Multiple Optima Research Articles

Utilizing time-linkage property in DOPs: An information sharing based Artificial Bee Colony algorithm for tracking multiple optima in uncertain environments

An information sharing artificial bee colony (ABC) algorithm has been proposed for locating and tracking multiple peaks in non-stationary environments. The niching method has been adapted by hybridizing two techniques. A modified variant of the fitness sharing has been used for detecting multiple peaks simultaneously and a speciation based technique is employed to keep the better individuals of the previous generation. The base algorithm used here is a modified variant of ABC that helps to synchronize the employer and onlooker forager swarms by synergizing the local information. The main crux of our algorithm is its independency of the problem dependent control parameters, like niche radius, and the absence of any hard-partitioning technique that leads to high computational burden. Our framework aims at bringing about a simple, robust approach that can be applied to a variety of dynamic functional landscapes. Experimental investigations are undertaken on standard benchmarks focussing on the competitive performance of our algorithm in contrast to the existing state-of-the-art to highlight the significance of our work.

Multiple Optima in Hoabinhian flaked stone artefact palaeoeconomics and palaeoecology at two archaeological sites in Northwest Thailand

High resolution analyses of flaked stone artefact technology coupled with palaeoecological reconstruction from oxygen isotope analyses of freshwater shells from two rockshelter in the highlands of Northwest Thailand are described. Previously undocumented scales of technological variation are observed in response to environmental variation across the prehistoric landscape and through time. Three models of human behavioural ecology are used to test predictions about how foragers adapted their stone artefact technology to variation in climatic conditions and proximity to stone resources. These models are found to be problematic and are modified by including multiple optima that reflect the specific ecological conditions under consideration.

Reconciliation revisited: handling multiple optima when reconciling with duplication, transfer, and loss.

Phylogenetic tree reconciliation is a powerful approach for inferring evolutionary events like gene duplication, horizontal gene transfer, and gene loss, which are fundamental to our understanding of molecular evolution. While duplication-loss (DL) reconciliation leads to a unique maximum-parsimony solution, duplication-transfer-loss (DTL) reconciliation yields a multitude of optimal solutions, making it difficult to infer the true evolutionary history of the gene family. This problem is further exacerbated by the fact that different event cost assignments yield different sets of optimal reconciliations. Here, we present an effective, efficient, and scalable method for dealing with these fundamental problems in DTL reconciliation. Our approach works by sampling the space of optimal reconciliations uniformly at random and aggregating the results. We show that even gene trees with only a few dozen genes often have millions of optimal reconciliations and present an algorithm to efficiently sample the space of optimal reconciliations uniformly at random in O(mn(2)) time per sample, where m and n denote the number of genes and species, respectively. We use these samples to understand how different optimal reconciliations vary in their node mappings and event assignments and to investigate the impact of varying event costs. We apply our method to a biological dataset of approximately 4700 gene trees from 100 taxa and observe that 93% of event assignments and 73% of mappings remain consistent across different multiple optima. Our analysis represents the first systematic investigation of the space of optimal DTL reconciliations and has many important implications for the study of gene family evolution.

A gravitational search algorithm for multimodal optimization

Gravitational search algorithm (GSA) has been recently presented as a new heuristic search algorithm with good results in real-valued and binary encoded optimization problems which is categorized in swarm intelligence optimization techniques. The aim of this article is to show that GSA is able to find multiple solutions in multimodal problems. Therefore, in this study, a new technique, namely Niche GSA (NGSA) is introduced for multimodal optimization. NGSA extends the idea of partitioning the main population (swarm) of masses into smaller sub-swarms and also preserving them by introducing three strategies: a K-nearest neighbors (K-NN) strategy, an elitism strategy and modification of active gravitational mass formulation. To evaluate the performance of the proposed algorithm several experiments are performed. The results are compared with those of state-of-the-art niching algorithms. The experimental results confirm the efficiency and effectiveness of the NGSA in finding multiple optima on the set of unconstrained and constrained standard benchmark functions.

Optimal emission-extraction policy in a world of scarcity and irreversibility

This paper extends the classical exhaustible-resource/stock-pollution model with irreversibility of pollution decay, meaning that after reaching some threshold there is no decay of the pollution stock. Within this framework, we answer the question how the potential irreversibility of pollution affects the extraction path. We investigate the conditions under which the economy will optimally adopt a reversible policy, and when it is optimal to enter the irreversible region. In the case of irreversibility it may be optimal to leave a positive amount of resource in the ground forever. As far as the optimal extraction/emission policy is concerned, several types of solutions may arise, including solutions where the economy stays at the threshold for a while. Given that different programs may satisfy the first order conditions for optimality, we further investigate when each of these is optimal. We show that it is never optimal for the economy to stay at the threshold for a while before entering the irreversible region. The optimality analysis is then illustrated by means of a calibrated example. To sum up, for any pollution level, we can identify a critical resource stock such that there exist multiple optima i.e. a reversible and an irreversible policy that yield exactly the same present value. For any resource stock below this critical value, the optimal policy is reversible whereas with large enough resources, irreversible policies outperform reversible programs.

Computational modeling of cast aluminum 2024 alloy matrix composites: Adapting the classical algorithms for optimal results in finding multiple optima

Many processing techniques have been developed successfully to manufacture metal matrix composites on the commercial scale. The most simplified approach to develop near net shaped aluminum based composites is by liquid metallurgy route as it is economical and can result in mass production. This research focuses on the performance of NN-FPSO for optimization of the parameters in processing metal matrix composites. The concept of the near-neighbor effect is integrated into the force-imitated mechanism and then applied into the PSO algorithm to improve its ability of locating multiple optima on MOPs. In this approach, a new information-sharing scheme is adopted. Each particle iteratively samples a region conducted by a compound acceleration vector, which is composed of the difference between the particle and its personal best position, attraction acceleration, and repulsion acceleration.

Multiple Optima in Gasoline Blend Planning

Gasoline is produced by blending several different components in ratios such that the blended mixture meets the required quality specifications. The blender produces different batches of gasoline by switching operation from one grade of gasoline to another. Blend planning horizon usually spans 10 to 14 days. Blend plan optimization minimizes the total blend costs by solving a multiperiod problem, where demands need to be satisfied in each period and some inventory is carried into the future time periods to meet the demands. Since blend component production is determined by a longer range refinery production plan, inventory carrying costs are not included in the objective function. It is shown that nonlinear programming (NLP) as well as mixed integer nonlinear programming (MINLP) solvers lead to different blend recipes and different blend volume patterns for the same total cost. The new algorithm described in this work systematically searches for multiple optimum solutions; this opens the way for blend pla...

Aggregate investor preferences and beliefs: A comment

A recent study in this journal presents encouraging results of a daunting simulation analysis of the statistical properties of a centered bootstrap approach to stochastic dominance efficiency analysis. However, by relying on the first-order optimality condition in a situation where multiple optima may occur, the empirical analysis draws the questionable conclusion that some of the toughest data sets in empirical asset pricing can be rationalized by the representative investor maximizing an S-shaped utility function, consistent with the so-called Prospect Stochastic Dominance criterion. Further research could be directed to developing global optimization algorithms and consistent re-sampling methods for statistical inference for general risky choice problems. • Standard portfolio and asset pricing theory assume risk aversion. • Risk seeking introduces the need for global optimization method. • First-order conditions are not sufficient for the global maximum. • A proper global optimality test finds market portfolio inefficiency. • The aggregated investor does not seem to obey the 'PSD' rule.

Efficient issue-grouping approach for multiple interdependent issues negotiation between exaggerator agents

Many real-world negotiations involve multiple interdependent issues, which makes an agent's utility functions complex, with nonlinear shapes and multiple optima. Traditional negotiation mechanisms were designed for linear utilities, and do not fare well in nonlinear contexts. One of the main challenges in developing effective nonlinear negotiation protocols is scalability; it can be extremely difficult to find high-quality solutions when there are many issues, due to computational intractability. One reasonable approach to reducing computational cost, while maintaining good quality outcomes, is to decompose the contract space into several largely independent sub-spaces. In this paper, we propose a method based on this concept. A mediator finds sub-contracts in each sub-space based on votes from the agents, and combines the sub-contracts to produce the final agreement. We demonstrate, experimentally, that our protocol allows high-optimality outcomes with greater scalability than previous efforts. We also demonstrate a method for addressing the potential problem of strategic non-truthful voting by the agents.

A Modified PSO Algorithm for Numerical Optimization Problems

By successively employing the interval search method, we developed the proposed algorithm MPSO, introducing three creative position vectors to replace the three worst fitness particles among the population in the PSO, to overcome the premature convergence situation that occurs when a problem with a large number of variables and (or) multiple optima is solved. The results obtained by applying the MPSO and the PSO on 6 benchmark functions show that, except for the randomly shifted Rosenbrock functions, the MPSO can successfully secure a solution that is close to the exact solution for each of the remaining five functions. We also showed that all benchmark functions are solvable by the MPSO if the maximum number of generations is raised to be as high as possible. With regard to the PSOs performance for the three different numbers of variables, it fails to obtain a solution that is close to the exact solution for all of the tested functions except for the Sphere function with 30 variables.

An evolutionary algorithm approach to generate distinct sets of non-dominated solutions for wicked problems

Many engineering design problems must optimize multiple objectives. While many objectives are explicit and can be mathematically modeled, some goals are subjective and cannot be included in a mathematical model of the optimization problem. A set of alternative non-dominated fronts that represent multiple optima for problem solution can be identified to provide insight about the decision space and to provide options and alternatives for decision-making. This paper presents a new algorithm, the Multi-objective Niching Co-evolutionary Algorithm (MNCA) that identifies distinct sets of non-dominated solutions which are maximally different in their decision vectors and are located in the same non-inferior regions of a Pareto front. MNCA is demonstrated to identify a set of non-dominated fronts with maximum difference in decision vectors for a set of real-valued problems.

Proportional Fair Resource Allocation on an Energy Harvesting Downlink

This paper considers the allocation of time slots in a frame, as well as power and rate to multiple receivers on an energy harvesting downlink. Energy arrival times that will occur within the frame are known at the beginning of the frame. The goal is to optimize throughput in a proportionally fair way, taking into account the inherent differences of channel quality among users. Analysis of structural characteristics of the problem reveals that it can be formulated as a biconvex optimization problem, and that it has multiple optima. Due to the biconvex nature of the problem, a Block Coordinate Descent (BCD) based optimization algorithm that converges to an optimal solution is presented. However, finding the optimal allocation with BCD entails a computational complexity that increases sharply in terms of the number of users or slots. Therefore, certain structural characteristics of the optimal power-time allocation policy are derived. Building on those, two simple and computationally scalable heuristics, PTF and ProNTO are proposed. Simulation results suggest that PTF and ProNTO can closely track the performance of BCD which achieves a good balance between total throughput and fairness.

A simulated weed colony system with subregional differential evolution for multimodal optimization

This article proposes a two-stage hybrid multimodal optimizer based on invasive weed optimization (IWO) and differential evolution (DE) algorithms for locating and preserving multiple optima of a real-parameter functional landscape in a single run. Both IWO and DE have been modified from their original forms to meet the demands of the multimodal problems used in this work. A p-best crossover operation is introduced in the subregional DEs to improve their exploitative behaviour. The performance of the proposed algorithm is compared with a number of state-of-the-art multimodal optimization algorithms over a benchmark suite comprising 21 basic multimodal problems and seven composite multimodal problems. Experimental results suggest that the proposed technique is able to provide better and more consistent performance over the existing well-known multimodal algorithms for the majority of test problems without incurring any serious computational burden.

The Endocrine Control Evolutionary Algorithm: an extensible technique for optimization

This paper proposes an optimization technique inspired by the endocrine system, in particular by the intrinsic mechanism of hormonal regulation. The approach is applicable for many optimization problems, such as multimodal optimization in a static environment, multimodal optimization in a dynamic environment and multi-objective optimization. The advantage of this technique is that it is intuitive and there is no need for a supplementary mechanism to deal with dynamic environments, nor for major revisions in a multi-objective context. The Endocrine Control Evolutionary Algorithm (ECEA) is described. The ECEA is able to estimate and track the multiple optima in a dynamic environment. For multi-objective optimization problems, the issue of finding a good definition of optimality is solved naturally without using Pareto non-dominated in performance evaluation. Instead, the overall preference of the solution is used for fitness assignment. Without any adjustments, just by using a suitable fitness assignment, the ECEA algorithm performs well for the multi-objective optimization problems.

Multimodal Optimization using Crowding Differential Evolution with Spatially Neighbors Best Search

Many real practical applications are often needed to find more than one optimum solution. Existing Evolutionary Algorithm (EAs) are originally designed to search the unique global value of the objective function. The present work proposed an improved niching based scheme named spatially neighbors best search technique combine with crowding-based differential evolution (SnbDE) for multimodal optimization problems. Differential evolution (DE) is known for its simple implementation and efficient for global optimization. Numerous DE-variants have been exploited to resolve diverse optimization problems. The proposed method adopts DE with DE/best/1/bin scheme. The best individual in the adopted scheme is searched around the considered individual to control the balance of exploitation and exploration. The results of the empirical comparison provide distinct evidence that SnbDE outperform the canonical crowding-based differential evolution. SnbDE has been shown to be efficient and effective in locating and maintaining multiple optima of selected benchmark functions for multimodal optimization problems.

Parameters control in GAs for dynamic optimization

Abstract The Control of Genetic Algorithms parameters allows to optimize the search process and improves the performance of the algorithm. Moreover it releases the user to dive into a game process of trial and failure to find the optimal parameters. Yet the control of parameters has received much attention in the case of static optimization problems, its investigation in the case of dynamic optimization problems (DOPs) is certainly a promising area of search. Indeed, in the case of DOPs the problem is not just to find the optima but to track the moving optima over time, so the parameters must be adapted to this dynamic environment. The proposed algorithm Parameters Control for Dynamic Optimization (PCDO) is based on Genetic Algorithm with Fitness Sharing (GAFS). To solve DOPs by controlling GAs parameters, PCDO uses several strategies. First, an unsupervised fuzzy clustering method is used to track multiple optimums and to perform GAFS. Second, a modified enthusiasm selection is used to adjust the selecti...

A Radial Framework for Estimating the Efficiency and Returns to Scale of a Multi-Component Production System in DEA

This chapter provides radial measurements of efficiency for the production process possessing multi-components under different production technologies. Our approach is based on the construction of various empirical production possibility sets. Then we propose a procedure that is unaffected affected by multiple optima for estimating returns to scale. The theoretical connections between the traditional black box and the proposed multi-component approach are established, which ascertains consistency in estimating the efficiency and returns to scale. Moreover, we introduce two homogeneity conditions, which clarify the difference between our approach and the existing one, and are important for evaluating performance in multi-component setting. Finally, an empirical study of the pollution treatment processes in China is presented, and compared to the results from black-box approach. Many insightful findings related to the operations of the pollution treatment processes in China are secured.

Micropropagation and cytogenetic assessment of Zingiber species of Northeast India.

An improved micropropagation protocol was developed for Zingiber moran and Z. zerumbet, two wild species of the genus Zingiber, found in Northeast India. The effects of growth regulators, sugar concentrations, and nutrients were tested on the rate of shoot initiation and multiplication. An increase in proliferation and multiplication occurred in modified Murashige and Skoog (MS) medium supplemented with benzyladenine and kinetin. About 2 % sucrose and 0.7 % agar were found to be the optimum for shoot multiplication and regeneration. Naphthalene acetic acid at 0.5 mg/L produced the best rooting response for both the species. Regenerated plantlets were acclimatized successfully and cytogenetic stability was confirmed by RAPD profiling and ploidy checks.

Multimodal size, shape, and topology optimisation of truss structures using the Firefly algorithm

This paper presents an efficient single-stage Firefly-based algorithm (FA) to simultaneously optimise the size, shape and topology of truss structures. The optimisation problem uses the minimisation of structural weight as its objective function and imposes displacement, stress and kinematic stability constraints. Unstable and singular topologies are disregarded as possible solutions by checking the positive definiteness of the stiffness matrix. Because cross-sectional areas are usually defined by discrete values in practice due to manufacturing limitations, the optimisation algorithm must assess a mixed-variable optimisation problem that includes both discrete and continuous variables at the same time. The effectiveness of the FA at solving this type of optimisation problem is demonstrated with benchmark problems, the results for which are better than those reported in the literature and obtained with lower computational costs, emphasising the capabilities of the proposed methodology. In addition, the procedure is capable of providing multiple optima and near-optimal solutions in each run, providing a set of possible designs at the end of the optimisation process.

Fuzzy genetic sharing for dynamic optimization

Recently, genetic algorithms (GAs) have been applied to multi-modal dynamic optimization (MDO). In this kind of optimization, an algorithm is required not only to find the multiple optimal solutions but also to locate a dynamically changing optimum. Our fuzzy genetic sharing (FGS) approach is based on a novel genetic algorithm with dynamic niche sharing (GADNS). FGS finds the optimal solutions, while maintaining the diversity of the population. For this, FGS uses several strategies. First, an unsupervised fuzzy clustering method is used to track multiple optima and perform GADNS. Second, a modified tournament selection is used to control selection pressure. Third, a novel mutation with an adaptive mutation rate is used to locate unexplored search areas. The effectiveness of FGS in dynamic environments is demonstrated using the generalized dynamic benchmark generator (GDBG).