{"id":3206,"date":"2018-12-19T14:25:56","date_gmt":"2018-12-19T19:25:56","guid":{"rendered":"http:\/\/www.serverpronto.com\/spu\/?p=3206"},"modified":"2019-01-01T14:32:40","modified_gmt":"2019-01-01T19:32:40","slug":"what-is-stochastic-optimization","status":"publish","type":"post","link":"https:\/\/www.serverpronto.com\/spu\/2018\/12\/what-is-stochastic-optimization\/","title":{"rendered":"What is Stochastic Optimization?"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">The Stochastic Optimization seeks the best decision in a scenario dependent on random events, dependent on chance, whether those events the prices of a product, the duration of a task, the number of people in the queue of a cashier, the number of breakdowns in a fleet of trucks, or even the approval of a regulation, come on, anything.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Stochastic?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Stochastic is a particularly feared word. It is since is known that most functional languages \u00e2\u20ac\u2039\u00e2\u20ac\u2039have been made a bad idea, by jealous experts who want to keep their secrets. There we have the legal jargon, the economic, or closer to our work; rumor has it that the creator of the C ++ language made it so complicated to differentiate good programmers from bad guys. The word &#8220;stochastic&#8221; is not dangerous; it means simply random, dependent on chance. The idea is quite simple, but as an adjective, it can complicate any discipline.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Problems of Stochastic Optimization<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The problems of stochastic optimization are in general much more complicated than those that do not consider chance, mainly because luck implies that we do not have a single scenario to be optimized, but a set of possible scenarios. For example, if we want to maximize the design of an energy distribution network, we will work in an uncertainty scenario, in which we do not know the actual demand for energy at the time of use of the system. Instead of the demand data, we would have an estimate, perhaps a finite set of possible demands with an associated probability. <br><br>With this, we can already intuit that the world of the company is full of stochastic problems, what is usually done to solve them ?. In scenarios with simple decisions, that is to say, few decision variables and with few states, all the possibilities can be explicitly enumerated using decision trees that are also very intuitive.<br><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Stochastic Optimization<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Although it is considered that this discipline was born in the 50s with Dantzig and Beale, historically optimization has had enough to be restricted to non-stochastic problems, essentially due to the complexity that stochastic problems entail. Facing real problems is still impossible in many cases, but advances in computing capacity and the development of optimization techniques have allowed problems to be solved until recently unthinkable. In addition, sometimes, only a stochastic approach can greatly improve the solution, which translates into cost savings, service improvement, increased benefits, among others, all of them factors not insignificant.<br><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">An optimization problem has:<br><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>a series of variables or decisions that must be taken.<\/li><\/ul>\n\n\n\n<ul class=\"wp-block-list\"><li>a series of restrictions that limit those decisions.<\/li><\/ul>\n\n\n\n<ul class=\"wp-block-list\"><li>and an objective function, a measure of cost or quality of the set of decisions taken.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The data associated with the constraints and the objective function are usually known values, but what if random events gave these values? Then the problem is stochastic optimization.<br><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">There are two particularly uncomfortable questions:<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What happens to feasibility when the restrictions are random?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A solution is feasible when it satisfies all the restrictions, but with arbitrary limits, we cannot speak strictly of feasibility but probability that a certain answer is viable. Thus, in the problem of planning the power distribution network, a restriction could be &#8220;the capacity of the distribution network is greater than or equal to the demand&#8221; but if the demand turns out to be very high, it can happen that we can not satisfy it.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">How to redefine the objective function?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The answer to this question is less obvious, we could redefine the objective function as the expected value of the previous objective function, but it could be more interesting to reduce the risk of the decision using the worst case scenario. In general, these types of problems have been addressed using linear programming.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What are these problems complicated?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The complexity of these problems lies in their size. Think of the seemingly harmless lady who leaves the hairdresser. Suppose you also have to decide whether to go by bus or walk to do a message. Each new random variable and each new decision multiply the possibilities. Instead of considering four possible outcomes we should consider tens or hundreds.<br><br> If we continue to consider elements of uncertainty that may threaten the woman, the number of possible outcomes will increase exponentially. Let&#8217;s go back now to the problem of planning the energy distribution network; the demand is random, the future prices of energy are arbitrary, the production of wind energy is absolute, as well as the costs of fuels. The outcome of any decision in this context will depend on what happens with each of those random events.<br><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Conclusion<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Most of the real problems are of stochastic nature; there are few businesses in which all the data are known in advance, we cannot keep avoiding them. The stochastic optimization can allow us to face problems that until now have been solved by &#8220;intuition,&#8221; by &#8220;common sense,&#8221; or because &#8220;of all life has been done like this,&#8221; in a more efficient way, providing solutions that will place us in clear advantage over our competitors.<br><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Stochastic Optimization seeks the best decision in a scenario dependent on random events, dependent on chance, whether those events the prices of a product, the duration of a task, the number of people in the queue of a cashier, the number of breakdowns in a fleet of trucks, or even the approval of a<\/p>\n","protected":false},"author":10,"featured_media":3207,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[371],"tags":[123,17,112,373,22,372,18],"class_list":["post-3206","post","type-post","status-publish","format-standard","has-post-thumbnail","category-optimization","tag-cloud","tag-dedicated-server","tag-hosting","tag-optimization","tag-server","tag-stochastic","tag-web-hosting"],"_links":{"self":[{"href":"https:\/\/www.serverpronto.com\/spu\/wp-json\/wp\/v2\/posts\/3206","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.serverpronto.com\/spu\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.serverpronto.com\/spu\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.serverpronto.com\/spu\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/www.serverpronto.com\/spu\/wp-json\/wp\/v2\/comments?post=3206"}],"version-history":[{"count":1,"href":"https:\/\/www.serverpronto.com\/spu\/wp-json\/wp\/v2\/posts\/3206\/revisions"}],"predecessor-version":[{"id":3208,"href":"https:\/\/www.serverpronto.com\/spu\/wp-json\/wp\/v2\/posts\/3206\/revisions\/3208"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.serverpronto.com\/spu\/wp-json\/wp\/v2\/media\/3207"}],"wp:attachment":[{"href":"https:\/\/www.serverpronto.com\/spu\/wp-json\/wp\/v2\/media?parent=3206"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.serverpronto.com\/spu\/wp-json\/wp\/v2\/categories?post=3206"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.serverpronto.com\/spu\/wp-json\/wp\/v2\/tags?post=3206"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}