Expensive combinatorial optimization of choice of subset from a large finite space












0












$begingroup$


I have a fairly general question -- what's a good (gradient-free) approach to optimizing an expensive function whose input is a choice of subset from a large finite population?



That is, I have a set $X$, an integer $n$, and a function $F: Y tomathbb{R}$, where $Y$ is the set of all $n$-element subsets of $X$ (and $|X| >> n$). Knowing nothing about F (in fact, assume it's expensive and free of any helpful structure. In the actual use case it's noisy as well, though I'm interested in a non-noisy answer too), what are good options to maximize $F$ on $Y$?



I'm in the process of doing this using a random search-style approach, where the choice of next subset is made by fixing some $m<n$ and redrawing $m$ elements of the subset at each step; I think that "number of elements not in common" constitutes a metric on $Y$, so it seems like this is sound, but it also looks naive to me. This problem seems pretty general and useful, so I'd love to be pointed to some other ideas.










share|cite|improve this question









$endgroup$

















    0












    $begingroup$


    I have a fairly general question -- what's a good (gradient-free) approach to optimizing an expensive function whose input is a choice of subset from a large finite population?



    That is, I have a set $X$, an integer $n$, and a function $F: Y tomathbb{R}$, where $Y$ is the set of all $n$-element subsets of $X$ (and $|X| >> n$). Knowing nothing about F (in fact, assume it's expensive and free of any helpful structure. In the actual use case it's noisy as well, though I'm interested in a non-noisy answer too), what are good options to maximize $F$ on $Y$?



    I'm in the process of doing this using a random search-style approach, where the choice of next subset is made by fixing some $m<n$ and redrawing $m$ elements of the subset at each step; I think that "number of elements not in common" constitutes a metric on $Y$, so it seems like this is sound, but it also looks naive to me. This problem seems pretty general and useful, so I'd love to be pointed to some other ideas.










    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      I have a fairly general question -- what's a good (gradient-free) approach to optimizing an expensive function whose input is a choice of subset from a large finite population?



      That is, I have a set $X$, an integer $n$, and a function $F: Y tomathbb{R}$, where $Y$ is the set of all $n$-element subsets of $X$ (and $|X| >> n$). Knowing nothing about F (in fact, assume it's expensive and free of any helpful structure. In the actual use case it's noisy as well, though I'm interested in a non-noisy answer too), what are good options to maximize $F$ on $Y$?



      I'm in the process of doing this using a random search-style approach, where the choice of next subset is made by fixing some $m<n$ and redrawing $m$ elements of the subset at each step; I think that "number of elements not in common" constitutes a metric on $Y$, so it seems like this is sound, but it also looks naive to me. This problem seems pretty general and useful, so I'd love to be pointed to some other ideas.










      share|cite|improve this question









      $endgroup$




      I have a fairly general question -- what's a good (gradient-free) approach to optimizing an expensive function whose input is a choice of subset from a large finite population?



      That is, I have a set $X$, an integer $n$, and a function $F: Y tomathbb{R}$, where $Y$ is the set of all $n$-element subsets of $X$ (and $|X| >> n$). Knowing nothing about F (in fact, assume it's expensive and free of any helpful structure. In the actual use case it's noisy as well, though I'm interested in a non-noisy answer too), what are good options to maximize $F$ on $Y$?



      I'm in the process of doing this using a random search-style approach, where the choice of next subset is made by fixing some $m<n$ and redrawing $m$ elements of the subset at each step; I think that "number of elements not in common" constitutes a metric on $Y$, so it seems like this is sound, but it also looks naive to me. This problem seems pretty general and useful, so I'd love to be pointed to some other ideas.







      combinatorics discrete-mathematics optimization numerical-methods discrete-optimization






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 18 at 21:37









      rwgprwgp

      12




      12






















          0






          active

          oldest

          votes












          Your Answer








          StackExchange.ready(function() {
          var channelOptions = {
          tags: "".split(" "),
          id: "69"
          };
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function() {
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled) {
          StackExchange.using("snippets", function() {
          createEditor();
          });
          }
          else {
          createEditor();
          }
          });

          function createEditor() {
          StackExchange.prepareEditor({
          heartbeatType: 'answer',
          autoActivateHeartbeat: false,
          convertImagesToLinks: true,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          imageUploader: {
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          },
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          });


          }
          });














          draft saved

          draft discarded


















          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3078787%2fexpensive-combinatorial-optimization-of-choice-of-subset-from-a-large-finite-spa%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown

























          0






          active

          oldest

          votes








          0






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes
















          draft saved

          draft discarded




















































          Thanks for contributing an answer to Mathematics Stack Exchange!


          • Please be sure to answer the question. Provide details and share your research!

          But avoid



          • Asking for help, clarification, or responding to other answers.

          • Making statements based on opinion; back them up with references or personal experience.


          Use MathJax to format equations. MathJax reference.


          To learn more, see our tips on writing great answers.




          draft saved


          draft discarded














          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3078787%2fexpensive-combinatorial-optimization-of-choice-of-subset-from-a-large-finite-spa%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown





















































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown

































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown







          Popular posts from this blog

          Human spaceflight

          Can not write log (Is /dev/pts mounted?) - openpty in Ubuntu-on-Windows?

          張江高科駅