Set Of Noninferior Solutions Research Articles

Optimization of α-tocopherol and ascorbyl palmitate addition for the stabilization of sardine oil

The purpose of the present work was to optimize the addition of natural antioxidants (α- tocopherol and ascorbyl palmitate) for the stabilization of sardine oil rich in omega-3 PUFA. The optimal values for peroxide value (PV), which minimizes primary oxidation products, were obtained at low concentrations of α-tocopherol (50–207 ppm), high content of ascorbyl palmitate (450 ppm) and 50 ppm citric acid. On the other hand, optimal values for p-anisidine value (AV), which minimizes secondary oxidation products, were found at medium concentrations of α-tocopherol (478–493 ppm), high contents of ascorbyl palmitate (390–450 ppm) and 50 ppm citric acid. The conflicting effect of α-tocopherol on the individual optimization of PV and AV motivated the generation of a Pareto front (set of non inferior solutions) employing the weighted-sum multi-objective optimization technique.

Application of multi-objective controller to optimal tuning of PID gains for a hydraulic turbine regulating system using adaptive grid particle swam optimization

A hydraulic turbine regulating system (HTRS) is one of the most important components of hydropower plant, which plays a key role in maintaining safety, stability and economical operation of hydro-electrical installations. At present, the conventional PID controller is widely applied in the HTRS system for its practicability and robustness, and the primary problem with respect to this control law is how to optimally tune the parameters, i.e. the determination of PID controller gains for satisfactory performance. In this paper, a kind of multi-objective evolutionary algorithms, named adaptive grid particle swarm optimization (AGPSO) is applied to solve the PID gains tuning problem of the HTRS system. This newly AGPSO optimized method, which differs from a traditional one-single objective optimization method, is designed to take care of settling time and overshoot level simultaneously, in which a set of non-inferior alternatives solutions (i.e. Pareto solution) is generated. Furthermore, a fuzzy-based membership value assignment method is employed to choose the best compromise solution from the obtained Pareto set. An illustrative example associated with the best compromise solution for parameter tuning of the nonlinear HTRS system is introduced to verify the feasibility and the effectiveness of the proposed AGPSO-based optimization approach, as compared with two another prominent multi-objective algorithms, i.e. Non-dominated Sorting Genetic Algorithm II (NSGAII) and Strength Pareto Evolutionary Algorithm II (SPEAII), for the quality and diversity of obtained Pareto solutions set. Consequently, simulation results show that this AGPSO optimized approach outperforms than compared methods with higher efficiency and better quality no matter whether the HTRS system works under unload or load conditions.

Is Multiobjective Optimization Ready for Water Resources Practitioners? Utility’s Drought Policy Investigation

Is Multiobjective Optimization Ready for Water Resources Practitioners? Utility’s Drought Policy Investigation

Genetic Algorithm based Multiobjective Optimal Power Dispatch based on Ideal Distance Minimization

In this paper, the cost of generation and system transmission losses have been considered as objectives for optimization. The multiobjective optimal power dispatch (MOPD) problem is formulated using weighting method and a number of noninferior solutions are generated in 2D space by varying weights for IEEE 5, 14 and 30 bus systems - manually using GA technique, by using GA toolbox of MATLAB R2008b. Ideal Distance minimization method has been used to obtain the optimal power system operation (Target Point, best compromise solution). This method employs the concept of an 'Ideal Point' (IP) to scalarize the problems having multiple objectives and minimizes the Euclidean distance between IP and a set of noninferior solutions.

Electrical power planning and scheduling in Taiwan based on the simulation results of multi-objective planning model

Based on the solitary electrical power system typically used in Taiwan, this study employed the constraint method, which is a multiobjective planning approach, and a set of non-inferior solutions with the associated marginal rate of substitution, which aimed to minimize power generation costs and CO2 emissions. The objective was to simulate and verify the feasibility of historical power generation scheduling. Subsequently, this study simulated power generation scheduling for a future target year and observed the power generation behavior under various circumstances, to determine how power departments can satisfy power-supply demands while reducing CO2 emissions. This study also provided suggestions for decision-making units to plan the future supply of electric power and assess reductions in CO2 emissions. The study results show that extending the operating period of nuclear power units is the optimal solution for reducing CO2 emissions in 2025. If the fluctuation in fixed costs caused by replacing existing power generator sets with new sets is not considered, increasing the efficiency of electric power generating sets can effectively reduce power generation costs and CO2 emissions. The increase amount of natural gas used to generate power repressed the supply of renewable energy, causing the cost to increase without significantly reducing CO2 emissions. The marginal rate of substitution for the relationship between total power generation costs and CO2 emissions becomes moderately flat because as the number of electric power generating sets, which can be manually scheduled, in the power generation system decreases, the cost of reducing CO2 emissions increases.

Multi-objective evolutionary algorithm for grid job scheduling based on adaptive neighborhood

A new adaptive neighborhood Multi-Objective Grid Task Scheduling Algorithm(ANMO-GTSA) was proposed in this paper for the multi-objective job scheduling collaborative optimization problem in grid computing.In the ANMO-GTSA,an adaptive neighborhood method was applied to find the non-inferior set of solutions and maintain the diversity of the multi-objective job scheduling population.The experimental results indicate that the algorithm proposed in this paper can not only balance the multi-objective job scheduling,but also improve the resource utilization and efficiency of task execution.Moreover,the proposed algorithm can achieve better performance on time-dimension and cost-dimension than the traditional Min-min and Max-min algorithms.

Optimisation of the hydrolysis of goat milk protein for the production of ACE-inhibitory peptides

Goat milk protein was hydrolysed with subtilisin and trypsin. As input variables, temperature was assayed in the interval 45-70 °C for subtilisin and 30-55 °C for trypsin, while the enzyme-substrate ratio varied from 1 to 5%. The effect of the input variables on the degree of hydrolysis and ACE-inhibitory activity (output variables) was modelled by second order polynomials, which were able to fit the experimental data with deviations below 10%. The individual maximum values of the degree of hydrolysis and the ACE-inhibitory activity were found at conflicting conditions of temperature and enzyme-substrate ratio. Since such maximum values could not be reached simultaneously, a bi-objective optimisation procedure was undertaken, producing a set of non-inferior solutions that weighted both objectives.

Optimization of bleaching conditions for sardine oil

This work studies the influence of the operational conditions (temperature: 90–130°C, activated clay amount: 1–5 wt% and contact time: 20–60min) on the bleaching process of degummed and neutralized sardine oil. The bleached oils were evaluated for free fatty acids, peroxide value, p-anisidine value, totox, oxidation stability (Rancimat) and color (CIELAB coordinates). Such measured variables were statistically modeled by full factorial experimental design and response surface methodology. An individual optimum value for totox of 21.38 (which minimizes oxidation products content) was obtained at 130°C, 5wt% of clay amount and 60min. Regarding the color quality, it was found a maximum value for hue-angle (89.19 at 99.2°C, 5wt% of clay and 56. 6min) and a minimum value for chroma (81.76 at 109.4°C, 5wt% of clay and 49.4min). The conflicting effect of temperature and time on the location of the individual optima motivated the generation of a Pareto front (set of non inferior solutions) employing the weighted-sum multi-objective optimization technique.

An Advanced Multi-Objective Genetic Algorithm Based on Borda Number

When applied to Multi-Objective Decision Making (MODM), genetic algorithm is plagued with two problems: how to appreciate non-inferior solutions and how to store them. Using Borda number as the fitness of a chromosome, an advanced Multi-Objective Genetic Algorithm ( MOGA) is provided in this paper, which can solve these problems in an easier way; and with the characteristic of Genetic Algorithm (GA) of producing a number of feasible solutions, this approach is able to obtain the set of non-inferior solutions without information of the decision-maker’s preferences. Finally, a simulated example to apply this algorithm to a multipurpose reservoir’s operation is provided, indicating the feasibility and effectiveness of this advanced MOGA.

Bidding based generator maintenance scheduling with triple-objective optimization

A new bidding based generating unit maintenance scheduling method under the electricity market environment is presented in this paper. The method can balance overall reliability and economy, and ensure the fairness to all generation companies (GENCOs). The unit maintenance scheduling is modeled as a triple-objective non-convex optimization problem with discrete variables and is solved using an improved version of the Non-dominated Sorting Genetic Algorithm (NSGA-II). A non-inferior solution set is directly produced from huge combinations. A few candidate solutions are selected from the non-inferior set by independent system operator (ISO) based on the overall reliability and economy, whereas the final maintenance schedule is determined by voting of GENCOs. The shares of vote are calculated from the bidding information of GENCOs and the right of each GENCO is fairly guaranteed. A case study of 50 units demonstrates the effectiveness of the proposed method.

A bi-objective modeling approach applied to an urban semi-desirable facility location problem

This paper introduces a mixed-integer, bi-objective programming approach to identify the locations and capacities of semi-desirable (or semi-obnoxious) facilities. The first objective minimizes the total investment cost; the second one minimizes the dissatisfaction by incorporating together in the same function “pull” and “push” characteristics of the decision problem (individuals do not want to live too close, but they do not want to be too far, from facilities). The model determines the number of facilities to be opened, the respective capacities, their locations, their respective shares of the total demand, and the population that is assigned to each candidate site opened. The proposed approach was tested with a case study for a particular urban planning problem: the location of sorted waste containers. The complete set of (supported or unsupported) non-inferior solutions, consisting of combinations of multi-compartment containers for the disposal of four types of sorted waste in nineteen candidate sites, and population assignments, was generated. The results obtained for part of the historical center of an old European city (Coimbra, Portugal) show that this approach can be applied to a real-world planning scenario.

A Simple Algorithm for Multi-Objective, Short-Term Hydrothermal Scheduling

This investigation proposes a new algorithm for the solution of multi-objective, short-term hydrothermal scheduling problems. In the common algorithm using weighting method, a set of weight vectors are fed infor each weight vector objective function values in the optimisation interval, and the corresponding fuzzy membership functions are computed and the best compromise solution is identified from the set of non-inferior solutions obtained. In the proposed algorithm, a set of weight vectors are genetically generated and the best solution is identified as described already. Further, the weight vectors are genetically modified and the process is repeated to identify the best solution using the modified weight vectors. The process is continued till change in the fitness value of the best solution is marginal. The investigation further proposes three methods to determine the objective function values in the optimisation interval, which is a major sub-process in the above algorithm. These are the Newton-Raphson method, a genetic search method and a random search method. A comparison is made among the performance data of the three methods, and the random search method is projected as the simple algorithm for multi-objective, short-term hydrothermal scheduling problem. A coal-constrained thermal unit is introduced in the investigation to make the scheduling problem more universal.

Optimal capacitors appointment though immune multi-objective algorithm

This work proposes a two-stage immune algorithm that embeds the compromise programming to perform multi-objective optimal compensator placement. A new problem formulation model that involves fuzzy sets to reflect the imprecise nature of objectives and incorporates multiple planning requirements is presented. The proposed approach finds a set of non-inferior (Pareto) solutions rather than any single aggregated optimal solution. Additionally, this developed approach eliminates the need for any user-definedweight factor to aggregate all objectives. Comparative studies are conducted on an actual system with encouraging results, demonstrating the effectiveness of the proposed approach.

Sensitivity Measure for Electric Power Load Dispatch Problem

This study performed sensitivity analysis of a multi-objective thermal power dispatch problem and explored a solution methodology exploiting the quality measure approach, which verifies that the non-inferior solutions are uniformly scattered in the objective space. The multi-objective thermal power dispatch problem having non-commensurable objectives, such as operating cost and minimal emissions, is undertaken to meet the systems' real and reactive power demands within generators' capacity constraints. Real and reactive power transmission line flows are obtained from generalized Z-bus distribution factors and are restricted within prescribed limits for the secure operation of a power system. A sensitivity measure is incorporated as a dispersion index to be minimized in order to investigate the effects of random variations in the model parameters of the optimal solution. A non-linear programming problem provides the framework for examining the objectives along with constraints in a weighted sum form of the multi-objective problem. The best objective weights are evaluated by conventional statistical measures, which characterize the correlation coefficients matrix evolution. A quality measure approach is exploited to compare the relative quality of a different set of non-inferior solutions before presenting it to the decision-maker for a final decision. The validity of the proposed method is demonstrated on a 30-bus IEEE power system.

Multiobjective Planning of Surface Water Resources by Multiobjective Genetic Algorithm with Constrained Differential Dynamic Programming

Owing to the conflict encountered between the two objectives of fixed cost in reservoir installation and operating cost in time-varying water deficit, multiobjective planning of surface water resources is a difficult job. Instead of combining these two objectives into just one objective using the weighting factor approach, this investigation proposes a novel method by integrating a multiobjective genetic algorithm MOGA with constrained differential dynamic programming CDDP. A MOGA is employed to generate the various combinations of reservoir capacity and estimate the noninferior solution set. However, applying this algorithm to solve the dynamics of the operating cost, the number of variables increasing with time will dramatically increase the use of computational resources. Conse- quently, the CDDP is herein adopted to distribute optimal releases among reservoirs to satisfy water demand as much as possible. Next, the effectiveness of the proposed methodology is verified by solving a multiobjective planning problem of surface water in southern Taiwan. This real application demonstrates that MOGA can be linked with CDDP to resolve a complex water resources problem. Additionally, the ability of MOGA on addressing multiple objectives simultaneously without converting to a weighted objective function provides the opportunity for significant advancement in multiobjective optimization. Finally, this investigation also proposes three suitable strategies of reservoir construction to decision makers with budget concerns through the analysis of all noninferior solutions.

Optimal placement of capacitors in distribution systems using an immune multi-objective algorithm

This work proposes a two-stage immune algorithm that embeds the compromise programming to perform multi-objective optimal capacitor placement. A new problem formulation model that involves fuzzy sets to reflect the imprecise nature of objectives and incorporates multiple planning requirements is presented. The proposed approach finds a set of non-inferior (Pareto) solutions rather than any single aggregated optimal solution. Additionally, this developed approach eliminates the need for any user-defined weight factor to aggregate all objectives. Comparative studies are conducted on an actual system with encouraging results, demonstrating the effectiveness of the proposed approach.

Stochastic multiobjective optimization model for allocating irrigation water to paddy fields

A stochastic multiobjective optimization model is presented to allocate irrigation waters to blocks of paddy fields in an agricultural district. Environmental uncertainty and temporal variation of water requirement at the fields are represented in the model formulation by employing a scenario-based description. To improve the efficiency of water use, two conflicting objectives, i.e., minimization of water withdrawal from a river and maximization of rice production, are expressed in linear objective functions. Water balances in a river, a field block and a channel network interconnecting with some blocks of paddy fields are considered as constraints. Adjusting a weight in a synthesized objective function results in producing a set of noninferior solutions, which could be useful in discussing water management alternatives in decision-making. The application of the presented model to a hypothetical irrigation district demonstrates that optimal water intake and allocations of irrigation waters could be produced.

Multi-objective simultaneous stowage and load planning for a container ship with container rehandle in yard stacks

The efficiency of a maritime container terminal primarily depends on the smooth and orderly process of handling containers, especially during the ship’s loading process. The stowage and associated loading plans are mainly determined by two criteria: ship stability and the minimum number of container rehandles required. The latter is based on the fact that most container ships have a cellular structure and that export containers are piled up in a yard. These two basic criteria are often in conflict. This paper is concerned with the ship’s container stowage and loading plans that satisfy these two criteria. The GM, list and trim are taken into account for the stability measurements. The problem is formulated as a multi-objective integer programming. In order to obtain a set of noninferior solutions of the problem, the weighting method is employed. A wide variety of numerical experiments demonstrated that solutions by this formulation are useful and applicable in practice.

A Multiobjective Evolutionary Algorithm for the Sizing and Siting of Distributed Generation

In the restructured electricity industry, the engineering aspects of planning need to be reformulated even though the goal to attain remains substantially the same, requiring various objectives to be simultaneously accomplished to achieve the optimality of the power system development and operation. In many cases, these objectives contradict each other and cannot be handled by conventional single optimization techniques. In this paper, a multiobjective formulation for the siting and sizing of DG resources into existing distribution networks is proposed. The methodology adopted permits the planner to decide the best compromise between cost of network upgrading, cost of power losses, cost of energy not supplied, and cost of energy required by the served customers. The implemented technique is based on a genetic algorithm and an /spl epsiv/-constrained method that allows obtaining a set of noninferior solutions. Application examples are presented to demonstrate the effectiveness of the proposed procedure.

Design for Operability: A Singular-Value Optimization Approach within a Multiple-Objective Framework

Design-for-operability is a field of active research in process systems engineering because of the high economic impact of design on operability. Dynamic operability has been widely studied by means of the so-called (open-loop) controllability and resiliency indices, which are mostly based on linearized (Laplace/frequency domains) models of the dynamic systems. In particular, the minimum singular value of the transfer function matrix is a fair measure of resilience to disturbances. Among the plethora of approaches to design for dynamic operability, a multiple-objective formulation between cost and controllability naturally arises because of the conflicting characters of the two objectives. In this contribution the cost/minimum-singular-value multiple-objective design problem is solved for the meaningful reactor-separator-recycle system and two different control strategies. The generation of the noninferior solution set is performed here within the framework of an eigenvalue optimization approach.