On statistical bounds of heuristic solutions to location problems

Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region. 

Confidence in heuristic solutions?

Solutions to combinatorial optimization problems frequently rely on heuristics to minimize an objective function. The optimum is sought iteratively and pre-setting the number of iterations dominates in operations research applications, which implies that the quality of the solution cannot be ascertained. Deterministic bounds offer a mean of ascertaining the quality, but such bounds are available for only a limited number of heuristics and the length of the interval may be difficult to control in an application. A small, almost dormant, branch of the literature suggests using statistical principles to derive statistical bounds for the optimum. We discuss alternative approaches to derive statistical bounds. We also assess their performance by testing them on 40 test p-median problems on facility location, taken from Beasley’s OR-library, for which the optimum is known. We consider three popular heuristics for solving such location problems; simulated annealing, vertex substitution, and Lagrangian relaxation where only the last offers deterministic bounds. Moreover, we illustrate statistical bounds in the location of 71 regional delivery points of the Swedish Post. We find statistical bounds reliable and much more efficient than deterministic bounds provided that the heuristic solutions are sampled close to the optimum. Statistical bounds are also found computationally affordable.

Optimization heuristic solutions, how good can they be? : With empirical applications in location problems

Combinatorial optimization problems, are one of the most important types of problems in operational research. Heuristic and metaheuristics algorithms are widely applied to find a good solution. However, a common problem is that these algorithms do not guarantee that the solution will coincide with the optimum and, hence, many solutions to real world OR-problems are afflicted with an uncertainty about the quality of the solution. The main aim of this thesis is to investigate the usability of statistical bounds to evaluate the quality of heuristic solutions applied to large combinatorial problems. The contributions of this thesis are both methodological and empirical. From a methodological point of view, the usefulness of statistical bounds on p-median problems is thoroughly investigated. The statistical bounds have good performance in providing informative quality assessment under appropriate parameter settings. Also, they outperform the commonly used Lagrangian bounds. It is demonstrated that the statistical bounds are shown to be comparable with the deterministic bounds in quadratic assignment problems. As to empirical research, environment pollution has become a worldwide problem, and transportation can cause a great amount of pollution. A new method for calculating and comparing the CO2-emissions of online and brick-and-mortar retailing is proposed. It leads to the conclusion that online retailing has significantly lesser CO2-emissions. Another problem is that the Swedish regional division is under revision and the border effect to public service accessibility is concerned of both residents and politicians. After analysis, it is shown that borders hinder the optimal location of public services and consequently the highest achievable economic and social utility may not be attained.

How does data quality in a network affect heuristic solutions?

To have good data quality with high complexity is often seen to be important. Intuition says that the higher accuracy and complexity the data have the better the analytic solutions becomes if it is possible to handle the increasing computing time. However, for most of the practical computational problems, high complexity data means that computational times become too long or that heuristics used to solve the problem have difficulties to reach good solutions. This is even further stressed when the size of the combinatorial problem increases. Consequently, we often need a simplified data to deal with complex combinatorial problems. In this study we stress the question of how the complexity and accuracy in a network affect the quality of the heuristic solutions for different sizes of the combinatorial problem. We evaluate this question by applying the commonly used p-median model, which is used to find optimal locations in a network of p supply points that serve n demand points. To evaluate this, we vary both the accuracy (the number of nodes) of the network and the size of the combinatorial problem (p). The investigation is conducted by the means of a case study in a region in Sweden with an asymmetrically distributed population (15,000 weighted demand points), Dalecarlia. To locate 5 to 50 supply points we use the national transport administrations official road network (NVDB). The road network consists of 1.5 million nodes. To find the optimal location we start with 500 candidate nodes in the network and increase the number of candidate nodes in steps up to 67,000 (which is aggregated from the 1.5 million nodes). To find the optimal solution we use a simulated annealing algorithm with adaptive tuning of the temperature. The results show that there is a limited improvement in the optimal solutions when the accuracy in the road network increase and the combinatorial problem (low p) is simple. When the combinatorial problem is complex (large p) the improvements of increasing the accuracy in the road network are much larger. The results also show that choice of the best accuracy of the network depends on the complexity of the combinatorial (varying p) problem.

Dasyurid dilemmas: problems and solutions for conserving Australia's small carnivorous marsupials

Dasyurid marsupials are distributed throughout the major terrestrial environments of Australia but since European settlement have suffered local and regional extinctions, range reductions and population declines. In this paper we examine the conservation status of small dasyurids (<500 g) and the threats they face. We also evaluate recovery procedures for threatened taxa and assess their success. Twenty-four percent of smaller dasyurids are classified as vulnerable, endangered or data deficient. Large body size and occupancy of one or two habitat types are correlated strongly with  endangerment species currently considered as 'low risk, near threatened' group closely with vulnerable and endangered species, indicating a risk of further declines. The processes contributing most to declines include habitat loss and fragmentation, altered fire regimes and predation. As of April 200 I, no Recovery Plans had been adopted by the Commonwealth Govemment for any small dasyund species. There is much information on the reproduction and development of smaller dasyurids, making them suitable for captive breeding. However, captive breeding programs have been limited. the  dibbler Paranrechinus apicalis being the only species bred systematically for reintroductions. There is a need for integration between captive breeding programs and recovery planning. as well as for more information on the population viability and metapopulation structures of small dasyurids genetic diversity of populations and inbreeding depression. We suggest a program of survey. research. management and education to Improve conservation outcomes for all small dasyurids.

Chemically induced phosphorescence from manganese(II) during the oxidation of various compounds by manganese(III), (IV) break and (VII) in acidic aqueous solutions

Chemiluminescence was observed during the manganese(III), (IV) and (VII) oxidations of sodium tetrahydroborate, sodium dithionite, sodium sulfite and hydrazine sulfate in acidic aqueous solution. From the corrected chemiluminescence spectra, the wavelengths of maximum emission were 689±5 and 734±5 nm when the reactions were performed in sodium hexametaphosphate and sodium dihydrogenorthophosphate/ orthophosphoric acid environments, respectively. The corrected phosphorescence spectrum of manganese(II) sulfate in a solution of sodium hexametaphosphate at 77 K exhibited two peaks with maxima at 688 and 730 nm. The chemical and spectroscopic evidence presented strongly supported the postulation that the emission was an example of solution-phase chemically induced phosphorescence of manganese(II) thereby, confirming earlier predictions that the chemiluminescence from acidic potassium permanganate reactions originated from an excited manganese(II) species.

Using environmental interventions to create sustainable solutions to problems to health and wellbeing

Recent research by Deakin University, in collaboration with Parks Victoria and its Strategic Partners, indicates that contact with nature may promote human health and wellbeing. International research indicates that simply viewing a natural scene or watching wildlife reduces stress and tension, improves concentration, remedies mental fatigue, boosts immunity, and enhances psychological health. This is aside from any physical health benefits flowing from reduced stress, increased exercise and improved air quality when contact with nature involves activities in natural environments. The literature suggests that interacting with nature through gardening or having a companion animal is also beneficial for health, and where these activities involve contact with other humans, might extend benefits beyond the individual to the community, through enhanced social capital. This paper sets out the potential scope of work flowing from the initial research, in terms of target groups, research foci, intervention strategies, and likely benefits, and reports on progress in establishing a program of Australian,based empirical research. It proposes the establishment of alliances between researchers and practitioners in a range of disciplines (including environmental health) to ensure that the links between contact with nature and human health and wellbeing are explored and expressed in ways that are both beneficial and sustainable.

An investigation of solubility of aliquat 336 in different extracted solutions

A major concern in solvent extraction processes is the loss of extractant into the aqueous phase due to its slight solubility in the aqueous phase. Similarly, in membrane extraction processes, extractant loss through extractant leakage from the membrane into the aqueous phase is also a concern. Several published membrane extraction studies using Aliquat 336 as the extractant, have expressed this concern, but none has studied extractant leakage quantitatively. It is the authors’ opinion that the extractant leakage should be considered as a technical parameter of a membrane. In our laboratory active progress has been made in using Aliquat 336 ‘entangled’ into the polymer membranes to remove heavy metal ions from wastewater samples. In this work, we studied the loss of Aliquat 336 from the point of view of its solubility in aqueous solutions. The results showed that the solubilities of Aliquat 336 in an aqueous phase acidified with 2 M HCl is about 0.1 g/100 m/ of the solution. This figure provides a useful guideline for evaluating the leakage of the Aliquat 336 extractant from the membranes.

Using chitosan as a thickener for electrospinning dilute PVA solutions to improve fibre uniformity

Chitosan was added to PVA aqueous solutions as a thickener to improve the electrospinning process. The presence of a small amount of chitosan considerably improved the uniformity of as-spun nanofibres. This improvement is attributed to its significant effect on the solution viscosity and conductivity, with only a slight impact on the surface tension. The concentration of the PVA required to produce bead-free and uniform nanofibres was reduced with the increase in chitosan concentration. The chitosan thickener suppressed the jet break-up and facilitated the jet stretching so that fine and uniform fibres could be electrospun even from a dilute PVA solution.

Investigation into the temporal stability of aqueous standard solutions of psilocin and psilocybin using high performance liquid chromatography

This paper reports an investigation into the temporal stability of aqueous solutions of psilocin and psilocybin reference drug standards over a period of fourteen days. This study was performed using high performance liquid chromatography utilising a (955% vlv) methanol: 10 mM ammonium formate,
pH 3.5 mobile phase and absorption detection at 269 nm. It was found that the exclusion of light significantly prolonged the useful life of standards, with aqueous solutions of both psilocin and psilocybin being stable over a period of seven days.

Herbrand's Theorem and Equational Reasoning: Problems and Solutions

The famous Herbrand's theorem of mathematical logic plays an important role in automated theorem proving. In the first part of this article, we recall the theorem and formulate a number of natural decision problems related to it. Somewhat surprisingly, these problems happen to be equivalent. One of these problems is the so-called simultaneous rigid E-unification problem. In the second part, we survey recent result on the simultaneous rigid E-unification problem.

Oral zinc sulfate solutions inhibit sweet taste perception

We investigated the ability of zinc sulfate (5, 25, 50 mM) to inhibit the sweetness of 12 chemically diverse sweeteners, which were all intensity matched to 300 mM sucrose [800 mM glucose, 475 mM fructose, 3.25 mM aspartame, 3.5 mM saccharin, 12 mM sodium cyclamate, 14 mM acesulfame-K, 1.04 M sorbitol, 0.629 mM sucralose, 0.375 mM neohesperidin dihydrochalcone (NHDC), 1.5 mM stevioside and 0.0163 mM thaumatin]. Zinc sulfate inhibited the sweetness of most compounds in a concentration dependent manner, peaking with 80% inhibition by 50 mM. Curiously, zinc sulfate never inhibited the sweetness of Na-cyclamate. This suggests that Na-cyclamate may access a sweet taste mechanism that is different from the other sweeteners, which were inhibited uniformly (except thaumatin) at every concentration of zinc sulfate. We hypothesize that this set of compounds either accesses a single receptor or multiple receptors that are inhibited equally by zinc sulfate at each concentration.