objective, and the strict algorithm is also developed to equivalently transform the main problem into the existing TEN-based problem.

Interactive multi-objective route planning for sightseeing on Time-Expanded Networks under various conditions

Abstract This paper proposes a versatile and interactive route planning problem for sightseeing under various conditions based on constraints of required traveling times and total satisfaction of sightseeing activities, which are time-dependent. In general, traveling times among sightseeing places and the satisfactions of activities also change dependent on various conditions such as weather, climate and season. It is important to represent a satisfying route to ensure the large satisfaction even if any assumable condition happens. In order to incorporate the above-mentioned situations, a multi-objective route planning problem is formulated as a network optimization problems based on Time-Expanded Network to represent time-dependent parameters in a static network. Furthermore, an interactive approach based on the Satisficing Trade-Off Method is introduced to transform the multi-objective into the single. In addition, the proposed problem is equivalently transformed into an extended model of network optimization problems by introducing parameters, and the interactive algorithm is developed.